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3D-RISM-MP2 Approach to Hydration Structure of Pt(II) and Pd(II) Complexes: Unusual H-Ahead Mode vs. Usual O-Ahead One Shinji Aono, Toshifumi Mori, and Shigeyoshi Sakaki J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.5b01137 • Publication Date (Web): 10 Feb 2016 Downloaded from http://pubs.acs.org on February 11, 2016

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Journal of Chemical Theory and Computation

3D-RISM-MP2 Approach to Hydration Structure of Pt(II) and Pd(II) Complexes: Unusual H-Ahead Mode vs. Usual O-Ahead One Shinji Aono,† Toshifumi Mori,‡ and Shigeyoshi Sakaki∗,† Fukui Institute for Fundamental Chemistry, Kyoto University, Nishihiraki-cho, Takano, Sakyo-ku, Kyoto 606-8103, Japan, and Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan and School of Physical Sciences, The Graduate University for Advanced Studies, Okazaki, Aichi 444-8585, Japan E-mail: [email protected]

∗ To

whom correspondence should be addressed Institute for Fundamental Chemistry, Kyoto University, Nishihiraki-cho, Takano, Sakyo-ku, Kyoto 6068103, Japan ‡ Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan and School of Physical Sciences, The Graduate University for Advanced Studies, Okazaki, Aichi 444-8585, Japan † Fukui

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Abstract Solvation of transition metal complex with water has been one of the fundamental topics in physical and coordination chemistry. In particular, Pt(II) complexes have recently attracted considerable interests for its relation to anticancer activity in cis-platin and its analogues, yet the interaction of water molecule and the metal center has been obscure. The challenge from theoretical perspective remains in that both the microscopic solvation effect and the dynamical electron correlation (DEC) effect have to be treated simultaneously in a reasonable manner. To this end, in this work we derive the analytical gradient for the three-dimensional reference interaction site model Møller-Plesset second order (3D-RISM-MP2) free energy. On the basis of the three-regions 3D-RISM self-consistent field (SCF) method recently proposed by us, we apply new layer of the Z-vector method to the CP-RISM equation as well as point-charge approximation to the derivatives with respect to the density matrix elements in the RISM-CPHF equation to remarkably reduce the computational cost. This method is applied to study the interaction of H2 O with the d8 square planar transition metal complexes in aqueous solution, trans-[PtII Cl2 (NH3 )(glycine)] (1a), [PtII (NH3 )4 ]2+ (1b), [PtII (CN)4 ]2− (1c) and their Pd(II) analogues 2a, 2b, and 2c, respectively, to elucidate whether the usual H2 O interaction through O atom (O-ahead mode) or unusual one through H atom (H-ahead mode) is stable in these complexes. We find that the interaction energy of the coordinating water and the transition metal complex changes little when switching from gas to aqueous phase, but the solvation free energy differs remarkably between the two interaction modes, thereby affecting the relative stability of the H-ahead and O-ahead modes. Particularly, in contrast to the expectation that the O-ahead mode is preferred due to the presence of positive charges in 1b, the H-ahead mode is also found to be more stable. The O-ahead mode is found to be more stable than the H-ahead one only in 2b. The energy decomposition analysis (EDA) at the 3D-RISM-MP2 level revealed that the O-ahead mode is stabilized by the electrostatic (ES) interaction while the H-ahead one is mainly stabilized by the DEC effect. The ES interaction is also responsible for the difference between the Pd(II) and Pt(II) complexes; since the electrostatic potential is more negative along the z-axis in the Pt(II) complex than in the Pd(II) one, the O-ahead mode prefers the Pd(II) complexes, whereas the H-ahead becomes predominant in the Pt(II) complexes.


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1 Introduction The solvation of transition metal complex with water has been one of the most fundamental research targets in coordination chemistry and physical chemistry, as the solvation significantly influences the molecular properties such as spectroscopy 1–4 and reactivity in ligand exchange and organometallic reactions 5 of transition metal complexes. In particular, the solvation of Pt(II) complexes has recently attracted considerable interests, because it deeply relates to the anticancer activity of cis-platin and analogues; 3,4,6–21 for example, cis-platin was theoretically investigated by various kinds of methods such as the PCM, 7–14 Monte Carlo simulation, 15 Car-Parrinello molecular dynamics (CPMD) simulations, 16–18 hybrid QM/MM calculations, 19 1D-RISM-SCF-SEDD, 20 and 3D-RISM-SCF. 21 In these systems, the negatively charged oxygen atom of water solvent is expected to approach the metal center, since a water molecule has lone pair orbitals on the oxygen atom and positively charged Pt(II) center has empty valence orbital(s) (Scheme 1a). However, the opposite interaction, i.e., the hydrogen atom of a water molecule approaching the metal center has been theoretically proposed 22,23 and experimentally observed with neutron diffraction analysis 22 and NMR spectroscopy 3,4 (Scheme 1b); for brevity, hereafter the oxygen- and hydrogenapproaching modes are denoted as “O-ahead" and “H-ahead" hydrations, respectively. This Hahead mode is surprising because the metal center has a character of a Lewis acid and tends to attract electron population from a Lewis base. Theoretical studies have been carried out to elucidate the origin of the H-ahead hydration, 3,4,22–24,26 which suggested that the electronic dispersion interaction, i.e. dynamical electron correlation (DEC) effect, between the O-H bond and the metal moiety is the source. 23,24,27 The contribution of the charge-transfer effects in the H-ahead hydration has also been discussed with a topological analysis. 26 While the origin of the H-ahead hydration has been discussed in both experimental and theoretical studies, many important questions regarding the interaction of water molecules with transition metal complexes still remains, e.g. (i) whether a Pt(II) complex can have any O-ahead hydration, (ii) what interaction is crucial in the O-ahead mode (if any exists), and (iii) how these differ in the Pd(II) analogues. To reveal these questions from a theoretical perspective, it is crucial to take ac3 ACS Paragon Plus Environment


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count of both the solvation and the DEC effects simultaneously in reasonable accuracy, since these two factors can significantly influence the relative stabilities of the H-ahead and O-ahead hydration modes. In this respect, in addition to the Møller-Plesset second order (MP2) and density functional theory (DFT) calculations in gas phase, 24,25 the polarizable continuum mode (PCM) calculation with the MP2 method 26 as well as the ab-initio MD simulation with the BLYP-D3 method 27 have been performed. Yet, a molecular picture of how the solvent affects the solvation structure still remains somewhat obscure. To evaluate a statistically-averaged solvation effect on the structures and properties of a molecule in solution, the reference interaction site model self-consistent field (RISM-SCF) method 28 is one of the most powerful tools as well as the PCMs, 29–32 COSMOs, 33,34 SSPE, 35 and SMX. 36 In the RISM-SCF method, electronic structure of a solute is calculated in the presence of equilibrium solvent distribution about the solute based on the statistical mechanics of liquid. 37,38 In other words, the RISM-SCF method can provide both the solute electronic structure and the equilibrium solvation structure simultaneously in an SCF manner at a reasonable computational cost. Because of this microscopic viewpoint, the RISM-SCF method has the advantage over the PCM methods at describing the local solvation structures such as hydrogen bonding networks, since PCM describes the solvent in a continuum manner. On the basis of electronic structure theories such as Hartree-Fock (HF), DFT, and multi-configurational (MC) SCF methods, which are solved under the variational principle, the analytical gradient of the RISM-SCF free energy 39 has been employed to determine the solute geometries and free energy profiles of chemical reactions in solution. In addition to the RISM-SCF free energy gradient, the analytical gradients for the RISM-MP2, RISM-CASPT2, and RISM-TDDFT free energies have been further analytically derived in the one-dimensional (1D) RISM method, thereby the influence of DEC to the geometry changes in solution can be taken into account for ground and excited states at a moderate computational cost. 40–42 To improve the description of the solvation structure and the solvation free energy, the RISM integral equation has been extended by many researchers based on the density functional theory of non-uniform polyatomic liquid proposed by Chandler et al.. 43 For instance, Beglov and Roux


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applied the 3D hyper-netted chain (HNC) equation to the distribution of mono-atomic LennardJones (LJ) solvent 44 and the 3D-RISM-HNC theory to the solvation of polar molecules in aqueous phase; 45,46 Kovalenko and Hirata derived the 3D generalization of the RISM method from the sixdimensional (6D) molecular Ornstein-Zernike integral equation, where the rotational degrees of freedom of solvent were averaged out. 47,48 Analytical gradients for the SCF solvation free energy was derived and then full geometry optimization of the solute molecule was performed at both the DFT and HF levels in solvent. 49,50 Compared to the conventional 1D-RISM-SCF method, the 3D-RISM-SCF method has many significant advantages. In particular, (i) the 3D-RISM theory improves the description of the cavity formation effect, which is overestimated in the 1D-RISMSCF calculation for a bulky solute molecule such as glucosides and transition metal complexes; (ii) the 3D-RISM-SCF method directly provides the spatial information of the solvation structure around the solute; and (iii) the electrostatic potential (ESP), directly calculated from the electronic wave-function of the solute, can be used to solve the 3D-RISM integral equation. This leads to the improvement in accuracy as well as convergence in the RISM-SCF cycle over the conventional 1D-RISM. 50 On the other hand, it is time-consuming to directly evaluate the ESP from the wavefunction of the solute in the entire 3D grid space. To solve this issue without loss of accuracy, we have recently proposed the three-regions 3D-RISM-SCF method 21,51 which divides the 3D grid space of solvent into the inner, outer, and switching regions. In the inner region, the ESP is directly evaluated with the electronic wave-function of the solute; in the outer region, the ESP is approximately evaluated with the point-charges on the solute sites; and in the switching region, the two approaches are smoothly connected by using a switching function. Note that this is an improvement over the method originally proposed by Yoshida and Hirata; 50 see Refs. [50] and [21] for details. Following the formalism of the 1D-RISM-MP2 free energy gradient, 40 we have recently developed the analytical gradient of three-dimensional (3D) RISM-MP2 free energy under the restrained electrostatic potential (RESP) point-charge approximation, 52 and determined the geometry of likecharged molecular cation pairs. 53 In that study, however, the excessively large constraints in the



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RESP charge were sometimes required to avoid the divergence problem in the RISM-SCF cycle, leading to the unreasonable charge distribution assigned on the solute sites. In order to extend the applicability of the 3D-RISM-MP2 method to more challenging and interesting systems including the bulky and charged systems such as glucosides and charged transition metal complexes, the solute-solvent ES interaction needs to be treated beyond the classical pure point-charge level employed in the previous RISM-MP2 methods. To this end, here we derive the free energy gradient for the three-regions 3D-RISM-MP2 method, in which the effect of the spatial electron density distribution is taken into account in the RISM-SCF cycle. In this study, we also applied the Zvector method to the coupled perturbed (CP) RISM terms involved in the derivatives. Since a large number of CP-RISM terms appear in the current case, here we introduce (i) the solute point-charge approximation to the derivatives with respect to the electronic density matrix elements and (ii) additional layer of the Z-vector method to remarkably reduce the computational cost (see next section). The three-regions 3D-RISM-MP2 method thus becomes widely applicable to the bulky and charged systems in which the DEC (or the “electronic dispersion") effect is important in determining the structures and properties of the solute in solution. In this study, we investigate the H-ahead and O-ahead modes of water interactions with several typical Pt(II) complexes, i.e. trans-[PtCl2 (NH3 )(glycine)] 1a, [Pt(NH3 )4 ]2+ 1b, and [Pt(CN)4 ]2− 1c, and their Pd(II) analogues 2a, 2b, and 2c, respectively, using the three-regions 3D-RISM-MP2 method. These three kinds of complex are selected here, considering the plausible possibility that the electrostatic potential induced by the ligands strongly affects the relative stabilities of the Hahead and O-ahead modes, i.e. the interaction between the coordinating water and the complex. We address the above-mentioned questions and also provide general understanding of the H-ahead and O-ahead hydration modes by incorporating both the electronic dispersion and microscopic solvation effects.


