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The Important Role of the Hydroxyl Group on the Conformational Adaptability in Bis(L-threoninato)copper(II) Compared to Bis(L-allothreoninato)copper(II): Quantum Chemical Study Marijana Marković,† Michael Ramek,‡ Claudia Loher,‡ and Jasmina Sabolović*,† †

Institute for Medical Research and Occupational Health, Ksaverska cesta 2, P.O. Box 291, HR-10001 Zagreb, Croatia Graz University of Technology, Institute of Physical and Theoretical Chemistry, Stremayrgasse 9, A-8010 Graz, Austria

‡

S Supporting Information *

ABSTRACT: Detailed structural properties of physiological bis(amino acidato)copper(II) complexes are generally unknown in solutions. This paper examines how stereochemical differences between the essential amino acid L-threonine and its diastereomer L-allo-threonine, which is rarely present in nature, may affect relative stabilities of bis(L-threoninato)copper(II) and bis(L-allo-threoninato)copper(II) in the gas phase and aqueous solution. These amino acids can bind to Cu(II) via the nitrogen and carboxylato oxygen atoms, the nitrogen and hydroxyl oxygen atoms, and the carboxylato and hydroxyl oxygen atoms. We term these coordination modes G, No, and Oo, respectively. The density functional theory (DFT) calculations with the B3LYP functional of the conformational landscapes for all possible coordination modes of both complexes revealed their very similar stability in the gas phase and in aqueous solution. The conformational analyses resulted in 196 and 267 conformers of isolated copper(II) chelates with Lthreonine and L-allo-threonine, respectively. The G-G coordination mode is the most stable, both in the gas phase and aqueous solution. Very similar energy values of the lowest-energy solvated cis and trans G-G conformers in implicitly accounted water medium are in accord with the experimental results that these isomers are present in aqueous solution at physiological pH values. The transition-state structures, activation Gibbs free energies, and reaction rates calculated using DFT/B3LYP and MP2 for the transformations from the most stable cis G-G and trans Oo-G conformers to trans G-G ones for the first time reveal several alternate coordination-mode transformation mechanisms in the copper(II) complexes with amino acids other than glycine. The trans Oo-G conformers are kinetically more stable than cis G-G ones in the gas phase. The only significant difference found between the two complexes is a more suitable position of the hydroxyl group in physiological bis(L-threoninato)copper(II) to form intramolecular hydrogen bonds, which may restrain its conformational space.

1. INTRODUCTION Low-molecular-weight bis-copper(II) complexes with histidine, glutamine, threonine, and cystine were found to be the predominant copper amino acid species in human blood plasma.1−4 They are part of an exchangeable plasma copper pool and involved in the copper transport in biological systems.3,4 In nondisease state, they take part in regulating the copper-dependent homeostatic processes. L-threonine (L-Thr) is one of two essential α-amino acids (the other one is L-serine) with a hydroxyl (alcohol) group on the side chain. It is also one of two essential α-amino acids with a chiral side chain (the second one is L-isoleucine). Its diastereomer, L-allo-threonine (L-aThr), is rarely present in nature. In L-Thr, Cα and Cβ have L- and D-chirality, respectively, whereas in L-aThr both C atoms are L-chiral. The binding of a metal ion to a bioligand determines the three-dimensional structure of the biomolecule, which can be related to its biological activity. Knowing the extent of the © XXXX American Chemical Society

effects of amino-acid side-chain interactions on the changes in the metal coordination sphere is a prerequisite to understand the impact of noncovalent interactions on the copper-binding sites in metalloproteins. L-Thr is part of a highly conserved amino acid sequence of metal-binding sites in various prokaryotic and eukaryotic copper transporters such as the yeast copper chaperon Atx1 and the P-type ATPase yeast protein Ccc2 (their human analogues are Atox1 and the Menkes and Wilson disease proteins ATP7A and ATP7B, respectively).5−7 The highly conserved metal-binding amino acid motif in Atox1, as well as in target Cu-domains of ATP7A/B, consists of a MX1CXXC motif, in which X1 is L-Thr. It is supposed that L-Thr promotes directional Cu(I) transfer from Atox1 to transporters ATP7A and ATP7B via a ligand exchange mechanism, where Cu(I) transitorily adopts a three-coordinate Received: May 11, 2016

A

DOI: 10.1021/acs.inorgchem.6b01157 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

copper(II) coordination polyhedron is an elongated octahedron, with its two ligands bound via Nam and O atoms in trans configuration, and two apically coordinated carbonyl oxygen atoms of neighboring molecules.16,17 So far, no experimental crystal structure of Cu(L-aThr)2 has been reported. Despite the experimental studies performed for the copper(II) complexes with L-Thr and L-aThr in solutions, evident structural information has been gained only on the copper(II) coordination mode. The fact that complete structural properties of Cu(L-aThr)2 and the physiological Cu(L-Thr)2 complex in different environments (gas phase, solutions, solid state) were generally unknown motivated us to perform first an in-depth, thorough, systematic gas-phase investigation of isolated Cu(LThr)2 and Cu(L-aThr)2 in the available conformational space by optimizing their molecular geometries using the density functional theory (DFT) method and the B3LYP19−22 functional. After that, we compared the gas-phase energy landscapes with the ones calculated for the lowest-energy conformers in aqueous solution. Knowledge of isolated complex conformers is a prerequisite to examine and rationalize the influence of intermolecular interactions on the overall complex geometry and the coordination modes in the crystal lattice and aqueous solutions. Another motivation was to do a follow-up study of our previous work on physiological bis(Lhistidinato)copper(II), which examined the relative stability of all possible copper(II) coordination modes and conformations of that complex in the gas phase, and several conformers surrounded with 2, 8, 10, 20, and 22 water molecules by DFT/ B3LYP calculations.23 We concluded that the intermolecular interactions and the arrangement of water molecules around the complex might affect different coordination mode formation.23 This paper examines how the stereochemical difference between L-Thr and L-aThr affects the Cu(L-Thr)2 and Cu(L-aThr)2 systems in the gas phase and in aqueous solution, their coordination modes, and the relative stabilities of their possible conformations. Although many different species of the Cu(II)/L-Thr and Cu(II)/L-aThr systems were detected to coexist in aqueous solutions, we focus on the structural properties of the physiological bis(amino acidato)copper(II) (Cu(aa)2) species. Understanding the structural properties of these compounds in different environments may be key to the comprehension why L-Thr but not L-aThr is an abundant building block of biomolecules.

geometry with cysteine ligands from Atox1 and the associated transporter.6,7 In each structure, the motif’s cysteine sulfur atom is hydrogen-bonded (H-bonded) to the side-chain oxygen of LThr on the opposite molecule. Hence, it is supposed that it may be a function of L-Thr to modulate the interactions between the chaperone and P-Type ATPases through H-bonding, which serves to bring the acceptor and donor cysteine sulfur atoms into the vicinity of the metal itself.6,7 Several experimental studies were performed on the copper(II) complexes with L-Thr and L-aThr to get information about their structure, coordination, and stability constants.8−17 Visible absorption and circular dichroism (CD) measurements of interactions between Cu(II) ions and L-Thr and L-aThr showed that at neutral pH in aqueous solution, Cu(II) is bound via the amino nitrogen (Nam) and carboxylate oxygen (O) atoms in bis(L-threoninato)copper(II), Cu(L-Thr)2, and bis(Lallo-threoninato)copper(II), Cu(L-aThr)2, complexes, respectively.8−11 It was found that at concentration of 0.03 M for the amino acids and 0.01 M for copper(II), and for 6 < pH < 8, the bis-complex was nearly a pure species in solution.8 At a pH above 9, the experimental results suggested that the hydroxyl group (Oh−Hh) deprotonates and the Oh atom together with Nam coordinate to Cu(II).8−11 The finding was confirmed by the 14N-superhyperfine structure in the electron paramagnetic resonance (EPR) spectra of copper(II) complexes with L-Thr and L-aThr, studied as a function of pD of the D2O solution and temperature.12 The EPR results suggest that the Nam and O atoms are coordinated to the copper(II), and both cis and trans isomers of Cu(L-Thr)2 and Cu(L-aThr)2 are in equilibrium in the interval 6 < pD < 9. At a pD of 9.4, from the changes in the superhyperfine lines of the EPR spectra, Noethig-Laslo et al. supposed that L-Thr in the copper(II) complex retained the N2O2 coordination but with hydroxyl instead of carboxylate oxygen atoms, while only one coordinated Nam was observed in Cu(L-aThr)2.12 The CD measurements of Cu(L-Thr)2 and Cu(L-aThr)2 in a neutral aqueous solution showed almost the same spectra for both complexes, except for a small difference in their intensities.8−11 These findings suggest that the vicinal effect caused by Cα, located in the five-membered chelate ring, is more effective than that of Cβ in the side chains of the diastereomers.10 Gergely at al. compared the thermodynamic data (which they obtained calorimetrically and using the temperature coefficient method) for the copper(II) complexes with polar amino acids L-Thr and L-serine (which have three possible donor atoms, i.e., Nam, O, and hydroxyl oxygen atom), and aliphatic αaminobutyric acid (which has only Nam and O as possible donor atoms).13 As the heats of formation of the L-Thr and Lserine complexes were greater than that of the chelate with αaminobutyric acid, Gergely at al. assumed there were more Cu−donor bonds in the former complexes; that is, that the nonionized hydroxyl groups formed weak coordinative bonds with copper(II) in the inner coordination sphere.13 The stability constants measured by potentiometry8,9,11,14 showed that Cu(L-Thr)2 was more stable than Cu(L-aThr)2 [e.g., in 0.1 mol L−1 NaNO3 and the 1:2 metal/ligand ratio at the temperature of 298.2 K, log β2 was determined to be 14.538(8) and 14.005(9), respectively].11 It was assumed that the observed stability differences could be explained by conformational energy differences.18 In the experimental X-ray crystal and molecular structure of bis(L-threoninato)copper(II) hydrate [Cu(L-Thr)2·H2O], the

2. THEORETICAL CALCULATIONS 2.1. Quantum Chemical Calculations. The stationary points [i.e., the minimum structures and transition-state (TS) structures] and relative energies of isolated Cu(L-Thr)2 and Cu(L-aThr)2 were calculated using the unrestricted DFT method with the B3LYP19−22 hybrid density functional and the LanL2DZ double-ζ basis set,24 augmented by a set of polarization25 and diffuse functions26 on N, O, and C atoms. The nonrelativistic effective-core potentials (ECPs) of Hay and Wadt (LanL2DZ) were used to describe the shielding effects of electrons in copper inner shells.27−29 This basis set will be named BS0 in the following. The choice of this combination of density functional and basis set was based on previous studies of anhydrous and aqua Cu(aa)2 complexes, in which the DFT/B3LYP results were verified against experimental X-ray crystal and molecular structures.23,30,31 Besides, the energetics calculated by B3LYP/BS0 for the stationary points of bis(glycinato)copper(II) (Cu(Gly)2)31 matched well with the corresponding energy values obtained with G3 calculations at the MP2 level.32 Both Cu(L-Thr)2 and Cu(L-aThr)2 are electrically neutral molecules with a spin multiplicity of 2. To verify whether the optimized B


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Inorganic Chemistry

2.2. Defining the Coordination Modes and Constructing Cu(L-Thr)2 and Cu(L-aThr)2 Initial Conformations. In the equatorial plane of the copper(II) complex, L-Thr or L-aThr can bind to Cu(II) via nitrogen (Nam), carboxylato oxygen (O), and hydroxyl oxygen (Oh) in three ways: (1) via Nam and O (i.e., the glycinato mode), (2) via Nam and Oh, or (3) via O and Oh. In this paper, we term them G, No, and Oo modes, respectively (Scheme 1).

geometries were local minima, frequency calculations were performed to ensure the absence of imaginary frequencies. The TS structures were determined by crafting individual geometry definitions with internal coordinates that left a single geometry parameter as the reaction path coordinate. For the cis−trans isomerization, the nonbonded intersubstituent Nam−Cu−C′−Cα torsion was chosen as the single geometry parameter, since this torsion angle can be included in a Z-matrix geometry definition for the complete range of the cis-to-trans interconversion without risking an accidental linear valence angle. The initial value of this reaction path coordinate was either set to a reasonable value or determined by means of an energy profile of a few points with frozen values of this variable. The remaining bond lengths, valence, and torsion angles were taken from one of the corresponding terminal minimum structures and left to be optimized in the TS searches. These were conducted with Hessian matrix re-evaluations at all intermediate structures. The optimized TS structures were confirmed by frequency analyses to have exactly one negative force constant with a normal mode along the reaction coordinate. The thermal correction to the Gibbs free energy was calculated at a temperature of 298.15 K in the standard way.33 The equilibrium geometries were also computed for selected conformers of Cu(L-Thr)2 and Cu(L-aThr)2 in aqueous medium by using implicit solvent effects (the dielectric constant for water ε = 78.3553), modeled with the integral equation formalism of polarizable continuum model (PCM)34−37 as it is implemented in Gaussian 09 suite of programs (SCRF = PCM),33 details of which are given elsewhere.37 The solute cavity was created via a set of overlapping spheres by using the UFF atomic radii,38 scaled by a factor of 1.1, and the density of surface elements was set to 5/Å2. The representation of the solvent excluded surface by a scaled van der Waals surface based on the UFF atomic radii was chosen as the best compromise between generality and accuracy for the calculation of molecular properties.37 De Bruin et al. tested different basis sets and ECPs for the cis and trans isomers of Cu(Gly)2·2H2O and showed that geometry optimization should be at least performed either with an ECP for Cu(II) in combination with the 6-311+G(d,p) basis set for C, N, O, and H atoms or with the all-electron triple-ζ 6-311+G(d,p) basis set.39 Otherwise, too small basis set could yield spurious minima. In the same study, the impact of incorporation of relativistic effects in the relativistic compact effective potential versus the nonrelativistic LanL2DZ ECPs for Cu(II) was found to be small.39 In a more recent computational study on comparing the performance of 18 density functionals and 14 basis sets to reproduce the copper−donor bond lengths and angles around the metal center in 50 experimental crystal structures of copper(II) and copper(I) complexes,40 even though the authors identified the best performing basis sets and density functionals among the tested ones, the general conclusion was that still there was no universally best behaving functional or basis set for the description of the geometry of copper complexes. In the present study, the use of BS0 for the systematic and exhaustive conformational analyses of the two title complexes was a good compromise between the accuracy and practicality. Moreover, to evaluate the reliability of the B3LYP/BS0 minimum structures and their relative energies, we also tested the performance of a larger allelectron def2-TZVP basis set41,42 (named BS1) for selected B3LYP/ BS0 gas-phase and aqueous minimum structures, and for all studied gas-phase TS structures. Def2-TZVP is a balanced basis set on all atoms at the triple-ζ level including polarization.41,42 To account for the relativistic effects of copper inner-shell electrons, the relativistic ECP MDF1043 for Cu was applied together with def2-TZVP (basis set BS2). MDF10 is a multi-configuration Hartree−Fock adjusted relativistic pseudopotential with perturbative corrections added from Dirac−Hartree−Fock results.43 To compare the performance of DFT/ B3LYP with a wave function method, gas-phase stationary points and their relative electronic and Gibbs free energies were also calculated at the second-order perturbation Møller−Plesset44−46 (MP2) level of theory using BS2 for the activation energy barriers. The Gaussian 09 program package was used for all quantum chemical calculations.33