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2 Theoretical Method 2.1 3D-RISM-MP2 free energy Before describing the three-regions 3D-RISM-MP2 free energy gradient, here we start by briefly summarizing the 3D-RISM-MP2 methods using the conventional pure point-charge approximation and the three-regions approach, respectively. The 3D-RISM-MP2 free energy AMP2 is defined by expanding the wave-function to the first order in the same manner as the 1D-RISM-MP2 method, 40 AMP2 = ⟨ΦHF | Hˆ gas (R) | ΦHF + Φ(1) ⟩ + ∆µ (Q(0) ) + ⟨ΦHF | Uˆ int (R; {gs }) | Φ(1) ⟩,

(1)

where Hˆ gas (R) is the solute electronic Hamiltonian in gas phase, ∆µ is the excess chemical potential (i.e. solvation free energy), and Uˆ int (R; {gs }) is the solute-solvent interaction energy operator. R, Q, and gs denote the solute nuclear coordinates, the electronic point-charges on the solute sites, 28 and the solvent distribution function of the solvent site s, respectively. ΦHF is the solute solv , under the HF wave-function in solution, which is evaluated by solving the Fock matrix, Fµν

consideration of the solvation structure {gs (r)}, gas solv Fµν = Fµν + ⟨χµ | Uˆ int (R; {gs }) | χν (R)⟩.

(2)

Here Fµν is the Fock matrix in gas phase and χµ and χν represent the atomic orbitals, respectively. gas

In the three-regions 3D-RISM-SCF method, 21 the second term in Eq. (2) is evaluated by the soluteES (R; {g }), 21,54 solvent electrostatic (ES) interaction energy matrix, Uµν s

ES Uµν (R; {gs }) = ρ ∑ qs s {

∫

dr gs (r)⟨χµ | VÊSP (R, r) | χν ⟩, } ˆα −1 Q Qˆ α VÊSP (R, r) ≡ w(r) ∑ |ˆri − r| − ∑ |Rα − r| + ∑ |Rα − r| , α α i∈electron


(3) (4)


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where rî is the position operator of electron i and w(r) is the switching function introduced in our previous work. 21 When w(r) is set to zero in the entire space r, Eqs. (1) to (4) returns to the pure point-charge approximation, which bas been used in the conventional RISM-MP2 method. 53 In the closed shell system, the 3D-RISM-MP2 free energy AMP2 in Eq. (1) is evaluated by Eq. (5) like the 1D-RISM-MP2, 40 RHF AMP2 = Esolute + ∆µ (0) +

1 occ vir 2(i j | ab) − (ib | a j) (i j | ab) . ∑ ∑ 4 i j ab εi + ε j − εa − εb

(5)

The sum of the first and the second terms is the RISM-RHF free energy and the third term is the second order correlation energy E (2) , where the subscripts i, j and a, b represent the occupied and virtual molecular orbitals (MOs), respectively. (i j|ab) is the two-electron MO integral and ε p is the solv . Note that ∆ µ (0) is one of the free orbital energy evaluated from the solvated Fock matrix, Fµν

energy functionals which is defined by the solute-solvent correlation functions converged at the RHF level. This formula depends on the closure relation employed to solve the 3D-RISM integral equations; see Ref. [47] for the definitions in the HNC and KH cases. In this study, we employed the KH closure for performing geometry optimization and then the HNC one for evaluating free energy curve and making EDA, as mentioned below.

2.2 3D-RISM-MP2 free energy gradient RHF and ∆ µ (0) with respect to R in the conventional (i.e. pure pointThe first derivatives of Esolute α

charge) and the three-regions 3D-RISM-SCF methods can be evaluated in a similar manner. 21 The


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first derivative of E (2) is given by Eq. (6),

∂ E (2) = ∂ Rα +

AO

(2)

µν

∑ Pµν ∑ (2)

µν

+

∑ µν

+

AO

∑ hXµν Pµν + ∑ SXµν Wµν +

∑ µν

s

(2) Pµν

∑ s

(2) Pµν

∑

(2)

µν

AO

∑

µνλ σ

(2)

(µν | λ σ )X Γµνλ σ

∫

} { dr Xs,Xµν (r)w(r) + Xs,µν (r)wX (r) ρ gs (r)

∫

{ } X X dr∑ Qα ,µν Vα s (r) + Qα ,µν Vα s (r) ρ gs (r)

∫

s

α

{

} dr Xs,µν (r)w(r) + ∑ Qα ,µν Vα s (r) ρ gXs (r), α

(6)

where the superscript X represents the derivative with respect to Rα and hXµν , (µν | λ σ )X , SXµν , and QXα ,µν are the derivative integrals of one- and two-electron, overlap, and electronic point-charge (2)

(2)

(2)

matrices in the atomic orbital (AO) basis, respectively. Pµν , Wµν , and Γµνλ σ have the similar (2)

forms as those in Ref. [55], but Pai requires solving the RISM-CPHF equation described below, (2)

and Wi j is written as (2) Wi j

occ vir

= −∑∑

t ab jk (ia | kb) −

k ab

] 1 MO (2) [ 1 (2) (εi + ε j )Pi j − ∑ Ppq G pqi j + G pq ji + 2Ypqi j . 2 2 pq

(7)

Here the subscripts p and q represent p-th and q-th MOs, tiabj is the double substitution amplitude, and Gaib j is defined by Eq. (8); see Supporting Information pages S3-S6 for the details and the definitions of Xs,µν , Vα s , and Yµν pq . Gaib j = 2(ai | b j) − (a j | bi).

(8)

The CPHF equation for the 3D-RISM-MP2 free energy gradient is derived in the same manner as the 1D-RISM-MP2. 40 By applying the Z-vector method, 56 the RISM-CPHF equation is



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rewritten as occ vir [

∑∑ j

] (2) (εa − εi )δab δi j + Gaib j + Gai jb + 2Yb jai Pb j

b

occ vir

= ∑ ∑ t ab jk ( ji | kb) − jk b

occ vir

− ∑ ∑ tibcj (ab | jc) − j bc

] 1 occ (2) [ Pjk G jkai + G jkia + 2Y jkai ∑ 2 jk 1 vir (2) Pbc [Gbcai + Gbcia + 2Ybcai ] . 2∑ bc

(9)

In the conventional 3D-RISM-MP2 method with the pure point-charge approximation, Ypqµν can be analytically evaluated at a moderate computational cost. In the three-regions 3D-RISM-MP2, however, the accurate evaluation of Ypqµν requires a huge computational cost. Hence we employed the pure point-charge approximation only in evaluating Ypqµν ; see Supporting Information pages S7-S8 for detail. It is noted that the evaluation of Yµν pq require solving the CP-RISM equation NAO × NAO times (where NAO is the number of the AO basis), whereas the pure point-charge approximation applied to the RISM-CPHF equation can dramatically decrease the number of the CP-RISM equation to be solved to only Nsolute (where Nsolute is the number of the solute sites). In addition, we introduced another Z-vector method to the CP-RISM equation to greatly decrease the cost of evaluating the RISM-MP2 free energy gradient, as summarized in Supporting Information pages S9-S11. The new Z-vector method successfully reduces the computational cost to the point where the free energy gradient for the three-regions 3D-RISM-SCF method with nonvariational electronic structure methods, e.g. 3D-RISM-MP2 and 3D-RISM-TDDFT, can be calculated at a moderate computational cost.

2.3 Energy decomposition analysis in the 3D-RISM-MP2 To discuss the components of the 3D-RISM-MP2 free energy, it is convenient to decompose the MP2 and solvation free energy ∆ µ MP2 terms by total free energy (Eq. (5)) into the solute energy Esolute


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Eqs.(10) and (11), MP2 RHF ES Esolute = Esolute + E (2) − ∑ Pµν Uµν (R; {gs }), (2)

µν

ES ∆µ MP2 = ∆µ (0) + ∑ Pµν Uµν (R; {gs }). (2)

µν

(10) (11)

MP2 + ∆ µ MP2 . We further implemented the 3D-RISM version of the KitauraNote that AMP2 = Esolute

Morokuma energy decomposition analysis (EDA) 57 and localized molecular orbital (LMO) EDA 58 to investigate the QM interaction between the metal complex and the water molecule, while taking solvation effects into consideration. Here, we briefly describe how to treat the solvation effect in the Kitaura-Morokuma EDA in solution. When a super molecule AB consists of two monomers A and B in solution, the total electronic solv , is represented, as follows: Hamiltonian, Hˆ AB

gas gas solv ES ES Hˆ AB (RB , gAB ) + Uˆ AB (RAB ). = Hˆ A (RA ) + Uˆ A-V (RA , gAB ) + Hˆ B (RB ) + Uˆ B-V

(12)

gas gas ES and U ES are the ˆ B-V Here Hˆ A and Hˆ B are the Hamiltonian of each monomer in gas phase, Uˆ A-V

electrostatic interaction between each monomer and the surrounding solvent molecules, gAB is the solvation structure around the super molecule AB, and Uˆ AB corresponds to the interaction between two monomers, A and B, respectively. The 3D-RISM-MP2 calculation of the super molecule AB ¯ AB and the solvation structure gAB . The monomer wave-functions, gives the QM wave-function Φ ¯ A (gAB ) and Φ ¯ B (gAB ), are calculated under the condition that the solvation structure is fixed to Φ gAB . Following the Kitaura-Morokuma EDA in gas phase, the electrostatic and the exchangerepulsion terms of the inter-molecular interaction between monomers A and B, EES and EEX +EREP , respectively, are given by; ¯ A (gAB )Φ ¯ B (gAB ) | Uˆ AB | Φ ¯ A (gAB )Φ ¯ B (gAB ) >, EES = < Φ

(13)

¯ A (gAB )Φ ¯ B (gAB ) | Uˆ AB | Φ ¯ A (gAB )Φ ¯ B (gAB ) > −EES , EEX + EREP = < A Φ

(14)



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where A is the anti-symmetrizing operator. The polarization, charge transfer, and mixing terms, hereafter denoted by EPOL , ECT , and EMIX , respectively, can also be defined easily by following the Kitaura-Morokuma EDA formula in gas phase, but considering the polarization of wave-functions induced by solvation of the super molecule. The DEC effect EDEC is defined as a difference MP2 RHF between Esolute,AB and Esolute,AB (see Eq. (10)).

To take the energy of the monomer in gas phase as the standard, we further introduce the MONOs and E MONOs , reelectronic reorganization and the gas phase energies of the monomer, EREORG gas

spectively, as follows:

MONOs EREORG =

∑

(

gas

¯ I (gAB ) | Hˆ − < ΦI (0) | Hˆ |Φ I

) | ΦI (0) > ,

(15)

I=A,B MONOs Egas =

∑

gas < ΦI (0) | Hˆ I | ΦI (0) > .

(16)

I=A,B

Here ΦA (0) and ΦB (0) are the wave-functions of the monomers A and B in gas phase, respectively. 59 Using these terms, we can analyze the Helmholtz free energy AMP2 AB of the super molecule AB in solution, as shown in Eqs. (17)-(19); MP2 MP2 + ∆µAB AMP2 = Esolute,AB , AB MONOs,MP2 MONOs,MP2 MP2 MP2 + Egas , Esolute,AB = Eint,AB + EREORG MP2 Eint,AB = EES + EEX + EREP + EPOL + ECT + EMIX + EDEC ,

(17) (18) (19)

MP2 is the solvation free energy of the super molecule AB which is calculated by the where ∆µAB MP2 , is 3D-RISM-MP2 method. The binding energy between monomers A and B in solution, Ebind,AB

represented by Eq. (20) using Eq. (18); MONOs,MP2 MP2 MP2 MONOs,MP2 Ebind,AB = Eint,AB + ∆EREORG + ∆Egas ,

(20)

with ∆ being the difference from the monomers in the infinite separation. In gas phase, the second 12 ACS Paragon Plus Environment

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MP2 . The subscript AB is hereafter omitted for simplicity. In the same manner, term vanishes in Ebind,AB

we can implement the LMO-EDA in solution by taking the solvation effect into consideration. Note that this EDA method at the RISM-MP2 level is similar to that in the PCM method, 60 as follows; the cavity surface is also defined initially in the PCM method, which determines the apparent surface charges (ASC) of the super molecule; all of the energy components in the interaction between the monomers are then calculated while freezing the cavity surface of the super molecule.