Scheme 1. Three Possible Chelation Modes of L-Thr and LaThr to Cu(II)

These three modes can be combined in the bidentate or tridentate chelation in Cu(L-Thr)2 and Cu(L-aThr)2 to form six possible coordination modes, namely, G-G, No-G, Oo-G, Oo-Oo, No-Oo, and No-No, with the O and/or Nam atoms in a trans or cis configuration in the equatorial plane. According to the theoretical and stereochemical reasoning given below, we constructed a total of 1498 initial geometries for each complex in the six coordination modes and optimized their geometries. We retained the hydroxyl Hh atom bound to Oh in all constructed conformations. Figures 1 and 2 illustrate the coordination modes with the most stable B3LYP/BS0 conformers of Cu(L-Thr)2 and Cu(L-aThr)2, respectively (described in detail in the Results and Discussion). Constructing G Mode Conformations. From the stereochemical point of view, each chelate ring of the Cu(L-Thr)2 and Cu(L-aThr)2 complexes can have 18 conformations. They are obtained by combining two conformations of the five-membered chelate ring with Cβ in an axial or in equatorial position with nine conformations of the L-Thr and L-aThr residues. The nine conformations are characterized by the Oh−Cβ−Cα−Nam and Hh−Oh−Cβ−Cα angles with approximate values of 60°, −60°, and 180°. The permutation of these 18 chelate-ring conformations in the bis-complex yielded 171 initial structures with trans configuration and 171 initial structures with cis configuration, that is, 342 starting geometries for each complex. The experimental X-ray crystal Cu(L-Thr)2 Cartesian and internal coordinates17 were used as the data to start subsequent construction of the geometries for the 684 initial structures. Constructing No Mode Conformations. Stereochemically, each chelate ring of Cu(L-Thr)2 and Cu(L-aThr)2 can have four conformations in the No coordination mode. Two conformations of the five-membered chelate ring with the COO group in an axial or in equatorial position were combined with two possible positions of Hh oriented above or below the five-membered ring. The permutation of these chelate-ring conformations in the trans and cis No-No coordination modes yielded 10 initial geometries for each configuration. By combining the No and G chelate-ring geometries in the No-G coordination mode, 72 trans and 72 cis initial geometries were obtained. Constructing Oo Mode Conformations. After a series of preliminary geometry optimizations, the six-membered chelate rings in the Oo mode were constructed from eight conformations characterized by the Cu−Oh−Cβ−Cα/Oh−Cβ−Cα−C/Cβ−Cα−C−O torsion angle triplets. The names and characteristic angle values chosen for these eight conformations are as follows: chair 1 (60°/−60° /60°), chair 2 (−60°/60°/−60°), boat 1 (0°/−60°/0°), boat 2 (0°/ 60°/0°), envelope 4up (30°/−70°/10°), envelope 4down (−30°/70°/ −10°), envelope 3up (60°/−60°/10°), and envelope 3down (−60°/ 60°/−10°). The details for these conformation definitions are given in the Supporting Information. We retained the Hh atom bonded to Oh in all of the constructed Oo mode geometries. The eight C


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Inorganic Chemistry

Figure 1. Six coordination modes of trans- and cis-Cu(L-Thr)2 illustrated by the most stable B3LYP/BS0 conformers in the respective modes (see the Supporting Information for conformer name notations). H bonds are presented by broken lines. The electronic energy ranking is as follows: te1te1 < te1-tap < ce1-ce1 < te4dm-te1-A < cap-ca4 < ctw1m-ce1 < ce3um-ctb1m < ctb2p-cap < cap-cap < ce3um-ctb1m < te3um-tep < tep-tep. In some No-G, Oo-No, and No-No minima, Hh moved from Oh to O−CO during geometry optimization. conformations were combined with the Hh atom oriented on both sides of the six-membered chelate ring, while the positions of Nam and CH3 group were defined by preserving the L-chirality of Cα. The permutation of these 16 possible chelate-ring conformations in the Oo-Oo coordination mode yielded 144 initial structures with trans and 144 initial structures with cis configuration, that is, 288 for each complex. By combining the Oo and G chelate-ring conformations in the OoG mode in both trans and cis configurations, 576 initial structures for each complex were obtained. The construction of trans and cis conformations in the Oo-No mode yielded 128 initial structures for each complex. 2.3. Calculation of the Reaction Rate Constants. To evaluate the reaction rate constants k, we applied the equations from standard TS theory: k min1 → min2 =

kBT −ΔGTS → min1/ RT e h

(1a)

k min2 → min1 =

kBT −ΔGTS → min2 / RT e h

(1b)

3. RESULTS AND DISCUSSION 3.1. Conformational Analyses of Cu(L-Thr)2 and Cu(LaThr)2. 3.1.1. Conformational Analyses of Isolated Cu(L-Thr)2 and Cu(L-aThr)2. From the 1498 initial geometries of each complex, the B3LYP/BS0 equilibrium structures of 196 different Cu(L-Thr)2 and 267 different Cu(L-aThr)2 conformers were obtained. This matches well with the quantum chemically computed conformational analyses of isolated neutral L-Thr and 48 49 L-aThr done by Xu and Lin and Szidarovszky et al., which showed that generally L-aThr can form a larger number of stable conformers than L-Thr. Figure S1 presents the illustrations and names of 196 Cu(L-Thr)2 and 267 Cu(LaThr)2 conformers. Table 1 displays the numbers of gas-phase minima in the corresponding coordination modes. The relative electronic energies and characteristic torsion angles of 463 Cu(L-Thr)2 and Cu(L-aThr)2 conformers are listed in Tables S1−S12. As several initial geometries ended in the same minimum structure, the check of Cu(L-Thr)2 electronic energies of such cases showed that they retained relatively steady values with standard deviations up to 0.36 kJ mol−1. For instance, 42 initial structures produced the same te1-te8 minimum whose lowest and highest electronic energy values are −1071.759 889 au and −1071.759 789 au, respectively. The standard deviation of the 42 energy values is 0.02 kJ mol−1. Tables S1−S12 present the lowest electronic energy value for each conformer. Most of the initial geometries were not stable in the gas phase. In the G-G mode conformers, the different stereochemical positions of the hydroxyl and methyl groups caused much more possible conformers of Cu(L-aThr)2 than Cu(L-

where ΔGTS→min1 and ΔGTS→min2 represent the difference between the Gibbs free energy values of the TS structure and two corresponding minimum structures, min1 and min2, h is Planck’s constant, kB is the Boltzmann constant, and R is the gas constant. The temperature T was set to 298.15 K. The possibility of quantum tunneling and its affecting the rate constant was evaluated using a Bell correction, Qtunnel:47

Q tunnel = (hv /2kBT )/sin(hv /2kBT )

(2)

where ν is the imaginary frequency corresponding to the parabolic barrier. The rate constant k multiplied by Qtunnel would give the tunneling-corrected reaction rate constant value. D


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Inorganic Chemistry

Figure 2. Six coordination modes of trans- and cis-Cu(L-aThr)2 illustrated by the most stable B3LYP/BS0 conformers in the respective modes (see the Supporting Information for the conformer name notations). H bonds are presented by broken lines. The electronic energy ranking is as follows: te8-te8 < ta1-tap < ca1-ca1 < te4dm-te8 < cap-ca3-A < ce3um-ca1 < te3dm-te3dm < ctb1p-cem < cep-cep < ctb2m-ce3um-A < te4dp-tap < tep-tep. In the G-No ta1-tap minimum, Hh moved from Oh to O−CO during geometry optimization.