3 Computational Details The geometry optimization was carried out by the three-regions 3D-RISM-MP2 method, as will be explained in the next section. The LANL08(f) basis sets were used for valence electrons of Pt and Pd, where the 60 and 28 core electrons were replaced with the Hay-Wadt effective core potentials (ECPs), respectively. 61 For all the other atoms, the 6-31++G** basis set was used for geometry optimization. We then employed the cc-pVTZ basis set with an additional diffuse function to each of Cl, O, and CN moieties, respectively, to calculate the energy difference and perform EDA. The former and latter basis sets are denoted as BS-I and BS-II, respectively. In the free energy calculation and the EDA, the MP2 correction was applied after solving the 3D-RISM-SCF cycle at the RHF level and then the BSSE correction was added by a counterpoise method. 21 To solve the 3D-RISM integral equation, we employed the KH closure 47 for the geometry optimization. Then, using the optimized geometries, we re-calculated the free energy curve and performed the EDA with the HNC closure 44–46 which is worse in convergence but better in accuracy than the KH closure; remember that the KH closure is the approximation of the HNC one to improve the convergence. 47 In the RISM-SCF calculation, analytical treatment of the electrostatic asymptotics of the 3D site correlation functions and electrostatic potentials was performed with the non-periodic asymptotics under the identically zero concentration of ionic species. On such condi-



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(as)

tion, the long-range asymptotics of the 3D site total correlation function hs (r) can be determined (as)

by evaluating hs (k = 0) with the polynomial extrapolation on a radial k-grid. 62,63 To examine the effect of bulk solvation, the calculations without the bulk solvent water, i.e. calculations “in gas phase", were also performed. As the initial step of the 3D-RISM-SCF method, the 1D-RISM calculation was carried out to set up the solvent-solvent total correlation functions at the density of ρ V = 0.997 g/cm3 , and temperature of T = 298.15 K, respectively. The point-charges and LJ parameters of water solvent were taken from the SPC model 64 by modifying the LJ parameters of H atom to σH =1.0 Å and

εH =0.056 kcal/mol. 28,65 For convenience, H1 represents the H site of coordinating water molecule which is closer to the metal center than the other site, denoted by H2 . The 1D-RISM calculation was performed on the grids of 1024 points, corresponding to the 1D space radius of 56.2 Å. In the 3D-RISM calculation, the LJ parameters of the solute molecule were taken from the AMBER 66 except for Pt and Pd. For Pt and Pd, we determined the LJ parameters by fitting the MP2 potential energy profile of these complexes with one water molecule; the obtained values were σPt =3.33 Å,

εPt =0.36 kcal/mol, σPd =3.25 Å, and εPd =0.40 kcal/mol, respectively. For the box size of the solvent space, we set cubic grids of 128 points/axis at an interval of 0.5 Å in the free energy calculations and the geometry optimizations, whereas a finer grid of 256 points/axis at an interval of 0.25 Å were used to evaluate the solvent spatial distribution function. In the three-regions 3D-RISM-MP2 calculations, the solvent space was divided into three regions using the boundary distances rin and rout set to 15.0 Å and 18.0 Å, respectively. 21 We implemented our own in-house codes of the present 3D-RISM-MP2 method and the analyses methods into the GAMESS-US (version 1-MAY-2013) program code, 67 and installed the NBO 5.9 program 68 in the GAMESS to analyze the natural bond orbital (NBO) charges and populations.


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4 Results and Discussion 4.1 Geometry and energy profile of water interaction with metal To investigate whether the unusual H-ahead hydration can be formed in aqueous phase, we performed the full geometry optimization of trans-[PtII Cl2 (NH3 )(glycine)] (1a), [PtII (NH3 )4 ]2+ (1b), [PtII (CN)4 ]2− (1c) and their Pd(II) analogues 2a, 2b, and 2c, respectively. One Pt or Pd complex and one water molecule were taken as a QM region, and to distinguish the QM water from the bulk solvent water, the QM water is denoted as “W". Hereafter, M and 4L represent the metal center and the four ligands coordinating with M, respectively. For simplicity, the H-ahead and O-ahead modes are described by the suffices “-H" and “-O", e.g. “1a-H" and “1a-O". Note that in the glycine complexes (1a and 2a), “mode I" and “mode II" denote the W existing in the different side and the same side as the -CH2 COOH, respectively. In gas phase, the full geometry optimization with the MP2 method provided the stable geometry only for the O-ahead mode, as shown in Table 1; see Supporting Information Table S2 for detailed geometrical parameters. When starting from the guess geometry of the H-ahead orientation, W approaches 4L rather than M during the geometry optimization; in the glycine complexes (1a and 2a), the H site of W approaches the Cl ligand, and in the tetra-cyano complex, it also approaches the CN ligand. In the tetra-ammine complex, on the other hand, W changes the orientation from the H-ahead to O-ahead hydration and the O site of W approaches the H site of NH3 . In aqueous phase, on the contrary, the 3D-RISM-MP2 calculation provided several stable Oahead hydration structures in 1b, 2a, 2b, and 2c and H-ahead hydration structures in 1a, 1b, 1c, and 2a, respectively, as shown in Table 1 and Figure 1, indicating the importance of the bulk solvation effect. In the glycine complexes, both modes I and II are stable in 1a-H and 2a-H. In 1a-O, only mode II is found. The stability decreases in the order; the H-ahead mode I ≥ the H-ahead mode II > the O-ahead mode II. The Pt-H1 distance (2.25 to 2.27 Å) in 1a-H is much shorter than that (3.85 Å) in 1a-O, which is consistent with the larger relative stability of 1a-H. The Pd-H1 distance in 2a-H is about 0.1 Å longer than the Pt-H1 distance in 1a-H, but the Pd-O distance in 2a-O is



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about 0.2 Å shorter than the Pt-O distance in 1a-O. These geometrical features suggest that the O-ahead mode is more favorably formed in the Pd complex than in the Pt complex. Consistently, the binding energy is larger in 2a-O than in 1a-O. In the Pt tetra-ammine complexes, both 1b-H and 1b-O are stable, while only 2b-O is stable in the Pd analogues. The Pt-H1 distance in 1b-H is about 0.2 Å longer than that in 1a-H, while the Pt-O distance in 1b-O is similar to that of 1a-O. The Pd-O distance in 2b-O is shorter than the Pt-O distance in 1b-O. Consistent with these geometry differences, the binding energy is smaller in 1b-H than in 1a-H and larger in 2b-O than in 1b-O; in other words, the O-ahead mode is more favorably formed in the Pd-tetra ammine complex than in the Pt analogue. In 1c and 2c, neither the H-ahead nor the O-ahead mode was found, similar to the case in gas phase. It is noted that W tends to interact with 4L rather than M, because the O site of W is repulsive with the negative net charge on the tetra-cyano complex and the H site of W is attractive with four cyanide ligands bearing a negative charge. Although 1c-H, 1c-O, 2c-H, 2c-O, and 2b-H were not optimized as the stable geometry, we need to make comparison between the H-ahead and O-ahead modes in these complexes to elucidate the source of the interaction between W and M(4L). To this end, the following procedures were employed: (i) We performed a constrained geometry optimization with the three-regions 3DRISM-MP2 method under the constraints that 4L exists on the xy molecular plane and W exists in the z-axis; see Scheme 2 for the definition of x, y, and z-axes. In other words, the O site of W was placed on the z-axis in the O-ahead orientation, and the H and O sites of W was placed on the z-axis in the H-ahead orientation, as shown in Scheme 2. We denote this partially optimized geometry as “model geometry". Indeed, this structure is reasonable for our purpose of investigating the interaction between W with M under the assumption that many water solvent molecules approach 4L; in such case the 4L moiety does not need to directly interact with W because it is surrounded by many bulk solvent molecules. (ii) We then calculated the free energy curve with the 3D-RISM-MP2 method against the distance between M and O site of W without any changes to the other moiety in the model structure; remember that the BSSE correction usually influences


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both the position and the stability of the energy minimum. Note that in the glycine complex (1a and 2a) both modes I and II were calculated because the glycine ligand induces the asymmetrical potential with respect to the z-axis (see Scheme 2a). The model geometries successfully converged except for 1c-O and 2c-O, as shown in Table 2; see Supporting Information Table S2 for details. In 1c-O and 2c-O, the above-mentioned constrained geometry optimization provided the unexpected result (neither O-ahead nor H-ahead mode) because the H site of W becomes closer to M than the O site during the partial geometry optimization due to the -2 charges of this complex. Thus, in these complexes the model geometry was defined by taking the M-O distance to be the same as that of 1a-O-I and 2a-O-I, respectively. Using these model geometries, we calculated the potential energy curve in gas phase and the free energy curve in aqueous phase using the gas phase Hamiltonian and the solvated Hamiltonian, respectively, as shown in Figures 2 and 3. Note that the geometries in gas and aqueous phases are identical, since only the M-O distance is varied while fixing the intra-molecular distances. As shown in Table 2, the O-H2 bond length of W depends only slightly on the type of M and the hydration structure, but the O-H1 bond length and the M-W inter-molecular distance are notably affected. In particular, the following characteristic features are found: (i) The O-H1 bond length in the H-ahead hydration becomes longer in the Pt complex than in the Pd complex and the O-H1 bond becomes longer than the O-H2 in both Pt and Pd complexes. (ii) The O-H1 bond length in the O-ahead hydration, on the other hand, differs only slightly between Pt and Pd complexes and the O-H1 bond length is almost the same as that of O-H2 ; these are also similar to that of a water molecule in aqueous solution (0.969 Å). (iii) The M-H distance in the H-ahead hydration is shorter in the Pt complex than in the Pd complex. (iv) On the contrary, the M-O distance in the O-ahead hydration is longer in the Pt complex than in the Pd complex. These trends arise from the dz2 orbital size, as will be discussed later. In the absence of the bulk solvation effect, the H-ahead hydration is more stable than the Oahead one in the glycine and tetra-cyano complexes, as shown in Figure 2(a), (c), (d), and (f). The H-ahead hydration provides the binding energies of 4 kcal/mol and 9 kcal/mol in 1a and



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1c, respectively, which are larger than in 2a and 2c by about 2 and 1 kcal/mol. These results indicate that the unusual H-ahead hydration can be preferably formed in both glycine and tetracyano complexes. In the tetra-ammine complex, on the other hand, the O-ahead hydration is more stable than the H-ahead one; see Figure 2(b) and (e). The binding energy (12 kcal/mol) in 1b is moderately smaller than 2b by about 1 kcal/mol. These indicate that the unusual H-ahead hydration can be formed in the neutral glycine and anionic tetra-cyano complexes while the usual O-ahead one is more stable in the cationic tetra-ammine complex, as expected from the classical viewpoint of electrostatic (ES) interaction. It is also noted that the H-ahead hydration is more stable in the Pt complex than in the Pd complex whereas the O-ahead hydration is somewhat preferred in the Pd complex. In the presence of the bulk solvation effect, i.e. when the effect is accounted for in the electronic wave-function in addition to the solvation free energy term, the free energy curve differs remarkably from the potential energy curve calculated with the Hamiltonian in gas phase, as shown in Figure 3. Note that the same geometries are employed between Figures 2 and 3. In the glycine complex, the H-ahead hydration becomes moderately less stable in aqueous phase than in gas phase. In the tetra-cyano complex, the H-ahead hydration is also largely destabilized in the aqueous phase. In the tetra-ammine complex, on the other hand, the O-ahead hydration becomes less stable in aqueous phase than in gas phase. Apparently, the solvation effect decreases the difference in stability between two hydration structures. In the Pt glycine complex 1a and tetra-cyano complexes of Pt and Pd (1c and 2c), the H-ahead hydration is more stable than the O-ahead one, while the two are equally stable in the Pd glycine complex 2a. In the Pd tetra-ammine complex 2b, the O-ahead hydration is more stable than the H-ahead one but as stable as the H-ahead one in the Pt tetra-ammine complex 1b. The above results indicate that the H-ahead hydration is more stable in the Pt complex than in the Pd complex while the O-ahead hydration is more stable in the Pd complex, resembling the case in gas phase. It should be noted that the usual O-ahead hydration is stable only in the Pd tetra-ammine complex, and the unusual H-ahead hydration is at least as stable as the O-ahead one


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in the neutral glycine and anionic tetra-cyano Pt and Pd complexes. In other words, the unusual H-ahead hydration is stable while the usual O-ahead one is not in more complexes than expected. These relative stabilities depend on both the solute energy (∆Esolute ) and the solvation free energy (∆∆µ ). In the following, we analyze the elements of ∆Esolute and ∆∆µ using EDA, i.e. Eqs. (10) and (11), to elucidate the source of the above differences, e.g., between the two hydration modes, the Pt and Pd complexes, and the energy curves in gas and aqueous phases.