(Figure 5) and hence changed the conformation to te1-ta5; that is, HO13−O13−C13−C12 (Hh−Oh−Cβ−Cα) transformed to 73.4° in the gas-phase minimum. On the contrary, the position of HO13 in the experimental crystal structure, which was determined from the electron density map,17 was such that it formed an H-bond with a carbonyl oxygen atom of an adjacent molecule. Obviously the intermolecular interaction directed its position in the solid phase. We examined if the greater conformational flexibility and a larger number of G-G conformers in Cu(L-aThr)2 compared to Cu(L-Thr)2 (Table 1) can be due to H bonding of the polar hydroxyl group (Table 2). Indeed, bonds Oh−Hh···O and Oh− Hh···Oh were formed in ∼63% of Cu(L-Thr)2 and 43% of Cu(LaThr)2 G-G conformers. Hence, a less pronounced conformational flexibility in Cu(L-Thr)2 compared to Cu(L-aThr)2 is due to the stereochemical difference. In Cu(L-Thr)2, the Oh−Hh group is in a better position to form intramolecular H bonds, which may restrain the molecular conformational space. This observation is supported by a higher number of Oo-G compared to G-G conformers in Cu(L-Thr)2 (Table 1). In the Oo-G conformers, due to the in-plane Cu−Oh bond being formed, the hydroxyl group is unavailable for an Oh−Hh···Oh bonding, and the G-mode chelate ring can have a larger conformational adaptability. Apart from that, the intramolecular H bonds are formed throughout all coordination modes. Besides the two H-bond types numbered in Table 1, there are also Nam−H···Oh and Nam−H···O bonds formed in some of the conformers depicted in Figure S1. The caOoOo11 conformer (Table S10) is especially peculiar because the copper(II)

Table 1. Number of Gas-Phase B3LYP/BS0 Minima in the Corresponding Coordination Modes Cu(L-Thr)2

Cu(L-aThr)2

mode

trans

cis

trans

cis

G-G No-G Oo-G Oo-Oo Oo-No No-No total

35 16 39 13 7 1 111

22 16 23 15 6 3 85

68 15 44 20 7 2 156

45 15 25 18 6 2 111

Thr)2 (Table 1). Namely, of 18 possible chelate-ring G-mode conformations, only six were obtained for Cu(L-Thr)2 (Figure 3), but 12 conformations were stable for Cu(L-aThr)2 (Figure 4). One of the G-G Cu(L-Thr)2 conformations unstable in the gas phase is the te3-ta5 conformer that corresponds to the Cu(L-Thr)2 conformation in the experimental X-ray crystal and molecular structure (Figure 5).16,17 The torsion angles in the experimental conformation are as follows: Cβ−Cα−N−Cu = −160.8°, Oh−Cβ−Cα−N = 46°, Hh−Oh−Cβ−Cα = −137.2° in the equatorial chelate ring, and Cβ−Cα−N−Cu = −97.6°, Oh− Cβ−Cα−N = −55°, Hh−Oh−Cβ−Cα = −60.3° in the axial chelate ring. During a geometry optimization initiated from the Cartesian coordinates of the experimental conformer, the Hh atom in the equatorial chelate ring (HO13 in Figure 5) reoriented to form an H-bond with the carbonyl oxygen O12 E


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Inorganic Chemistry

Figure 3. Six possible chelate-ring conformations in isolated Cu(L-Thr)2 differentiated by the values of denoted torsion angles. In the conformer names, “t” and “c” stand for trans and cis configuration, “a” and “e” denote Cβ in the axial and equatorial positions, and the digits denote the combinations of Oh−Cβ−Cα−N and Hh−Oh−Cβ−Cα characteristic values.

Figure 4. Twelve chelate-ring conformations obtained for isolated Cu(L-aThr)2 differentiated by the values of denoted torsion angles. The definition of conformer names is given in Figure 3.

G-G conformers were the most stable for both Cu(L-Thr)2 and Cu(L-aThr)2. The most stable trans- and cis-Cu(L-Thr)2 conformers had the same equatorial−equatorial conformation, namely, te1-te1 and ce1-ce1, respectively (Figure 1). In Cu(LaThr)2 the most stable trans and cis conformers were te8-te8 and ca1-ca1, respectively (Figure 2). In three of these conformers, te1-te1, ce1-ce1 (Figure 1), and te8-te8 (Figure 2), two intramolecular Hh−Oh···OC bonds were formed.

coordination polyhedron is a distorted tetrahedron (Cu−O = 2.366 Å), and an Nam−H···O bond is formed. However, as its relative energy is rather high (165.8 kJ mol−1), its true existence in the gas phase seems to be improbable. 3.1.1.1. Relative Energy Distributions among the Coordination Modes. The relative B3LYP/BS0 energy distributions among the conformers of Cu(L-Thr)2 and Cu(L-aThr)2 in the gas phase are given in Figures 6 and 7, respectively. The trans F


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Inorganic Chemistry

reactions revealed that the thermochemical properties of LThr and L-aThr were quite similar in the gas phase.49 The B3LYP/BS0 energy difference between the most stable cis and trans G-G conformers is 43.7−43.8 kJ mol−1 for both complexes. The result that in the gas phase the G-G mode trans conformers are more stable than the cis conformers is in accord with previous DFT/B3LYP23,30−32,39 and molecular mechanics calculations30,31,50,51 for several other Cu(aa)2 complexes. For instance, the B3LYP/BS0 energy difference between the cis and trans minima of Cu(Gly)2 is 56.7 kJ mol−1.31 In seven conformers having at least one No coordination (i.e., in five trans No-G, one cis Oo-No, and one cis No-No conformers), the geometry optimization transferred the Hh atom from Oh to the carboxylate group (the most stable among them are illustrated in Figures 1 and 2). Their energy values are systematically lower than for the conformers with the same coordination mode but intact Oh−Hh bonds (Figures 6 and 7). These lower-energy minima are consistent with the well-known fact that in the gas phase and in matrix isolation amino acids exist in neutral form (with NH2 and COOH groups), whereas in crystals or in water medium at physiological pH they form zwitterions. Although the crystal structure determinations of Cu(L-Thr)2 16,17 and bis-copper(II) complexes with D,Lthreonine52 and L,L- and D,L-serine53−55 did not reveal any metal−hydroxyl interactions, the in-plane Cu−Oh−Hh coordination pattern could be present in crystal structures, for example, a methanol molecule coordinated to the copper(II) in the equatorial plane in [4-bromo-2-(pyridin-2ylmethylaminomethyl)phenolato](methanol)copper(II) perchlorate.56 In aqueous solutions, potentiometric and calorimetric measurements in the pH range of 3−11 of a series of copper(II) complexes with ligands containing alcoholic hydroxyl group (L-serine, D,L-isoserine, 1,3-diaminopropan-2ol, D,L-4-amino-3-hydroxybutyric acid, and L-(+)-threo-2amino-1-phenylpropane-1,3-diol) suggested that in the monomeric complexes the deprotonation of a hydroxyl group of one ligand and its coordination to the copper(II) occurred only above pH ≈ 9, while Oh−Hh of the other ligand was bound in a protonated form to the metal ion.57 It was also presumed that in the initial pH interval of complex formation the two latter ligands coordinated to copper(II) via the amino and hydroxyl groups.57 Without considering these seven minima, the cis No-G and cis Oo-No lowest-energy conformers are more stable than their trans counterparts by 54−55 kJ mol−1 in Cu(L-Thr)2 and by 46.1 kJ mol−1 in Cu(L-aThr)2 (No-G mode only). Otherwise, the trans conformers are more stable than the cis ones in the majority of coordination modes. 3.1.1.2. The Analysis of the Copper(II) Coordination Polyhedra. We analyzed the in-plane Cu−donor bond lengths and six valence angles around the copper atom in the six coordination modes of Cu(L-Thr)2 and Cu(L-aThr)2 (Tables S13 and S14, respectively) to examine the effect of different Cβ chirality in the two complexes on the copper(II) coordination geometry. In the same coordination modes of both complexes, the bond lengths and valence angles around the copper(II) adopt the mean values within their corresponding standard deviation values (Tables 3, S13, and S14). Hence, the copper(II) coordination geometry is obviously not significantly affected by the altered orientation of the hydroxyl and methyl groups in the diastereomers but by the coordination mode. The finding is in accord with the experimental observation based on similar CD spectra of solvated Cu(L-Thr)2 and Cu(L-aThr)2 in

Figure 5. Superposition of the Cu(L-Thr)2 molecular structures from the experimental crystal structure of Cu(L-Thr)2·H2O17 (pink), B3LYP/BS0 vacuum equilibrium structure (green), and B3LYP/BS0 optimized structure in aqueous medium using PCM (blue).

Table 2. Number of H-Bonds (< 2.5 Å) Formed in 36 Cu(LThr)2 and 49 Cu(L-aThr)2 G-G Conformers H bond

Cu(L-Thr)2

Cu(L-aThr)2

Oh−Hh···O Oh−Hh···Oh

40 7

57 3

Figure 6. Relative gas-phase B3LYP/BS0 electronic energy values, ΔVvacuum, for 111 trans-Cu(L-Thr)2 (●) and 85 cis-Cu(L-Thr)2 (○) conformers differentiated by the denoted six coordination modes. The electronic energy of the most stable conformer (tGG1; te1-te1) is the reference value (Vvacuum = −1071.762 571 29 au). The No-G, Oo-No, and No-No minima in which Hh transferred from Oh to O−CO via geometry optimization are denoted by a star.

There was no H bond in the most stable cis-Cu(L-aThr)2, ca1ca1. Instead, the latter minimum formed two apical bonds between Cu(II) and Oh with distances of 2.557 and 2.564 Å (Figure 2). Such a geometry with an apical hydroxyl group corresponds to the structure proposed by Gergely et al. on the basis of thermochemical measurements in aqueous solution.13 The numbers of conformers with the apical Cu−donor bonds in all coordination modes (Table 3) show that the Cu···Oh weak apical coordination is quite abundant in both Cu(L-Thr)2 and Cu(L-aThr)2 G-G conformers. The energy of the most stable Cu(L-aThr)2 te8-te8 conformer is by 7.4 kJ mol−1 greater than the one for the Cu(L-Thr)2 te1-te1 conformer. Likewise, the computational conformational analyses of neutral isolated L-Thr and L-aThr by Xu et al.48 and Szidarovszky et al.49 showed that the relative electronic energy of the most stable L-aThr to L-Thr conformers was not higher than 3.1 kJ mol−1. Additionally, the calculation of the enthalpy and free energy changes for the protonation, deprotonation, and secondary deprotonation G


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Inorganic Chemistry

Figure 7. Relative gas-phase B3LYP/BS0 electronic energy values, ΔVvacuum, of 156 trans- (●) and 111 cis-Cu(L-aThr)2 (○) conformers (the reference energy value is given in Figure 6) differentiated by the six coordination modes. The No-G minima in which Hh transferred from Oh to O− CO via geometry optimization are denoted by a star.

Table 3. Means and Standard Deviations (in parentheses) of the B3LYP/BS0 Cu−Donor Apical Bond Lengths ( 9; Cu(L-Thr)2 had the N2O2 coordination (i.e., the No-G mode), while only one Nam atom was observed coordinated in Cu(L-aThr)2, presumably in the trans configuration (i.e., the Oo-G mode).12 3.1.3. Comparison of the B3YLP/BS0 and B3LYP/BS1 Lowest-Energy Conformers in the Gas Phase and Aqueous Solution. The B3LYP/BS0 lowest-energy gas-phase conformers for each coordination mode (Table S15) were taken as the starting structures for B3LYP/BS1 geometry optimizations in the gas phase and using PCM to account for the effects of aqueous surroundings on the conformer geometry and relative energy. The B3LYP/BS1 relative electronic and Gibbs free energies are given in Table S16, while Figure 9 illustrates the relationship between the relative electronic energies calculated with smaller BS0 and larger BS1 basis sets. The BS1 gas-phase geometry optimizations of the selected BS0 conformers yielded the same conformers as the B3LYP/ BS0 geometry optimizations, except in one case. The exception

offered an explanation for this outcome, that is, trans isomers have lower intramolecular energy than cis isomers, but more favorable intermolecular interactions are formed by cis than trans isomers, which may make them equally stable in aqueous solution.31,50,51 The relative energies of cis and trans conformers in other coordination modes also leveled more or less within 10 kJ mol−1 (Figure 8, Table S15). Moreover, the energy differences between the lowest-energy G-G and other coordination mode conformers are smaller in aqueous medium than in the gas phase (Table S15). The relative energies of conformers in which Hh is bound to the carboxylate group are practically equal (or lower by a few kJ mol−1) in the gas phase and aqueous solution (Table S15). Furthermore, their energy values are similar to those of solvated conformers with Oh−Hh bonding in the same coordination mode (Figure 8, Table S15). In several cases, a change from either Oo and/or No mode to the G-mode occurred during the PCM geometry optimization (Table S15). From the energy distribution landscapes in Figure 8, we can see that the relative energies of No-G and Oo-G conformers group together around 50 kJ mol−1, whereas those of No-Oo, No-No, and Oo-Oo conformers group around 110 kJ mol−1. Conversely to the gas phase, the trans Oo-G coordination becomes less stable than the trans No-G one in aqueous solution, especially for Cu(L-Thr)2, while both lowestJ


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Inorganic Chemistry

S2), between the most stable te1-te1 and ce1-ce1 conformers were assessed as a one-step reaction because of the same chelate-ring conformations in the minima. Like for Cu(Gly)2,32 the cis−trans isomerization happened via a ring-twisting mechanism, in which two chelate rings twisted with respect to each other without breaking bonds between copper(II) and its four donor atoms. Similar to the TS structure obtained for Cu(Gly)2,32 a longer Cu−N distance is formed in TStrans↔cis,1 and TStrans↔cis,2 (2.258 and 2.265 Å, respectively, in Figure S2), while other copper−donor bond lengths remain more or less unchanged. In Cu(L-aThr)2, the cis−trans isomerization was studied between the te8-te8 and ca1-ca1 conformers with different chelate-ring conformations. Two alternate cis−trans isomerization reactions seemed worthwhile candidates. Their potential energy profiles are illustrated in Figure 10. The first reaction