4.2 Energy decomposition analysis (EDA) of the interaction between complex and W Prior to discussing the EDA results, we first examine the binding free energies, i.e. the energy differences from the infinite separation, e.g., Abind = A(M-4L + W) − A(M-4L) − A(W). Table 3 MP2 MP2 lists the binding free energy AMP2 bind and its components, Ebind and ∆∆ µrism in the presence of bulk MONOs and ∆E MONOs and page S12 solvation effect; see Supporting Information Table S3 for ∆Ereorg gas MP2 MP2 between the H-ahead and O-ahead hydrations for detailed comparison of AMP2 bind , Ebind , and ∆∆ µ

as well as the text below. Comparison between the H-ahead and O-ahead hydrations for the glycine complex (1a and 1b) MP2 ) prefers the O-ahead hydration whereas the solute term shows that the solvation term (∆∆µrism MP2 ) stabilizes the H-ahead one. Furthermore, while the solvation term are similar between the (Ebind

Pt and Pd complexes, the stabilization of the H-ahead mode by the solute term becomes smaller in the Pd case by about 2 kcal/mol (compared to the Pt complex). As a result, while the H-ahead hydration is preferred in the Pt complex, the O-ahead hydration becomes more stable in the Pd MP2 between the H-ahead complex. In other words, these results indicate that the difference in Ebind

and O-ahead hydrations characterizes the preference of the H-ahead and O-ahead solvations in the MP2 in E MP2 is mostly glycine Pt and Pd complexes, respectively. Note that the interaction term Eint bind

responsible for these differences (see Table 3). MP2 and ∆∆ µ MP2 differ reIn the charged systems (1b, 2b, 1c, and 2c), on the other hand, both Ebind

markably between the H-ahead and O-ahead solvations (> 10 kcal/mol in absolute value), and more 19 ACS Paragon Plus Environment


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importantly, the two terms somewhat compensate each other (the sum is only about 1 kcal/mol). MP2 ) stabilizes the H-ahead hydraInterestingly, while the changes in solvation free energy (∆∆µrism

tion in the cationic complexes (1b and 2b), the effect destabilizes the H-ahead hydration in the anionic complexes (1c and 2c). The interaction energy Eint term in aqueous phase can be investigated in more detail by the EDA of the super molecules with the wave functions polarized by solvation, as shown in Table 4A; see Table 4B for the EDA in gas phase. Though the Pauli exclusion principle is not considered correctly in evaluating CT and PL terms in the Kitaura-Morokuma analysis, it is likely that the error induced by this weak point is not very large because we used this analysis to make comparison of two coordination structures. 69,70 It is of considerable interest to investigate how much the bulk solvation effect influences the binding energies of H-ahead and O-ahead modes. As shown in Tables 4A and 4B, the difference in binding energy between these two interaction modes arises from the reorganization energies MP2 of monomers, which are induced by the solvation structure around the super molecule, and Eint

terms are hardly influenced by the bulk solvation unexpectedly. Though the Pt complex and W are more polarized in solvent than in gas phase, as shown in Table 5 and Supporting Information Table MP2 is influenced little by the solvation, suggesting that bulk S4 (see the components of 4L), the Eint MP2 value. In other words, the E solvation effects are canceled in Eint ES and EPOL +ECT +EMIX terms

are different between gas and aqueous phases but the difference nearly cancel out in the sum, thus MP2 are similar between the two phases. the interaction energy Eint

In Table 4A, it is noted that the dynamical electron correlation (DEC) effect EDEC strongly prefers the H-ahead hydration over the O-ahead one in every case, where EDEC is defined as the energy difference between the Hartree-Fock and MP2 calculated interaction energies, EDEC (= MP2 − E RHF ). In particular, in 1a, 1c, and 2c, the H-ahead complex is unstable (has positive Eint int

binding energy) at the RHF level but becomes stable at the MP2 level. Besides EDEC , EES plays a crucial role in stabilizing the H-ahead hydration in the glycine and tetra-cyano complexes, and is pronounced in the Pt complex than in the Pd ones. For instance, the ES stabilization is larger in


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the O-ahead hydration of 2a whereas the H-ahead one is rather stabilized in 1a. More importantly, while in the tetra-cyano complexes both EDEC and EES prefer the H-ahead hydration, in the tetraammine complexes the large stabilization of the O-ahead hydration by EES overwhelms EDEC to prefer the O-ahead hydration at the Eint level. (Note the compensating strong solvation effect discussed above.) Overall, we find that EES itself (or the raw value of EES ) becomes smaller in the Pt complexes than the Pd ones for the H-ahead hydration, but becomes larger for the O-ahead hydration, respectively, thereby plays an important role in providing the difference between the Pt and Pd complexes (see Table 4A). To clarify the reason for the difference in ES stabilization between the Pt and Pd complexes, we depicted the ESP generated by the complex and its difference between the Pt and Pd complexes, as shown in Figure 4. Apparently, the ESP in the region near W is more negative in the Pt complex than in the Pd complex. This difference arises from the fact that the Pt 5d orbital has larger size than the Pd 4d. Especially in the glycine complex, the ESP is remarkably different between the Pt and Pd complexes; 1a exhibits a negative ESP along the z-axis (near Pt), which attracts the positively charged H site of W, while 2a shows a slightly positive ESP along the z-axis to draw the negatively charged O site of W. This difference in ESP between the Pt and Pd complexes is also responsible for the geometrical features that the O-H1 bond length in the H-ahead hydration is longer in the Pt complex than in the Pd one whereas the M-O bond length in the O-ahead hydration is shorter in the Pd complex (Tables 1 and 2), i.e. the negative ESP about the Pt complex pulls the H site of W but pushes the O site away, as shown in Scheme 3a. The tetra-ammine complexes, 1b and 2b, show positive ESPs in the z-axis; this ESP is less positive in 1b than in 2b, indicating that the positively charged H site of W is more repulsive with 2b than with 1b and the negatively charged O site of W is more attracted to 2b than to 1b. These agree with the trend that the O-H1 bond length in H-ahead hydration becomes longer in the Pt complex than in the Pd complex but the M-O bond length in the O-ahead hydration becomes shorter in the Pd complex, as shown in Scheme 3b. The large difference in the binding energy among the glycine, tetra-ammine, and tetra-cyano complexes also arises from the ESP; the positive



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ESP in 1b and 2b strongly destabilizes the H-ahead hydration whereas the negative ESP in 1c and 2c rather stabilizes the H-ahead hydration, compared to the moderate ESP in 1a and 2a. Overall, it is concluded that both the DEC effect and the electrostatic interaction play crucial roles in determining the relative stabilities of the two hydration modes but in a different manner.

4.3 Natural bond orbital (NBO) charge analysis and charge transfer (CT) character induced by H-ahead and O-ahead hydrations One can expect the lone pair of W participates in stabilizing the O-ahead hydration. 26 Hence, we next discuss the CT character by evaluating the NBO charges 68 of the super molecule and each monomer under the consideration of the solvation around the super molecule, as shown in Table 5; see Supporting Information Table S5 for the NBO populations of valence orbitals on the metal center. In the O-ahead hydration, a small positive charge is found on W, which is larger in the Pd complex than in the Pt complex; this suggests that the CT occurs from W to the Pd complex more than to the Pt complex, although the magnitude is only up to 0.01 e. Rather, the positive charge on M increases in the presence of W, to a similar extent to the increase in the negative charge on 4L (or the decrease in the positive charge on 4L). These results indicate that the CT from 4L to M becomes weak when W is present by about 0.02 e in 1a, 1b, and 1c, 0.04 e in 2a and 2b, and 0.03 e in 2c, respectively. Note that while the positive charge on M increases by adding W, it does not mean that the CT occurs from M to W because the increase of positive charge on M mainly comes from the weakening of the CT from 4L to M. Thus it is concluded that the CT from W to M is unexpectedly small in the O-ahead hydration, which is consistent with the results of EDA showing that ECT is small (Table 4A). In the H-ahead hydration, on the other hand, the CT occurs from the complex to W in contrast to the O-ahead hydration because W has a negative NBO charge (about -0.03 e in 1a, -0.02 e in 1b and 1c, -0.01 e in 2a, 2b, and 2c). Here the σ ∗ orbital of O-H1 plays a role of an acceptor orbital. These results indicate that the CT is larger in the Pt complex than in the Pd one. The 22 ACS Paragon Plus Environment

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increase in the σ ∗ character in the Pt complex is consistent with the longer O-H1 bond length in the Pt complex than in the Pd one. 71 Despite the CT from the complex to W, the positive NBO charge on M decreases in the presence of W, as shown in Table 5; see the values in parentheses for the change in the NBO charges by adding W. This change in the NBO charge on M arises from the strengthening of the CT from 4L to M in the complex-water system. The results clearly show that the negative charge on 4L decreases (or the positive charge on 4L increases) and the positive charge on M decreases in the presence of W, respectively. These NBO charges indicate that the CT from 4L to M is enhanced when W is present by about 0.05 e in 1a and 2a, 0.03 e in 1b and 2b, 0.04 e in 1c and 2c, respectively; in addition, the negative charge accepted by M partially transfers to W. It is noted that, in the O-ahead hydration, the CT from W to M is larger in the Pd complex than in the Pt complex, whereas in the H-ahead hydration, the CT from M to W is larger in the Pt complex (than in the Pd complex). These population changes occur similarly in all the complexes even when the bulk solvation effect is not considered; see Supporting Information Table S4 for the NBO charges in gas phase. In summary, the CT between M and 4L depends on the W interaction mode in the following manner; the CT from 4L to M is enhanced in the H-ahead hydration as the positive charge on the approaching H atom stabilizes the orbital energy of M, while in the O-ahead hydration the CT is suppressed due to the negative charge on the O site of W which destabilizes the orbital energy of M. The weak CT from W to the complex is considered as one of the reasons for the weak stabilization of the O-ahead hydration, even in the neutral Pt and Pd complexes. To understand the origin of this weak CT character in the O-ahead hydration, we looked for the acceptor orbital of M in the CT from W. As shown in Table 5 and Supporting Information Table S5, however, a characteristic orbital is not found because the CT between M and 4L is larger than that between M and W; indeed, the change in the NBO population on M when W is added appears to be the opposite to that induced by the CT from M to W. It may seems that the ndz2 orbital plays a role of the acceptor orbital in the O-ahead hydration because it expands towards W. However, its population change is very small, indicating that the



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CT from W to the nd2z is very weak; this is not surprising because the nd2z orbital is almost doublyoccupied, and indeed plays a role of the donor orbital in the H-ahead hydration, as shown in Supporting Information Table S5. Also, the NBO population of the (n + 1)pz orbital changes only slightly in the presence of W in both the H-ahead and O-ahead hydrations. The (n + 1)s orbital may also be the acceptor orbital in the O-ahead hydration, too; yet, the (n + 1)s orbital population decreases in the presence of W, and the amount of decrease is similar to the increase in the negative charge on 4L (or the decrease in the positive charge on 4L), suggesting that the (n + 1)s does not participate in the CT from W but in the CT from 4L. Based on these results, it is concluded that the (n + 1)s and (n + 1)pz orbitals hardly contribute to the CT from W in the O-ahead hydration, somewhat unexpectedly, hence the stabilization of the O-ahead hydration arises only from the ES interaction between the complex and W. As a result, the O-ahead hydration is stable only when the ES stabilization is large, i.e., in the cationic tetra-ammine complex.