is the Cu(L-aThr)2 Oo-No ctb1p-cem conformer, which transformed to the No-G tem-ta1 conformer in the gas phase (Table S16, Figure 9). All of the PCM calculations resulted in the same conformers by BS0 (Table S15) and by BS1 (Table S16). The differences between the BS0 and BS1 relative energies of the same examined conformers range from 9.8 to −13.2 kJ mol−1 in ΔVvacuum [their mean absolute deviation (MAD) amounts to 4.6 and 4.1 kJ mol−1 for Cu(L-Thr)2 and Cu(L-aThr)2, respectively], from 5.1 to −12.7 kJ mol−1 in ΔVwater (MAD is 4.4 and 5.4 kJ mol−1 for Cu(L-Thr)2 and Cu(L-aThr)2, respectively), and from 4.5 to −12.8 kJ mol−1 in ΔGwater. The largest relative energy differences belong to the highest-energy No-No conformers (Figure 9); their ΔVvacuum and ΔVwater values are systematically lower for ∼12 kJ mol−1 by BS0 than by BS1. Despite that, as may be seen in Figure 9, the relationship of the differences between ΔVvacuum and ΔVwater values estimated by BS0 and BS1 is such that they are much smaller than the relative energies of lowest-energy conformers of each coordination mode estimated by either BS0 or BS1 (Tables S15 and S16). Such relationship supports the consistency of the B3LYP/BS0 findings. 3.2. Potential Energy Profiles and Reaction Rate Constants for the Coordination Mode Transformations in the Gas Phase. In the gas phase, for both complexes the B3LYP/BS0 lowest-energy cis G-G conformers (Tables S1 and S7) have energy values close to the lowest-energy trans Oo-G conformers (Tables S3 and S9). Note that these conformers have rather high B3LYP/BS0 energies relative to their corresponding lowest-energy trans G-G conformers: 43.8 and 49.4 kJ mol−1 (ce1-ce1 and te4dm-te1-A, respectively) in Cu(LThr)2, 43.7 and 48.2 kJ mol−1 (ca1-ca1 and te4dm-te8, respectively) in Cu(L-aThr)2. Their corresponding B3LYP/ BS1 relative electronic energies are 41.0 and 46.9 kJ mol−1 (ce1-ce1 and te4dm-te1-A, respectively), 49.1 and 46.3 kJ mol−1 (ca1-ca1 and te4dm-te8, respectively). Thus, a transformation to the trans G-G conformers would be energetically favorable in the gas phase. These results raised the following question: which of the coordination modes, either cis G-G or trans Oo-G, could be kinetically more stable? To answer the question and assess the thermodynamic and kinetic stability of the coordination modes in the gas phase, that is, without the impact of intermolecular interactions, we calculated the TS structures for the interconversions between the most stable trans and cis G-G conformers, and the most stable trans Oo-G and trans G-G conformers in the gas phase by using the B3LYP/BS0 basis set. To examine the method/basis set effect on the energy barrier values, the B3LYP/BS0 minima and TS structures were the starting geometries for subsequent B3LYP/BS1, B3LYP/BS2, and MP2/BS2 stationary point calculations to get their electronic and Gibbs free energies (Table 4). Because the MP2 calculations are rather time-consuming for the studied complexes, we limited them to selected minima and TS structures (Table 4) to obtain the energy barriers for the cis− trans G-G isomerization and the trans Oo-G to trans G-G coordination-mode transformation. In the B3LYP/BS1, B3LYP/BS2, and MP2/BS2 stationary points, the torsion angles and reaction coordinates in the minimum and TS conformations, respectively, did not substantially change from the starting B3LYP/BS0 ones; their values are within the ranges of specific values for a particular conformer and a TS structure. 3.2.1. cis−trans Isomerization in the G-G Mode. In Cu(LThr)2, two TS structures, TStrans↔cis,1 and TStrans↔cis,2 (Figure

Figure 10. DFT/B3LYP gas-phase potential energy profiles for two alternate G-G mode cis−trans isomerization reactions between the Cu(L-aThr)2 conformers te8-te8 and ca1-ca1 calculated with the basis sets denoted as follows: (+) BS0; (○) BS1; (*) BS2. The BS0 minimum structures are defined in Table S7 and Figure S1, and TS structures are illustrated in Figure S3.

includes stepwise transformations of the chelate-ring conformations between te8-te8 and te1-te1, isomerization between te1-te1 and ce1-ce1, and three-step interconversions between ce1-ce1 and ca1-ca1. The second reaction consists of subsequent interconversions in the chelate-ring conformations between te1-te1 and ta1-ta1 and isomerization between the ta1ta1 and ca1-ca1 conformers having the same axial−axial, a1-a1, chelate-ring conformation. For the first reaction, two TS structures, TS″trans↔cis and TS″trans↔cis,a, were obtained analogously to the ones found for Cu(L-Thr)2 (Figures S3 and 10; Figure 10 specifies the lowerenergy TS″trans↔cis). The longer Cu−N bond distances are 2.257 and 2.269 Å in TS″trans↔cis and TS″trans↔cis,a, respectively (Figure S3). In the second reaction, interestingly, along the cis−trans isomerization reaction a five-coordinate TS structure was created due to the forming and breaking of a Cu−Oh bond. Two five-coordinate TS geometries, TS′trans↔cis and TS′trans↔cis,a, were obtained (Figures S3 and 10; Figure 10 indicates the lower-energy TS′trans↔cis). Although these structures accompany K


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Inorganic Chemistry the formation of Cu−Oh bond, the second isomerization mechanism can also be characterized as a ring-twisting one. Here, the G-G mode chelating atoms, Nam and O, stay coordinated to Cu(II). However, not only Cu−Nam but also Cu−O lengthened in the chelate ring undergoing transformation (i.e., Cu−N = 2.255 Å, Cu−O = 2.102 Å, Cu−Oh = 2.084 Å in TS′trans↔cis; Cu−N = 2.200 Å, Cu−O = 2.070 Å, Cu−Oh = 2.180 Å in TS′trans↔cis,a, Figure S3). The formation of intermediate five-coordinate TS′ structures between ta1-ta1 and ca1-ca1 lowered the activation energy for the trans-to-cis transformation in the second reaction compared to the first one by all B3LYP and MP2 computations (Figure 10 and Table 4). Since the PCM calculations gave very similar stability of the trans and cis G-G conformers in aqueous solutions (Figures 8 and 9 and Tables S15 and S16), whether the same cis−trans interconversion mechanisms would be actual also in solution, and how the intermolecular interactions would affect the energy barriers remains to be examined in a forthcoming study. For example, compared to the gas-phase results, the PCM calculations of Cu(Gly)2 stationary points in aqueous solution revealed a slightly lower energy difference between the trans isomer and the TS structure but a considerably larger energy difference between the cis isomer and the TS structure.31 3.2.2. trans Oo-G to trans G-G Coordination Mode Transformations. The O−C′−Cα−N angle of the chelate ring undergoing coordination mode transformation was the reaction coordinate. In Cu(L-Thr)2, the transformation between trans G-G and Oo-G conformers was a two-step reaction; first te1-te1 transformed to te1-te8 over TS7 (Figure S2), and then te1-te8 transformed to te4dm-te1-A over the TS structure, TSOo↔G,1 (Figure S2). In Cu(L-aThr)2, mode transformation was a one-step reaction between the te8-te8 and te4dm-te8 minima. We found two TS structures, namely, TSOo↔G,2 and TSOo↔G,3 (Figure S3). In all of these three TSOo↔G geometries, the copper(II) is three-coordinate (Figures S2 and S3), as the transformations proceed by the in-plane Cu−Oh bond breaking prior to the chelate-ring reorientation to form the Cu−Nam bond. 3.2.3. Comparison of the DFT/B3LYP and MP2 Gibbs Free Energies. Table 5 lists the mean and MAD values of the differences between relative Gibbs free energies calculated by different method/basis set for the minimum and TS structures given in Table 4. The means of relative B3LYP Gibbs free energies estimated by the three basis sets show that BS0 values are closer on average to the BS1 than BS2 values, while the differences between ΔGBS0 with both ΔGBS1 and ΔGBS2 have very close MAD values. Respective differences between ΔG energy values calculated using BS1 and BS2 show greater standard deviation and MAD (Table 5). Hence, the statistical analysis reveals a greater deviation between the ΔG data calculated with the larger all-electron def2-TZVP basis set (BS1) and def2-TZVP with the relativistic MDF10 ECP for Cu(II) (BS2) than with the smaller BS0 having the nonrelativistic LanL2DZ ECPs for Cu(II). The B3LYP ranking of the relative energies between the examined minimum structures (Table 4) is the same by the three basis sets, which again proves equal appropriateness of BS0 to BS1 and BS2 for the Cu(aa)2 systems. The inspection of the Cu(L-aThr)2 minimum structures calculated with the three basis sets revealed that the apical Cu··· Oh distances were shorter by the basis sets having ECPs than by BS1. For instance, in the Cu(L-aThr)2 ta1-ta1 conformer these distances are 2.922 and 3.078 Å by BS1, 2.632, and 3.082 Å by

Table 5. Mean, Standard Deviation (SD), and Mean Absolute Deviation (MAD) Values (kJ mol−1) of the Differences between the Relative Gibbs Free Energies Calculated for N Minimum and TS Structures, and ΔGTS→min2 and ΔGTS→min2 Energy Barriers using MP2/BS2, and B3LYP with the BS0, BS1, and BS2 Basis Setsa,b N = 28 ΔGBS0−ΔGBS1 ΔGBS0−ΔGBS2 ΔGBS1−ΔGBS2 N = 16 ΔGBS0−ΔGMP2 ΔGBS1−ΔGMP2 ΔGBS2−ΔGMP2 ΔGTS→min (N = 14)b BS0−MP2 BS1−MP2 BS2−MP2

mean (SD)

MAD

1.3 (3.2) 4.6 (2.9) 3.3 (4.2)

2.3 2.4 3.0

5.1 (13.6) 3.7 (16.7) 0.5 (12.7)

9.9 11.6 8.8

0.0 (7.6) 2.1 (9.9) 3.7 (7.3)

6.8 8.3 6.0

a The relative Gibbs free energies, ΔG, are given in Table 4. bThe ΔGTS→min energy barriers include ΔGTS→min1 and ΔGTS→min2 for seven transformation reactions calculated using MP2/BS2 (Table 6); the B3LYP/BS0, B3LYP/BS1, B3LYP/BS2, and MP2/BS2 ΔGTS→min values are abbreviated with BS0, BS1, BS2, and MP2, respectively.

BS2, and 2.801 and 3.039 Å by BS0. They are even more shortened to 2.641 and 2.639 Å by MP2/BS2. It may be that more pronounced interactions between the copper(II) and apically placed Oh lowered the BS2 relative energies of the axial−axial conformers compared to the BS1 ones (Table 4). Although the MAD values for the differences of the B3LYP and MP2 relative Gibbs free energies (Table 5) are rather large because of their considerably different ΔG values for the set of Cu(L-aThr)2 ta1-ta1 and ca1-ca1 minima and their corresponding TS structures (Table 4), interestingly and most importantly, the MP2 and B3LYP energy barriers ΔGTS→min1 and ΔGTS→min2 for the G-G trans−cis isomerization have similar values. Namely, the B3LYP energy barriers differ from the MP2/BS2 values within 7.9, 13.3, and 3.2 kJ mol−1 by BS0, BS1, and BS2, respectively. The differences in the energy barriers are the largest for the TSOo↔G,1 to trans Oo-G one; the B3LYP energy barriers differ from the MP2/BS2 value by 14.3, 19.0, and 16.3 kJ mol−1 by BS0, BS1, and BS2, respectively. Generally, there is a better match between the B3LYP and MP2 energy barriers than between the B3LYP and MP2 Gibbs free energies of the minimum and TS structures (Tables 4 and 5). 3.2.4. Reaction Rates. The differences in the Gibbs free energy values calculated by DFT/B3LYP and MP2 (Table 4) between each TS structure and the corresponding two minima were used to calculate the reaction rate constants defined by eqs (1) (Table 6). The evaluation of the possibility of quantum tunneling via a Bell correction, eq 2, showed no significant tunneling contributions, as all Qtunnel values are very close to 1 (Table S17). Thus, multiplying each Qtunnel (Table S17) with corresponding k rate constants (Table 6) did not significantly affect the rate constant values given in Table 6. This result is concurrent with the reaction rate constants calculated by means of variational TS theory for the gas-phase cis−trans isomerization in Cu(Gly)2, that no significant impact of tunneling was found at temperatures above 200 K.32 At 298.15 K, if an energy difference between a TS and a minimum is lowered by 4.184 kJ mol−l, then a reaction rate L


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Inorganic Chemistry

Table 6. kmin1→min2 and kmin2→min1 Reaction Rate Constants (s−1) for the Interconversions between Denoted Gas-Phase Minima (min1 and min2) and Their Corresponding TS Structures Calculated from Eqs (1)a B3LYP/BS0 min1

a

min2

TS

kmin1→min2

te8-te8 te1-te8 te1-te1 te1-ta1 ta1-ta1 ta1-ta1 ca1-ca1 ce1-ca1 te1-te1 te1-te1 te8-te8 te8-te8

te1-te8 te1-te1 te1-ta1 ta1-ta1 ca1-ca1 ca1-ca1 ce1-ca1 ce1-ce1 ce1-ce1 ce1-ce1 te4dm-te8 te4dm-te8

TS1 TS2 TS3 TS4 TS′trans↔cis TS′trans↔cis,a TS6 TS5 TS″trans↔cis TS″trans↔cis,a TSOo↔G,2 TSOo↔G,3

3.9 × 2.6 × 7.1 × 5.3 × 85.37 6.46 5.3 × 2.9 × 0.30 0.01 5.9 × 2.3 ×

te1-te1 te1-te1 te1-te1 te1-te8

ce1-ce1 ce1-ce1 te1-te8 te4dm-te1-A

TStrans↔cis,1 TStrans↔cis,2 TS7 TSOo↔G,1

0.19 0.01 1.3 × 106 6.1 × 10−9

108 108 1010 1010

1010 1010

10−9 10−9

B3LYP/BS1

kmin2→min1 5.4 × 4.7 × 9.7 × 7.3 × 5.8 × 4.4 × 7.7 × 4.3 × 5.0 × 2.2 × 0.21 0.08

108 108 1011 1011 106 105 1010 1010 106 105

4.8 × 106 1.9 × 105 4.2 × 107 0.02

kmin1→min2 Cu(L-aThr)2 9.0 × 108 7.1 × 108 6.0 × 1010 8.6 × 1010 9.67 3.39 2.0 × 1011 3.5 × 1011 0.60 0.04 1.5 × 10−7 1.6 × 10−8 Cu(L-Thr)2 0.53 0.03 3.5 × 106 4.4 × 10−8

B3LYP/BS2

MP2/BS2

kmin2→min1

kmin1→min2

kmin2→min1

1.5 × 1.5 × 1.4 × 1.9 × 1.0 × 3.6 × 1.5 × 1.5 × 5.8 × 3.9 × 2.88 0.30

7.7 × 7.4 × 1.5 × 7.7 × 5.9 × 78.76 2.8 × 2.8 × 4.68 0.23 2.2 × 9.5 ×

1.4 × 2.3 × 6.2 × 3.8 × 5.2 × 6.9 × 1.4 × 9.4 × 1.4 × 6.9 × 2.09 0.89

109 109 1012 1012 106 105 1011 1011 106 105

6.3 × 106 3.9 × 105 7.7 × 107 0.15

108 108 1011 1010 102 1010 1010

10−7 10−8

2.17 0.11 3.2 × 106 1.0 × 10−8

109 109 1011 1011 106 105 1011 1010 107 105

2.0 × 107 1.0 × 106 2.4 × 107 0.05

kmin1→min2

kmin2→min1

2.1 × 103

1.6 × 106

3.98

4.6 × 107

1.0 × 10−9

0.01

2.45 0.14 2.5 × 105 9.6 × 10−11

5.8 3.3 7.1 7.1

× × × ×

107 106 106 10−5

The Gibbs free energies used for the rate constant calculations are given in Table 4.