4.4 Analysis of the solvation free energy and its spatial contribution It is interesting to elucidate the reason why the solvation free energy remarkably decreases the difference in stability between the two hydration modes. For this purpose, we need detailed knowledge of the solvation effect. On the linear response assumption that the averaged electrostatic V and Lennard-Jones (LJ) potentials U linearly depend on the solute point-charges Q and LJ parameters √ ε , respectively, the solvation free energy can be evaluated by a half of the averaged solute-solvent interaction energy. Particularly, the former relation was often observed in the calculations based on simulations with explicit solvent 72,73 and used in the implicit (dielectric continuum) solvation models. Therefore here we employed the LRA to analyze the solvation free energy ∆µ in this subsection, as employed in Ref. [74]. Table 6 shows the solvation free energy ∆µ LRA and the contributions from the metal and ligand moieties calculated by Eq. (21) based on the LRA. 1 U-V,RHF (2) ES ∆µ LRA,MP2 = Eint + ∑ Pµν Uµν (R; {gs }), 2 µν


(21)

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U-V,RHF where Eint is the averaged solute-solvent interaction energy evaluated by {gs (r)} from the

three-regions 3D-RISM-RHF method. Here, the point-charge approximation was employed to analyze the components of the linear response solvation free energy on each solute site. 75 The difference in solvation free energy between the H-ahead and O-ahead hydrations is almost the same between the Pt and Pd complexes. In the glycine complexes 1a and 2a, the stabilization by the solvation free energy is slightly larger in the O-ahead hydration than in the H-ahead one by about 3 kcal/mol. In the tetra-ammine complexes 1b and 2b, the H-ahead hydration is more stabilized than the O-ahead one by about 19 kcal/mol, while in the tetra-cyano complexes 1c and 2c, the O-ahead one is preferred by about 10 kcal/mol. 76 The components of ∆µ LRA clearly shows what contributes to the difference in the solvation free energy; in the glycine complex, the H-ahead hydration is more stabilized than the O-ahead one by the solvation around the NH3 ligands and W but destabilized by the solvation around the Cl ligands. In the tetra-ammine complex, the solvation around the NH3 ligands also contributes to prefer the H-ahead hydration to the O-ahead one. In the tetra-cyano complex, on the other hand, the O-ahead hydration is more stabilized than the Hahead one by the solvation around the CN ligands. These features agree with the tendency that the H-ahead hydration enhances the CT from 4L to M whereas the O-ahead hydration suppresses this CT (see above). To investigate the origin of the above differences in the solvation free energy in more detail, we calculated the changes in the solvation structure, ∆g(r), and the change in the spatial distribution function of solvation free energy, ∆∆µSDF (r), when W changes from the O-ahead hydration to H-ahead one, respectively. 77 Here the spatial distribution function of the solvation free energy, ∆µSDF (r), is defined at the MP2 level by Eq. (22); ] [ { } 1 1 1 (2) MP2 (hs (r))2 − cs (r) − hs (r)cs (r) + gs (r)qVs ∑ Pµν ⟨χµ | VÊSP (R, r) | χν ⟩ . ∆µSDF (r) = ρ V ∑ β 2 2 µν s (22) where the first term is the same as the 3D-extended solvation free energy in the spatial decomposition analysis of the thermodynamics 78 and the second term is the MP2 correction term. Note



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that the integration of ∆µSDF (r) over the entire solvation space provides the total solvation free energy, ∆µ LRA,MP2 . Figures 5 A1, B1, C1, and A2, B2, C2 show the ∆g(r) of the bulk H and O and the ∆∆µSDF (r) for 1a, 1b, and 1c, respectively. The differences are taken as changes from the O-ahead to the H-ahead hydration in all figures, with blue and red indicating the increase and decrease, respectively. When the O-ahead mode changes to the H-ahead one, we find the following three characteristic changes in the difference in the solvation structures of 1a, 1b, and 1c (Figures 5 A1, B1, and C1): (i) The distribution of the solvent H site, gH (r), is smaller around the O site of W in the O-ahead hydration than in the H-ahead hydration due to the outward-facing O-H1 bond (see the red region in Scheme 4a). On the other hand, the distribution of the solvent O site, gO (r), decreases upon changing from the O-ahead hydration to the H-ahead one (see Scheme 4b). (ii) In the H-ahead hydration, the solvent O site tends to approach the H1 site of W, hence ∆gO (r) is positive about the H1 site moiety (defined in the H-ahead hydration structure). ∆gH (r) is instead negative as the H1 atom repels the solvent H sites; see the blue donut ring in Scheme 4b. (iii) Since the CT from 4L to M is enhanced in the H-ahead hydration and the H1 site of W attracts the negatively charged site of solvent molecule through the ES interaction, ∆gO (r) increases near the NH3 ligands while ∆gH (r) decreases near the Cl and CN ligands; see the blue region around 4L in Scheme 4b. For simplicity, hereafter we refer to the three changes as solvation structure changes (i), (ii), and (iii), respectively. The ∆∆µSDF (r) is given by the sum of the three changes. In all cases (Figures 5 A2, B2, and C2), the blue region is found around the O site of W, which reflects the change (i). The changes (ii) and (iii), on the other hand, affect ∆∆µSDF (r) in a different manner between three complexes: In the glycine complex (1a), neither blue nor red region is found about the H1 site of W, presumably because the free energy change by ∆gO (r) and ∆gH (r) is canceled out (Figure 5 A2); in other words, the solvation structure change (ii) has little effect due to the neutrality of M-4L. Red region is found about the Cl ligands, as shown in Figure 5 A2, but this destabilization is mostly canceled by the stabilization of W by solvation, appearing as the blue region about the O site of W. Thus in


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this complex, the solvation does not largely influence the relative stabilities of the two hydration modes (Figures 2(a) and 3(a)). In the tetra-ammine complex (1b), blue region is found about the H1 site of W and 4L, as shown in Figure 5 B2. Because the tetra-ammine complex has the +2 charge, the solvent O site strongly interacts with M-4L; gO (r) increases around M and 4L due to the solvation changes (ii) and (iii), and enhances ∆∆µSDF (r), as shown by the blue region around M-4L (Figure 5 B2); see Supporting Information Figure S1(a) for the bottom view of change (ii). These changes stabilize the H-ahead mode but destabilizes the O-ahead mode (see also Figures 2(b) and 3(b)). In the tetra-cyano complex, red region is found about the H1 site of W and 4L, as shown in Figure 5 C2. Because the tetra-cyano complex has the −2 charge, the solvent O site is repulsive with M-4L. However, the solvation structure changes (ii) and (iii) tend to increase gO (r) around M and 4L, respectively, and suppress ∆∆µSDF (r) around the area, as shown by the red region around M-4L (Figure 5 C2); see Supporting Information Figure S1(b) for the bottom view of change (ii). These changes destabilizes the H-ahead mode and stabilizes the O-ahead mode. In summary, when the O-ahead mode changes to the H-ahead one, the change in the solvation structure, ∆g(r), is similar among the glycine, tetra-ammine, tetra-cyano complexes because of their similar changes in the CT character; yet the change in spatial contribution of the solvation free energy, ∆∆µSDF (r), is significantly different among them because of the difference in the total net charge of the complexes. These results provide clear explanation to why the solvation effect is moderate in the glycine complex but is remarkable in the tetra-ammine and tetra-cyano complexes, and furthermore reveals how the solvation effects affects the two hydration modes in the tetra-ammine and tetra-cyano complexes in the opposite direction.

5 Conclusions In the present paper, we developed the analytical 3D-RISM-MP2 free energy gradient. The Zvector method was employed in two parts to significantly reduce the computational cost of evalu-



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ating the CP-RISM terms in the derivatives. To improve the convergence of the RISM-SCF cycle without loss of accuracy, we employed the three-regions 3D-RISM-MP2 approach and introduced the point-charge approximation in the derivatives (RISM-CPHF equation). This three-regions 3DRISM-MP2 method was applied to determine the geometry and solvation structure of the usual O-ahead and unusual H-ahead hydrations in the Pt and Pd complexes. The EDA and the linear response free energy analysis were performed at the 3D-RISM-MP2 level to reveal; (whether a Pt(II) complex can have the O-ahead hydration, what interaction is crucial in the O-ahead and H-ahead hydrations, and which hydration mode is more favorable in the Pd(II) analogues. In the absence of the bulk solvation effect, only the tetra-ammine complex takes the O-ahead hydration because of the large stabilization by the ES interaction between the complex and the O site of water. The neutral glycine complex prefers the H-ahead hydration due to the stabilization by the DEC effect. The tetra-cyano complex also form the H-ahead hydration because of the large stabilization by the ES interaction between M and the H site of W in addition to the DEC effect. Unexpectedly, the CT from W to M is weak in the O-ahead hydration, and hence the stabilization by the CT interaction is small. In the H-ahead hydration, on the other hand, the CT from M to W occurs to provide the larger CT stabilization than in the O-ahead one. Interestingly, the O-ahead hydration is more stable in the Pd complex than in the Pt complex and the H-ahead hydration becomes less stable in the Pd complex than in the Pt complex. This is because the ESP along the z-axis of the complex is less negative in the Pd complex than in the Pt complex, owing to the difference in the dz2 orbital size. The free energy profiles in aqueous phase differs from those without the bulk solvation. This indicates that the solvation free energy considerably influences the relative stabilities of the Hahead and O-ahead hydrations. In the glycine complex, the stabilization by solvation is slightly smaller in the H-ahead hydration than in the O-ahead one, because most of the destabilization near the Cl ligand is canceled by the stabilization near W. As a result, the relative stability of the H-ahead hydration only slightly decreases by solvation. In the tetra-ammine complex, the large stabilization of the O-ahead hydration in the solute moiety is significantly suppressed by solvation.


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In the tetra-cyano complex, the large stabilization of the H-ahead hydration in the solute moiety is also suppressed by solvation. This is because the solvent O site interacting with the H1 site of W enhances the stability of the H-ahead hydration via the ES attraction with the +2 charge of the tetra-ammine complex but destabilizes the H-ahead hydration via the ES repulsion with the −2 charge of the tetra-cyano complex. As a result, the difference in stability between the two hydration modes becomes smaller in aqueous phase in all cases. It is noted that the usual O-ahead hydration is favored only in the tetra-ammine Pd complex, because the very large ES stabilization between the O site of W and the positive charge of the complex cannot be canceled by the solvation effect. In other complexes, the unusual H-ahead hydration can be formed unexpectedly, in which the DEC effect plays important role.

Acknowledgement This work was financially supported by Grand-in-Aids for Specially Promoted Science and Technology (No. 22000009), Grants-in-Aid for Scientific Research (No. 15H03770), a Grantin-Aid for Science Research on Innovative Areas (No. 15H00940, Stimuli-responsive Chemical Species), and Grand Challenge Project (IMS, Okazaki, Japan) from the Ministry of Education, Culture, Sports, Science and Technology.