Generally, ktrans→cis and kG→Oo for transformations from the examined trans G-G conformers to either cis G-G or trans Oo-G conformers are at least by 1 × 107 s−1 smaller than kcis→trans and kOo→G. These results suggest a distinct kinetical stability of trans G-G conformers and a firm possibility of quick transformation from cis to trans G-G isomers as well as trans Oo-G to trans G-G conformers at room temperature. As expected, the activation energies for conformational changes are much lower than for the coordination mode transformations (Figure 10 and Table 4). The reaction rates (Table 6) suggest that the axial−equatorial conformational changes (the rotation around the N−Cα bond) may occur 1000 times faster than the conformational changes in amino acid side chain. Such side-chain conformational changes were calculated between the e1 and e8 chelate-ring conformations (the rotations around the Cα−Cβ and Cβ−Oh bonds; Figures 3 and 4). Interestingly, the activation barrier between te1-te1 and te1-te8 is higher in Cu(L-Thr)2 than in Cu(L-aThr)2 (over the TS7 and TS1 structures, respectively, Table 4 and Figures S2 and S3), which reflects a more pronounced steric hindrance for the conformational changes in the former complex.

constant is 5.4 times larger according to eqs 1. By keeping that in mind, the corresponding rate constants (Table 6) estimated using the DFT/B3LYP and MP2 ΔG values (Table 4) can differ within 1 order of magnitude. However, independently of the applied method/basis set, the comparison of the rate constants estimated for the same reactions showed a consistent relationship regarding differences in orders of magnitude between kmin1→min2 and kmin2→min1 (Table 6). With this respect, the acquired B3LYP/BS0 energy barriers are equally applicable data for qualitative analyses of the rate constants as those obtained by the larger BS2 basis set and the MP2 method. The reaction rates for the cis−trans isomerization reactions between the equatorial−equatorial conformations are of the same orders of magnitude in Cu(L-Thr)2 and Cu(L-aThr)2 (i.e., 1 × 107 s−1 faster for cis-to-trans than for trans-to-cis, Table 6). However, in the isomerization reaction between the axial−axial cis and trans Cu(L-aThr)2 minima, kcis→trans is of the same order of magnitude as for the equatorial−equatorial conformation (1 × 105 to 1 × 107 s−1, Table 6) but trans → cis transformation may be ca. from 1 × 102 to 1 × 103 times faster than in the equatorial−equatorial reaction. Relatively large kcis→trans values (Table 6) suggest spontaneous transformations from cis to trans G-G conformers in the gas phase at room temperature. However, the trans → cis reaction rate values from 3.4 to 2.1 × 103 s−1 (Table 6) suggest that isomerization, mediated via the Cu−Oh bonding in TS′trans↔cis and TS′trans↔cis,a, might allow also the trans-to-cis isomerization between axial−axial conformers in the gas phase. The Oo-G to G-G transformation with the Cu−Oh bond breaking along the chelate-ring opening requires much higher activation energy than the ring twisting without breaking of coordinative copper(II)−donor bonds (Table 4). Consequently, the cis-to-trans G-G isomerization reaction rates are approximately from 1 × 107 to 1 × 109 s−1 higher than for the trans Oo-G to trans G-G transformations. Hence, the studied lowest-energy trans Oo-G conformers are kinetically more stable than the cis G-G ones.

■

CONCLUSIONS The thorough DFT conformational analyses of all possible coordination modes of Cu(L-Thr)2 and Cu(L-aThr)2 using B3LYP/BS0 showed that the G-G coordination mode is the most stable both in the gas phase and aqueous solution. The result is in accordance with experimental evidence8−13 that only the G-G mode is present for the electrically neutral complexes in aqueous solution at ambient temperature and physiological pH values. In the gas phase, the lowest-energy cis G-G minima have comparable energy values with the lowest-energy trans Oo-G conformers. The calculation of the TS structure for their transitions to the most stable trans G-G conformers (which are ∼50 kJ mol−1 more stable), and evaluation of the reaction rates reveal that the isomerization from cis G-G to trans G-G is faster than the transformation from trans Oo-G to trans G-G. In the M


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Inorganic Chemistry former process, the reaction proceeds via a chelate-ring twisting mechanism without breaking the copper−donor bonds. The latter process, which involves the ring-opening mechanism with the breaking of the Cu−Oh bond, requires much higher activation energy than for the ring twisting. Interestingly, we detected that cis−trans G-G isomerization can also proceed via a TS structure that can be characterized as a five-coordinate cis Oo-G conformation (TS′trans↔cis, Figure 10). This can lower the activation energy for the trans-to-cis G-G transformations. In both cases, the reaction rates estimated by DFT/B3LYP with the BS0, BS1, and BS2 basis sets as well as by MP2/BS2 suggest that transformations to the most stable trans G-G conformers should be a quick process in the gas phase at room temperature. To the best of our knowledge, this is the first time that several alternate isomerization and transformation reactions revealed possible interconversion mechanisms in the copper(II) complexes with amino acids other than glycine. Very similar energy values of the lowest-energy cis and trans G-G conformers of both complexes in aqueous solution are in accord with the experimental EPR results that both trans and cis isomers of Cu(L-Thr)2 and Cu(L-aThr)2 are present in aqueous solution at physiological pH.12 The No-G coordination mode in aqueous solution, with either protonated or deprotonated Oh bound to Cu(II), is calculated as the second most stable coordination mode after the G-G one. This is in good agreement with the experimental EPR12 and CD8−11 finding that the unprotonated Oh is bound to Cu(II) in solution at pH above 9 in the No mode. Nevertheless, relatively large energy differences between the solvated G-G and No-G conformers (∼40 kJ mol−1) and the transformation from the No and Oo modes to the G mode in aqueous solution by the PCM geometry optimization suggest that the G-G mode should be not only thermodynamically but also kinetically the most stable in aqueous solution at physiological conditions. The PCM calculated Gibbs free energy values of the studied most stable solvated Cu(L-Thr)2 and Cu(L-aThr)2 conformers are practically the same. This computational finding cannot explain why a higher stability of Cu(L-Thr)2 than Cu(L-aThr)2 in aqueous solutions was obtained by means of stability constant measurements. A significant difference was observed in the number of G-G conformers in the gas phase between Cu(L-Thr)2 and Cu(LaThr)2. Namely, Cu(L-Thr)2 conformers are keener to form intramolecular H bonds, which consequently restrains conformational flexibility of Cu(L-Thr)2 compared to Cu(L-aThr)2. It might be that this more pronounced tendency of L-Thr than L-aThr for restrained conformational flexibility, as observed in the copper(II) complexes, led to the selection of L-Thr over LaThr for the formation of directional H bonds in the polypeptides and proteins as, for example, in the copper transport proteins and generally for L-Thr to be more abundant in biological systems.

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aThr)2, and the TS structures in Cu(L-Thr)2 and Cu(LaThr)2 calculated via DFT/B3LYP and basis set BS0. Listing of characteristic torsion angles and relative electronic energy values of the 196 conformers of Cu(L-Thr)2 and 267 conformers of Cu(L-aThr)2, means and standard deviations of B3LYP/BS0 Cu− donor in-plane bond lengths and six valence angles around the copper atom in conformers of Cu(L-Thr)2 and Cu(L-aThr)2, the aqueous minima obtained by geometry optimization using PCM of the most stable vacuum trans and cis Cu(L-Thr)2 and Cu(L-aThr)2 conformers in the six coordination modes along with their relative vacuum electronic energies, and relative aqueous electronic and Gibbs free energies, the B3LYP/ BS1 gas-phase and aqueous minima obtained by geometry optimization of lowest-energy B3LYP/BS0 conformers of each coordination mode along with their B3LYP/BS1 relative electronic and Gibbs free energies, the imaginary frequencies of the TS structures calculated by DFT/B3LYP and MP2 and corresponding Qtunnel factors. (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +385 1 4682 526. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.M. is thankful for the financial support of “Scholarship of the Scholarship Foundation of the Republic of Austria for Postdocs” given via Ö AD. This work has been supported by the Croatian Science Foundation under the Project No. IP2014-09-3500. Computational resources were provided by the Graz Univ. of Technology and by the Isabella cluster (isabella.srce.hr) at the Zagreb Univ. Computing Centre.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b01157. Description of the procedure for assignment of chair/ boat/twisted boat/envelope/other twist conformations in the Oo coordination mode. Illustrations of 196 conformers of Cu(L-Thr)2 and 267 conformers of Cu(LN


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