Supporting Information Available Complete reference of 67, details of free energy gradient for 3D-RISM-MP2, geometrical parameters determined by full and partial geometry optimizations, free energy and its components in aqueous phase, NBO charges in gas phase, NBO populations of valence orbitals on metal center in aqueous phase. This material is available free of charge via the Internet at http://pubs.acs.org/.



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(58) Su, P.; Li, H. J. Chem. Phys. 2009, 131, 014102. MONOs is induced by solvent molecules around the super molecule, which indi(59) Note that EREORG

cates how much the electronic structures of monomers are distorted when going from gas phase to solution. (60) Cammi, R.; Olivares Del Valle, F. J.; Tomasi, J. Chem. Phys. 1988, 122, 63-74. (61) Roy, L. E.; Hay, P. J.; Martin, R. L. J. Chem. Theory Comput. 2008, 4, 1029-1031. (62) Kaminski, J. W.; Gusarov, S.; Wesolowski, T. A.; Kovalenko, A. J. Phys. Chem. A 2010, 114, 6082-6096; Gusarov, S.; Pujari, B. S.; Kovalenko, A. J. Comput. Chem. 2012, 33, 1478-1494 (63) Perkyns, J. S.; Lynch, G. C.; Howard, J. J.; Pettitta. B. M. J. Chem. Phys. 2010, 132, 064106; (64) Berendsen, H. J. C.; Postma, J. P. M.; van Gunstern, W. F.; Hermans, J. Intermolecular Forces; Pullman, B. Ed.; Reidel, Dordrecht, 1981, pp 331-342. (65) Sato, H.; Hirata, F.; Kato, S. J. Chem. Phys. 1996, 105, 1546-1551. (66) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M., Jr.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A. J. Am. Chem. Soc. 1995, 117, 5179-5197. (67) Schmidt, M. W.; Baldridge, K. K.; Boatz J. A. et al. J. Comput. Chem. 1993, 14, 1347-1363. See the Supporting Information for the complete reference. (68) Glendening, E. D.; Badenhoop, J. K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M.; Weinhold, F. NBO 5.0. Theoretical Chemistry Institute, University of Wisconsin, Madison, 2001. (69) Glendening E. D.; Streitwieser, A. J. Chem. Phys. 1994, 100, 2900.


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(70) Though the CT term is very underestimated in the Kitaura-Morokuma analysis, the error is not very large in comparison because the NBO analysis shows that CT is small in both of H-ahead and O-ahead interaction modes. (71) This means that the longer O-H1 bond length arises from the CT to the O-H σ ∗ MO, and the difference in ESP around ML4 is responsible for the longer O-H1 bond in the Pt complex (see also subsection 4.2). (72) Jean-Charles, A.; Nicholls, A.; Sharp, K.; Honig, B.; Tempczyk, A.; Hendrickson, T. F., Still, W. C. J. Am. Chem. Soc. 1991, 113, 1454-1455. (73) Nina, M.; Beglov, D. Roux, B. J. Phys. Chem. 1997, 101, 5239-5248. (74) Yamazaki, S.; Kato, S. J. Chem. Phys. 2005, 123, 114510. (75) Although the geometry and solvation structure are not determined by using the pure point charge approximation, it is necessary to employ the pure point charge approximation here to assign the solvation free energy to each solute site. (76) The PCM method also provides similar results; see Supporting Information Table S6 for ∆µpcm . (77) Strictly speaking, to compare the solvation effect between the O-ahead and H-ahead hydrations, we used the geometry of O-ahead hydration at the metal-O distance of 3.3 Å which is the optimized distance. The geometry of the H-ahead hydration is determined by rotating W around the O site of W to take the structure in which the H1 site of water exists in the z-axis and M, O, and H2 sites of W exist on the same molecular plane as the geometry of the O-ahead hydration. This is because we wish to investigate the source of the difference in the solvation effect between the O-ahead and H-ahead hydrations in a simplified model. It is noted that the solvation free energies of these geometries differ little from those of free energy minimum geometries when available.



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(78) Yamazaki, T.; Kovalenko, A. J. Chem. Theory Comput. 2009, 5, 1723-1730.


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Table 1: Stable structures determined by the full geometry optimizations and relative stabilities of H and O-ahead hydrationsa .

Geom.b Existencec r(O-H1 ) r(O-H2 ) r(Pt-H1 ) r(Pt-O) e ∆AMP2 rism (noBSSE) f ∆AMP2 rism

Geom.b Existencec r(O-H1 ) r(O-H2 ) r(Pd-H1 ) r(Pd-O) e ∆AMP2 rism (noBSSE) f ∆AMP2 rism

Pt complex 1b, [Pt(NH3 )4 ]2+ H-I O-I yes yes (no) (yes) 0.972 0.971 (-) (0.970) 0.970 0.971 (-) (0.970) 2.45 3.99 (-) (3.81) 3.38 3.32 (-) (3.12) -2.0 -1.1 -0.3 0.6 Pd complex 2a, PdCl2 (NH3 )(glycine) 2b, [Pd(NH3 )4 ]2+ H-I H-II O-I O-II H-I O-I yes yes yes yes no yes (nod ) (no) (no) (yes) (no) (yes) 0.970 0.971 0.970 0.970 0.971 (-) (-) (-) (0.966) (-) (0.970) 0.971 0.970 0.969 0.970 0.970 (-) (-) (-) (0.965) (-) (0.970) 2.36 2.40 3.33 3.65 3.64 (-) (-) (-) (3.66) (-) (3.60) 3.33 3.36 2.97 3.06 2.98 (-) (-) (-) (3.00) (-) (2.91) -1.2 -0.9 -1.5 -1.9 -1.4 0.5 0.7 0.2 -0.2 0.3 1a, PtCl2 (NH3 )(glycine) H-I H-II O-I O-II yes yes no yes (nod ) (no) (no) (yes) 0.978 0.978 0.970 (-) (-) (-) (0.966) 0.971 0.970 0.970 (-) (-) (-) (0.966) 2.27 2.25 3.85 (-) (-) (-) (3.96) 3.25 3.23 3.33 (-) (-) (-) (3.31) -3.7 -3.6 -1.2 -1.2 -1.0 0.6

a Calculated

1c, [Pt(CN)4 ]2− H-I O-I no no (no) (no) (-) (-) (-) (-) (-) (-) (-) (-) 2c, [Pd(CN)4 ]2− H-I O-I no no (no) (no) (-) (-) (-) (-) (-) (-) -

(-) (-) -

by three-regions 3D-RISM-MP2. Unit is in Å. b H-I, H-II, O-I, and O-II represents the H-ahead hydration I, II, and O-ahead one I, and II, respectively. c “Yes" represents that the interaction mode of the optimized geometry is the same as the initial one, and vice versa. d In parentheses are gas phase optimization results. e, f Calculated by the BS-II withoute and with f the BSSE correction. The infinite separation is taken as the standard (energy zero).



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 53

Table 2: Stable structures determined by the partial geometry optimizationsa .

Geom.b Existencec r(O-H1 ) r(O-H2 ) r(Pt-H1 ) r(Pt-O)

Geom.b Existencec r(O-H1 ) r(O-H2 ) r(Pd-H1 ) r(Pd-O)

Pt complex 1a, PtCl2 (NH3 )(glycine) 1b, [Pt(NH3 )4 ]2+ H-I H-II O-I O-II H-I O-I yes yes yes yes yes yes (yesd ) (yes) (yes) (yes) (yes) (yes) 0.976 0.977 0.969 0.970 0.971 0.971 (0.974) (0.976) (0.966) (0.966) (0.963) (0.969) 0.970 0.971 0.969 0.970 0.970 0.971 (0.966) (0.966) (0.966) (0.966) (0.965) (0.969) 2.29 2.31 3.81 3.89 2.48 3.96 (2.31) (2.29) (3.67) (4.03) (2.47) (3.78) 3.27 3.29 3.39 3.37 3.45 3.36 (3.29) (3.25) (3.07) (3.37) (3.33) (3.10) Pd complex 2a, PdCl2 (NH3 )(glycine) 2b, [Pd(NH3 )4 ]2+ H-I H-II O-I O-II H-I O-I yes yes yes yes yes yes (yesd ) (yes) (yes) (yes) (yes) (yes) 0.970 0.970 0.970 0.970 0.966 0.971 (0.969) (0.969) (0.966) (0.966) (0.961) (0.969) 0.970 0.971 0.970 0.970 0.970 0.971 (0.965) (0.965) (0.966) (0.966) (0.966) (0.969) 2.38 2.39 3.47 3.70 2.55 3.67 (2.37) (2.41) (3.46) (3.71) (2.50) (3.62) 3.35 3.36 2.99 3.10 3.51 2.98 (3.34) (3.38) (2.83) (3.05) (3.46) (2.93)

a Calculated

1c, [Pt(CN)4 ]2− H-I O-I yes noe (yes) (no) 0.978 0.969 (0.981) (-) 0.970 0.969 (0.966) (-) 2.26 3.74 (2.39) (-) 3.24 3.39 (3.37) (-) 2c, [Pd(CN)4 ]2− H-I O-I yes noe (yes) (no) 0.972 0.969 (0.976) (-) 0.971 0.969 (0.966) (-) 2.30 3.38 (2.45) (-) 3.27 2.99 (3.42) (-)

by three-regions 3D-RISM-MP2. Unit is in Å. b H-I, H-II, O-I, and O-II represents the H-ahead hydration I, II, and O-ahead one I, and II, respectively. c “Yes" represents that the interaction mode of the optimized geometry is the same as the initial one, and vice versa. d In parentheses are gas phase optimization. e Because the partial geometry optimization provided the unexpected result (neither O-ahead nor H-ahead mode), model geometries of 1c and 2c were determined by adding one more constraint that r(M-O) was fixed to that of 1a-O-I and 2a-O-I, respectively.


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3: Free energy and its components of the complex-water system.a

1a, PtCl2 (NH3 )(glycine) Geom. H-I H-II O-I O-II MP2 Abind -1.1 -0.9 1.4 0.7 (-3.7b ) (-4.3) (-0.6) (0.1) components of AMP2 bind MP2 ∆∆µrism 3.6 4.6 2.4 0.7 MP2 Ebind -4.7 -5.7 -1.0 0.0 MP2 components of Ebind MP2 Eint -4.0 -4.8 -0.6 0.3 Others -0.7 -0.9 -0.4 -0.3

Pt complex 1b, [Pt(NH3 )4 ]2+ H-I O-I 0.3 0.6 (2.8) (-11.3) -4.7 5.0

13.4 -12.8

3.0 -11.2 2.0 -1.6 Pd complex 2a, PdCl2 (NH3 )(glycine) 2b, [Pd(NH3 )4 ]2+ Geom. H-I H-II O-I O-II H-I O-I MP2 Abind 0.8 1.2 0.9 0.3 2.1 0.4 (-2.4b ) (-2.9) (-1.4) (-0.4) (3.9) (-12.8) components of AMP2 bind MP2 ∆∆µrism 4.6 6.0 3.1 1.3 -3.6 14.9 MP2 Ebind -3.8 -4.8 -2.2 -1.0 5.7 -14.5 MP2 components of Ebind MP2 Eint -2.6 -3.2 -1.4 -0.6 3.9 -12.5 Others -1.2 -1.6 -0.8 -0.4 1.8 -2.0 a Calculated

1c, [Pt(CN)4 ]2− H-I O-I -1.0 0.8 (-8.2) (2.7) 8.3 -9.3

-2.3 3.1

-8.2 -1.1

3.2 -0.1

2c, [Pd(CN)4 ]2− H-I O-I 0.0 0.7 (-9.2) (3.2) 8.5 -8.5

-2.8 3.5

-7.2 -1.3

3.9 -0.4

at the model geometry with three-regions 3D-RISM-MP2. Unit is in kcal/mol. b In parentheses MP2 . are the binding energy in gas phase, Ebind



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 53

Table 4A: EDA of the interaction energy between the complex and the (QM) water in aqueous phase.a

Geom. MP2 Eint MP2 components of Eint EDEC RHF Eint RHF components of Eint EES EEX +EREP EPOL +ECT +EMIX (EPOL ) (ECT ) (EMIX ) Geom. MP2 Eint MP2 components of Eint EDEC RHF Eint RHF components of Eint EES EEX +EREP EPOL +ECT +EMIX (EPOL ) (ECT ) (EMIX )

1a, PtCl2 (NH3 )(glycine) H-I H-II O-I O-II -4.0 -4.8 -0.6 0.3 -5.7 1.7

-6.4 1.6

-0.8 0.2

-1.4 1.7

Pt complex 1b, [Pt(NH3 )4 ]2+ H-I O-I 3.0 -11.2 -4.0 6.9

-0.1 -11.0

-4.9 -5.9 -2.2 -1.6 10.1 11.3 2.8 4.3 -3.5 -3.8 -0.4 -1.0 (-5.3) (-5.9) (-0.4) (-1.3) (-3.4) (-3.6) (-0.6) (-0.9) (5.2) (5.7) (0.6) (1.2)

6.9 -10.9 5.5 2.5 -5.4 -2.6 (-5.3) (-2.1) (-3.0) (-1.5) (3.0) (1.0) Pd complex 2a, PdCl2 (NH3 )(glycine) 2b, [Pd(NH3 )4 ]2+ H-I H-II O-I O-II H-I O-I -2.6 -3.2 -1.4 -0.6 3.9 -12.5 -4.7 2.1

-5.3 2.1

-0.8 -0.6

1c, [Pt(CN)4 ]2− H-I O-I -8.2 3.2 -6.1 -2.1

-1.0 4.2

-7.1 10.9 -5.9 (-11.4) (-3.8) (9.3)

3.1 2.7 -1.6 (-2.0) (-0.9) (1.3)

2c, [Pd(CN)4 ]2− H-I O-I -7.2 3.9

-1.2 0.6

-3.3 7.2

0.1 -12.6

-5.5 -1.7

-1.3 5.2

-0.6 -1.6 -6.2 -4.7 5.0 6.1 5.9 5.9 -2.3 -2.4 -0.3 -0.6 (-2.9) (-3.2) (-1.2) (-1.2) (-1.7) (-1.7) (-1.0) (-1.0) (2.3) (2.5) (1.9) (1.6)

10.1 2.7 -5.6 (-5.5) (-2.2) (2.1)

-13.7 5.1 -4.0 (-4.1) (-2.0) (2.1)

-4.3 6.8 -4.2 (-7.5) (-2.1) (5.6)

-0.1 6.7 -1.4 (-3.9) (-1.5) (4.0)

a Calculated

at the model geometry with three-regions 3D-RISM-MP2. Unit is in kcal/mol. In parentheses are components of the EPOL +ECT +EMIX term.


Page 41 of 53

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 4B: EDA of the interaction energy between the complex and the (QM) water in the absence of the bulk solvation effect.a

Geom. MP2 Eint MP2 components of Eint EDEC RHF Eint RHF components of Eint EES EEX +EREP EPOL +ECT +EMIX (EPOL ) (ECT ) (EMIX ) Geom. MP2 Eint MP2 components of Eint EDEC RHF Eint RHF components of Eint EES EEX +EREP EPOL +ECT +EMIX (EPOL ) (ECT ) (EMIX ) a Calculated

1a, PtCl2 (NH3 )(glycine) H-I H-II O-I O-II -3.8 -4.6 -0.7 0.1 -5.6 1.8

-6.3 1.6

-0.9 0.2

-1.6 1.7

Pt complex 1b, [Pt(NH3 )4 ]2+ H-I O-I 2.7 -11.3 -4.0 6.7

-0.3 -11.0

-4.9 -6.2 -2.0 -1.9 10.1 11.4 2.7 4.4 -3.4 -3.6 -0.6 -0.8 (-5.2) (-5.7) (-0.7) (-1.0) (-3.3) (-3.5) (-0.6) (-0.9) (5.1) (5.6) (0.7) (1.1)

4.3 -11.2 5.2 2.2 -2.9 -2.0 (-3.4) (-2.0) (-2.3) (-0.9) (2.8) (0.9) Pd complex 2a, PdCl2 (NH3 )(glycine) 2b, [Pd(NH3 )4 ]2+ H-I H-II O-I O-II H-I O-I -2.4 -3.0 -1.6 -0.8 3.8 -12.8 -4.6 2.2

-5.2 2.2

-0.9 -0.7

1c, [Pt(CN)4 ]2− H-I O-I -8.4 2.7 -6.3 -2.1

-1.4 4.1

-8.5 11.2 -4.8 (-10.4) (-4.0) (9.6)

2.3 2.9 -1.1 (-1.7) (-0.8) (1.4)

2c, [Pd(CN)4 ]2− H-I O-I -7.4 3.2

-1.4 0.6

-3.2 7.0

-0.2 -12.6

-5.7 -1.7

-1.8 5.0

-1.2 -2.2 -5.5 -4.4 5.1 6.3 6.1 6.1 -1.7 -1.9 -1.2 -1.1 (-2.3) (-2.6) (-2.0) (-1.6) (-1.4) (-1.6) (-1.2) (-1.1) (2.0) (2.3) (2.0) (1.6)

6.8 2.6 -2.4 (-2.6) (-1.4) (1.6)

-14.4 4.9 -3.1 (-3.4) (-1.5) (1.8)

-5.7 7.0 -3.0 (-6.4) (-2.2) (5.6)

-0.5 7.0 -1.5 (-5.2) (-1.5) (5.2)

at the model geometry with gas phase MP2 calculation. Unit is in kcal/mol.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 53

Table 5: NBO charges on the complex-water system in aqueous phase.a

Pt complex 1a, PtCl2 (NH3 )(glycine) 1b, [Pt(NH3 )4 ]2+ Geom. H-I H-II O-I O-II H-I O-I q(Pt) 0.570 0.570 0.609 0.609 0.710 0.734 (-0.024b ) (-0.024) (+0.022) (+0.023) (-0.018) (+0.020) q(W) -0.029 -0.026 0.002 0.003 -0.016 0.001 q(4L) -0.541 -0.544 -0.610 -0.612 1.306 1.265 (+0.053) (+0.050) (-0.024) (-0.026) (+0.034) (-0.021) components of 4L q(L1 )c -0.593 -0.590 -0.615 -0.615 0.327 0.316 (+0.023) (+0.022) (-0.007) (-0.007) (+0.009) (-0.006) q(L2 ) -0.592 -0.592 -0.615 -0.615 0.327 0.316 (+0.009) (+0.008) (-0.007) (-0.007) (+0.010) (-0.005) q(L3 ) 0.336 0.336 0.334 0.321 0.327 0.316 (+0.012) (+0.010) (+0.002) (+0.000) (+0.012) (-0.004) 0.308 0.302 0.296 0.298 0.326 0.316 q(L4 ) (+0.009) (+0.010) (-0.012) (-0.012) (+0.003) (-0.006) Pd complex 2a, PdCl2 (NH3 )(glycine) 2b, [Pd(NH3 )4 ]2+ Geom. H-I H-II O-I O-II H-I O-I q(Pd) 0.615 0.616 0.697 0.692 0.728 0.780 (-0.038b ) (-0.037) (+0.032) (+0.031) (-0.028) (+0.032) q(W) -0.010 -0.008 0.005 0.005 -0.006 0.003 q(4L) -0.605 -0.608 -0.702 -0.697 1.278 1.217 (+0.048) (+0.045) (-0.037) (-0.036) (+0.034) (-0.035) components of 4L q(L1 )c -0.630 -0.628 -0.667 -0.663 0.319 0.305 (+0.022) (+0.020) (-0.013) (-0.011) (+0.008) (-0.009) q(L2 ) -0.631 -0.628 -0.667 -0.663 0.320 0.303 (+0.008) (+0.008) (-0.013) (-0.011) (+0.010) (-0.010) q(L3 ) 0.342 0.342 0.322 0.329 0.319 0.303 (+0.010) (+0.008) (+0.002) (0.000) (+0.012) (-0.008) q(L4 ) 0.314 0.309 0.309 0.300 0.320 0.305 (+0.008) (+0.009) (-0.015) (-0.014) (+0.004) (-0.008) a Calculated

1c, [Pt(CN)4 ]2− H-I O-I 0.427 0.461 (-0.022) (+0.012) -0.021 0.006 -2.406 -2.467 (+0.043) (-0.018) -0.608 -0.622 (+0.017) (-0.005) -0.588 -0.603 (+0.003) (-0.005) -0.604 -0.622 (+0.015) (+0.005) -0.606 -0.620 (+0.008) (-0.013) 2c, [Pd(CN)4 ]2− H-I O-I 0.353 0.403 (-0.030) (+0.018) -0.007 0.012 -2.346 -2.415 (+0.037) (-0.030) -0.593 -0.611 (+0.015) (-0.008) -0.573 -0.588 (+0.002) (-0.009) -0.591 -0.609 (+0.015) (+0.004) -0.590 -0.608 (+0.005) (-0.017)

at the model geometry with three-regions 3D-RISM-MP2. Unit is in e. b In parentheses are the change in NBO charge induced by W under the consideration of solvation around the super molecule, i.e. complex+W. c (L1 , L2 , L3 , L4 ) represents (Cl, Cl, Am, Gly) in glycine complex, (Am, Am, Am, Am) in tetra-ammine complex, and (Cy, Cy, Cy, Cy) in tetra-cyano complex, where Am, Gly, and Cy represent the NH3 , glycine, and cyanide ligands, respectively.


Page 43 of 53

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 6: Solvation free energy analysis of the complex-water system in aqueous phase.a

Geom. MP2 ∆µrism

1a, PtCl2 (NH3 )(glycine) H-I H-II O-I O-II -13.5 -12.5 -14.7 -16.4

LRA,MP2 ∆µrism -46.0 -44.6 LRA,MP2 components of ∆µrism Pt -1.0 -1.3 W -10.0 -8.8 4L -35.0 -34.5 components of 4L L1b -9.9 -9.5 2 L -8.5 -9.0 L3 -6.0 -6.1 4 -10.6 -9.9 L

Geom. MP2 ∆µrism

Pt complex 1b, [Pt(NH3 )4 ]2+ H-I O-I -177.4 -159.3

-47.1 -48.2

-200.9

-181.6

-209.1

-219.8

-0.9 -1.6 -8.6 -8.5 -38.4 -38.1

-1.4 -4.6 -194.9

6.5 -2.2 -185.9

-68.6 -14.9 -125.6

-73.1 -9.8 -136.9

-33.1 -26.3 -32.9 -33.3

-35.5 -28.7 -38.0 -34.7

-47.2 -45.4 -47.5 -45.0 -50.6 -47.4 -49.6 -48.1 Pd complex 2a, PdCl2 (NH3 )(glycine) 2b, [Pd(NH3 )4 ]2+ H-I H-II O-I O-II H-I O-I -14.0 -12.6 -15.5 -17.3 -175.6 -157.1

LRA,MP2 ∆µrism -46.5 -45.2 LRA,MP2 components of ∆µrism Pd -0.6 -0.6 W -8.6 -7.8 4L -37.3 -36.8 components of 4L L1b -11.0 -10.9 2 L -9.6 -10.0 L3 -6.0 -6.2 4 L -10.7 -9.7

1c, [Pt(CN)4 ]2− H-I O-I -178.2 -188.5

-12.2 -12.7 -12.2 -12.7 -3.4 -2.9 -10.0 -9.8

2c, [Pd(CN)4 ]2− H-I O-I -178.3 -189.6

-47.8 -49.1

-199.5

-179.7

-208.9

-220.3

1.0 0.6 -6.5 -6.8 -42.3 -42.9

-17.3 -6.0 -176.2

-17.4 -1.8 -150.5

-63.3 -12.9 -132.7

-70.1 -6.3 -143.9

-14.2 -14.6 -14.2 -14.6 -3.4 -3.4 -10.5 -10.3

-42.8 -43.0 -45.8 -44.6

-39.0 -39.3 -41.2 -41.0

-34.8 -28.2 -35.1 -34.5

-36.7 -29.3 -41.0 -36.9

a Calculated

at the model geometry with three-regions 3D-RISM-MP2. Unit is in kcal/mol. b (L1 , L2 , L3 , L4 ) represents (Cl, Cl, Am, Gly) in glycine complex, (Am, Am, Am, Am) in tetra-ammine complex, and (Cy, Cy, Cy, Cy) in tetra-cyano complex, where Am, Gly, and Cy represent the NH3 , glycine, and cyanide ligands, respectively.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(a) usual H2O orientation 2 H z H1 Oδ−

Page 44 of 53

(b) unusual H2O orientation H2 O

z

H1 L δ+

L

L

M L

δ+

δ+

L

M L

L

L

Scheme 1: Usual and unusual H2 O interaction with the d8 square planer complex.


Page 45 of 53

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a) trans-M IICl 2 (NH 3 )(glycine) - H 2 O Z-axis

moved

moved

Y-axis

X-axis

H-ahead mode I

H-ahead mode II O-ahead mode I O-ahead mode II

(b) [M II(NH 3 ) 4 ] 2+ - H 2 O

(c) [M II(CN) 4 ] 2- - H 2 O moved

moved

H-ahead mode I O-ahead mode I

H-ahead mode I O-ahead mode I

Scheme 2: Selection of the QM region for the evaluation of free energy curves.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(a)

(b) 2a 2b distance r

M ESP

1a

H

ESP

O H more repulsive: 1a > 2a more attractive: 1a > 2a

more repulsive: 2b > 1b

O 1b M

more attractive: 2b > 1b distance r

r(H-O) more decreases in 2b than in 1b.

r(H-O) more increases in 1a than in 2a.

Scheme 3: Relation between the O-H1 bond length of W and the ESP around ML4 .


Page 46 of 53

Page 47 of 53

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

H probability is small.

(b) H

H2

H1 O

H O

H

δ-

change-(i) H probability increases. H 2 (O probability decreases.)

O

δ+ H

O

1

H L

L

L

L

M L

change-(ii) O probability increases. (H probability decreases.)

M L

H

O

L

δ+: CT

H

L change-(iii) O probability increases. (H probability decreases.)

Scheme 4: Solvation changes near W when changing from the O-ahead to H-ahead hydrations.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(a) trans-PtCl2 NH3 (glycine) - H2 O H 2O 2.29

2.28

2.02

NH3

2.25

2.28

2.02

Cl NH3

H-ahead mode I

(b) [Pt(NH 3 ) 4 ] 2+ - H 2 O

H 2O

H 2O

3.33

H 2O 2.02

H-ahead mode II

NH3

Cl

O-ahead mode II

H 2O 2.32

2.45

2.28

2.02

Cl

Page 48 of 53

NH3 H-ahead mode I

2.02

NH3 O-ahead mode I

Figure 1: Stable structures of the Pt complexes determined by the full geometry optimization with the three-regions 3D-RISM-MP2. Note that both H-ahead and O-ahead hydrations are not found in the tetra-cyano complex, as mentioned in the main text.


(b) 1b, [Pt(NH3 )4 ] 2+ - H 2O

(a) 1a, PtCl2 NH3 (glycine) - H2 O

O-ahead mode

0

-4

3

3.5

4

4.5

5

r(Pt-Ow) [Å]

5.5

6

O-ahead mode

-4

4

4.5

O-ahead mode

-12

3

3.5

4

4.5

5

5.5

6

5

r(Pd-Ow) [Å]

5.5

6

-16

2.5

3

3.5

4

4.5

5

5.5

6

8

H-ahead mode

0 -4

-16 2.5

H-ahead mode

O-ahead mode I mode II

r(Pt-Ow) [Å] (f) 2c, [Pd(CN)4 ]2- - H2 O

4

-8

0

-8

O-ahead mode

H-ahead mode I mode II

H-ahead mode


4 0

-4

O-ahead mode

-8

-12

-12

H-ahead mode 3.5

-8

O-ahead mode


4

-4

8

∆E gas [kcal/mol]

4

3

H-ahead mode

-4

r(Pt-Ow) [Å] (e) 2b, [Pd(NH3 )4 ] 2+ - H 2O

8

-8 2.5

0

-16 2.5

(d) 2a, PdCl2 NH3 (glycine) - H2 O

0

4

-12

H-ahead mode

-8 2.5

8

∆E gas [kcal/mol]

4

(c) 1c, [Pt(CN)4 ] 2- - H2 O

8

∆E gas [kcal/mol]

∆E gas [kcal/mol]

8

∆E gas [kcal/mol]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


∆E gas [kcal/mol]

Page 49 of 53

3

3.5

4

4.5

5

5.5

6

-16

2.5

r(Pd-Ow) [Å]

3

3.5

4

4.5

5

5.5

6

r(PdOw) [Å]

Figure 2: Potential energy curves of ∆Egas calculated with the gas phase Hamiltonian. Note that the geometries are optimized in solution, i.e. identical to those used in Figure 3.



(b) 1b, [Pt(NH3 )4 ] 2+ + W

(a) 1a, PtCl2 NH3 (glycine) + W

O-ahead mode

0

-2

H-ahead mode

-4 -6 2.5

3

3.5

4

4.5

5

5.5

6

0

3

∆A rism [kcal/mol]

H-ahead mode

2 0

O-ahead mode 4

4.5

r(Pd-O) [Å]

5

5.5

4.5

5

5.5

6

4

6

H-ahead mode

0

O-ahead mode 3

3.5

4

4.5

5

2

H-ahead mode


0

-4 2.5

3

3.5

4

4.5

5

5.5

6

8

2

-4 2.5

4

r(Pt-O) [Å] (f) 2c, [Pd(CN)4 ]2- + W

6

-2

-4 3.5

4

8

6

3

3.5

O-ahead mode


6

-2

O-ahead mode

r(Pt-O) [Å] (e) 2b, [Pd(NH3 )4 ] 2+ + W

8

-6 2.5

H-ahead mode

2

-4 2.5

(d) 2a, PdCl2 NH3 (glycine) + W

-2

4

-2

r(Pt-O) [Å]

4

6


2

8


6 4

(c) 1c, [Pt(CN)4 ] 2- + W

8



8


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 50 of 53

4

O-ahead mode

2

6


0

H-ahead mode

-2

5.5


6

-4 2.5

r(Pd-O) [Å]

3

3.5

4

4.5

5

5.5

6

r(Pd-O) [Å]

Figure 3: Free energy curves of ∆Arism calculated with the solvated Hamiltonian in aqueous phase. Note that the geometries are determined by varying only the M-O distance from the model geometries; the model geometries are optimized under the constraints that 4L exists on the xy molecular plane and W exists in the z-axis (see page 17 in main text for details).


Difference in electrostatic potential, V 1a- V 2a

Z-axis (X=0 and Y=0)

4 3 2 1 V2a : Pd 0 -1 V1a : Pt -2 -6 -4 -2

H3N

M

N-gly

Cl

XZ-plane (Y=0)

Z [Å]

Electrostatic potential [V]

(a) 1a - 2a, MCl 2 NH 3 (glycine) Electrostatic potential along Z-axis

0 2 4 6 Z [Å] (b) 1b - 2b, [M(NH 3 ) 4 ] 2+ Electrostatic potential along Z-axis

6 4 2 0 -2 -4 -6 -6 -4 -2

0 2 X [Å]

M

Cl

YZ-plane (X=0)

4

1 0.5 0 -0.5 -1

6 4 2 0 -2 -4 -6

6

-6 -4 -2

0 2 Y [Å]

4

Difference in electrostatic potential, V 1b- V 2b

NC

M

CN

NC

XZ-plane (Y=0)

6

1 0.5 0 -0.5 -1

Z [Å]

Z [Å]

-6 -4 -2

0 2 X [Å]

M

6

CN

YZ-plane (X=0)

6 4 2 0 -2 -4 -6

Z [Å]

Z-axis (X=0 and Y=0) -2 -3 -4 V2c : Pd -5 -6 -7 V1c : Pt -8 -6 -4 -2 0 2 4 Z [Å]

Z [Å]

Electrostatic potential [V]

6

Z-axis (X=0 and Y=0)

10 H3N M N3H H3N M N3H 9 2b XZ-plane (Y=0) YZ-plane (X=0) V : Pd 6 6 8 4 4 7 2 2 0 0 6 -2 -2 1b 5 V : Pt -4 -4 -6 -6 4 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 -6 -4 -2 0 2 4 6 Z [Å] X [Å] Y [Å] (c) 1c - 2c, [M(CN) 4 ] 2Electrostatic potential along Z-axis Difference in electrostatic potential, V 1c- V 2c Electrostatic potential [V]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Z [Å]

Page 51 of 53

4

6 4 2 0 -2 -4 -6

6

1 0.5 0 -0.5 -1 -6 -4 -2

0 2 Y [Å]

4

6

Figure 4: ES potential generated by the complex and its difference between Pt and Pd complex.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(A) 1a, PtCl 2 NH 3 (glycine) + W

(A1) change in solvation structure

∆gO(r) change in orientation O decreases H1 z

O

∆gH(r)

glycine M

NH3

(A2) change in solvation free energy

∆∆µ SDF (r)

H increases

stabilized

H

H1 Cl

Page 52 of 53

Cl

induce

O

O

O

H1

H1

H1

Pt

Pt

Pt

O increases from O- to H-ahead mode

(B) 1b, [Pt(NH 3 ) 4 ] 2+ + W

sum of ∆∆µSDF(r): +0.4 kcal/mol

H decreases

(B2) change in solvation free energy

(B1) change in solvation structure

∆gO(r) change in orientation O decreases hidden ( inside ) H H

∆gH(r)

destabilized

∆∆µ SDF (r)

H increases

destabilized

O

z H1 NH3

NH3

O

O

O

H1

H1

H1

Pt

Pt

M NH3 induce

NH3


(C) 1c, [Pt(CN) 4 ] 2- + W

H decreases

(C1) change in solvation structure

∆gO(r) change in orientation O decreases H1

Pt

sum of ∆∆µSDF(r): -18.9 kcal/mol

∆gH(r)

stabilized

(C2) change in solvation free energy

H increases

∆∆µ SDF (r) stabilized

H O

z H1 CN

CN

O

O

O

H1

H1

H1

Pt

Pt

M CN

CN

induce


H decreases

Pt

sum of ∆∆µSDF(r): +10.3 kcal/mol

destabilized

Figure 5: Differences in the solvation structure and the spatial contribution to the solvation free energy between the O-ahead and H-ahead hydrations. Isovalues of ∆g(r) are 0.15, 0.25, 0.15 in Figures A1, B1, and C1, respectively, and those of ∆∆µSDF (r) are 0.15, 0.70, 0.50 kcal/(mol·Å3 ) in Figures A2, B2, C2, respectively.


Page 53 of 53

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Graphical TOC Entry Which of O-ahead and H-ahead modes is stable ? (a) (b) (c) H

H2 O

O

H2 O

H

M

M

MIICl2(NH3 )(glycine)

H2 O

M

[MII(NH3 )4 ]2+

[MII(CN)4 ]2-


and Pd(II) Complexes - ACS Publications - American Chemical Society

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