A Mixed Quantum-Classical Molecular Dynamics Study of anti-Tetrol

Article pubs.acs.org/JPCB

A Mixed Quantum-Classical Molecular Dynamics Study of anti-Tetrol and syn-Tetrol Dissolved in Liquid Chloroform: Hydrogen-Bond Structure and Its Signature on the Infrared Absorption Spectrum Kijeong Kwac and Eitan Geva* Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, United States

ABSTRACT: The intramolecular hydrogen-bond structure of stereoselectively synthesized syn-tetrol and anti-tetrol dissolved in deuterated chloroform is investigated via a mixed quantum-classical molecular dynamics simulation. An extensive conformational analysis is performed in order to determine the dominant conformations, the distributions among them, and their sensitivity to the method for assigning partial charges (RESP vs AM1-BCC). The signature of the conformational distribution and method of assigning partial charges on the infrared absorption spectra is analyzed in detail. The relationship between the spectra and the underlying hydrogen-bond structure is elucidated.

I. INTRODUCTION Hydrogen bonds (H-bonds) play an important role in determining the thermodynamical and dynamical properties of a vast number of important chemical and biological systems.1 As a result, H-bond structure and dynamics of water and alcohols, both commonly encountered protic solvents, have received much experimental and theoretical attention.2−38 In a series of recent papers, we have employed a mixed quantum-classical methodology to elucidate the structure and dynamics of H-bonded methanol oligomers that form in methanol/CCl4 mixtures and their signature of the linear and nonlinear infrared (IR) spectra of the hydroxyl stretch.14−16 We have shown that consistency with experimentally measured spectra required employing polarizable force fields and accounting for the damping of the polarizability at short distances. The H-bonding structure and dynamics were analyzed in detail and their signature on the absorption, emission, and pump−probe IR spectra of the hydroxyl stretch elucidated. Five different hydroxyl stretch subpopulations were identified and spectrally assigned in methanol/CCl4 mixtures: monomers (α), H-bond acceptors (β), H-bond donors (γ), simultaneous H-bond donors and acceptors (δ), and simultaneous H-bond donors and double-acceptors (ε). The fundamental transition frequencies of the α and β subpopulations were found to be narrowly distributed and to overlap, thereby giving rise to a © 2013 American Chemical Society

single narrow band whose intensity is significantly diminished by rotational relaxation. The fundamental transition frequency distributions of the γ, δ, and ε subpopulations were found to be broader and to partially overlap, thereby giving rise to a single broad band which is red-shifted relative to the αβ band. The propensity of a methanol molecule to form H-bonds was shown to increase upon photoexcitation of its hydroxyl stretch, thereby leading to a sizable red-shift of the corresponding emission spectrum relative to the absorption spectrum.15 Treating the relaxation from the first excited to the ground state as a non-adiabatic process, and calculating its rate within the framework of Fermi’s golden rule and the harmonicSchofield quantum correction factor, we were also able to predict a lifetime which is of the same order of magnitude as the experimental value.15 Nonlinear mapping relations between the hydroxyl transition frequency and bond length and the electric field along the hydroxyl bond axis were established, which can be used to reduce the computational cost of the mixed quantum-classical treatment to that of a purely classical molecular dynamics simulation.15 Finally, we have shown that the momentum jump accompanying relaxation from the excited state to the ground state leads to breaking of H-bonds involving Received: August 12, 2013 Revised: December 5, 2013 Published: December 9, 2013 16493

dx.doi.org/10.1021/jp4080724 | J. Phys. Chem. B 2013, 117, 16493−16505

The Journal of Physical Chemistry B

Article

hydroxyls, are treated classically. In what follows, we refer to the quantum-mechanical hydroxyl as the system and the classical DOF as the bath. The mixed quantum-classical Hamiltonian of the overall system (system + bath) is given by

the relaxing hydroxyl and elucidated the distinct signature that this non-equilibrium relaxation process has on the pump− probe spectrum of this system.16 Recently, Vöringer and co-workers performed a similarly extensive experimental IR investigation on stereoselectively synthesized 1,3-poly alcohols, which serve as a low-dimensional spectroscopic model system for a hydrogen-bonded network.39,40 Those authors measured the linear and nonlinear IR spectra of the hydroxyl stretch in these linear tetrols (when dissolved in deuterated chloroform). More specifically, the allsyn and all-anti configurations of the tetrols were compared in order to study the effect of different H-bonding patterns on the IR spectra (see Figure 1). Importantly, the H-bonding

Ĥ (q ̂, p ̂ , Q, P) = KB(P) + Kq(p ̂) + V (Q, q)̂

(1)

Here, P = (P1, P2, ..., PN) and Q = (Q1, Q2, ..., QN) are the bath coordinates and momenta, respectively, p̂ and q̂ are the coordinate and momentum operators of the quantummechanical system, respectively, KB(P) is the bath kinetic energy, Kq(p̂) is the system kinetic energy, and V(Q, q̂) is the overall potential energy. For a given bath configuration, the adiabatic energy levels and wave functions of the system can be obtained by solving the adiabatic Schrödinger equation: Hq(q ̂, p ̂ ; Q)Ψj(q; Q) = Ej(Q)Ψj(q; Q)

(2)

Here, Hq(q̂, p̂; Q) is the system’s adiabatic Hamiltonian, which depends parametrically on the bath configuration, Q: Hq(q ̂, p ̂ ; Q) = Kq(p ̂) + V (Q, q)̂

(3)

Within our mixed quantum-classical approach, the bath DOF evolves according to the classical equation of motion with a force that depends on the state of the quantum system. To this end, we numerically solve the system’s adiabatic Schrödinger equation at each time step, to obtain the system’s adiabatic wave functions, {Ψj(q; Q)}, and energy levels, {Ej(Q)}. We represent the adiabatic wave function on a 41-point 1D grid whose range is given by 0.46 Å ≤ q ≤ 1.46 Å. Once we obtain the adiabatic wave functions, {Ψj(q; Q)}, the force on the classical DOF is calculated via

Figure 1. Chemical structure of anti-tetrol (A) and syn-tetrol (B). The hydroxyl numbering convention is defined as shown. The three carbon and one oxygen atoms in the gray area defines the dihedral angle ψ.

F(Q) = −

∫ dqΨ*j (q , Q)∇Q V (Q, q)̂ Ψj(q , Q)

(4)

All the simulations in this paper were carried out using the AMBER 10 program package,41 where the source code has been modified in order to implement the mixed quantumclassical algorithm. B. Force Fields. The vibrational stretch mode of the quantum hydroxyl stretch is described by a Morse potential

structures in tetrols are similar to those of H-bonded methanol oligomers that form in methanol/CCl4 liquid mixtures. At the same time, the fact that the hydroxyls are attached to a carbon backbone and oriented in a well controlled manner relative to one another requires one to address backbone conformations and the role they play in dictating H-bond structure and its spectroscopic signature. In the present paper, we apply our mixed quantum-classical methodology, previously used to investigate H-bond structure and dynamics in methanol/CCl4 liquid mixtures, to elucidate the H-bond structure of all-syn and all-anti tetrols dissolved in deuterated chloroform. The remainder of this paper is organized as follows. Simulation techniques and computational methodology are outlined in section II. Results are presented and discussed in section III. Summary and concluding remarks are provided in section IV.

VOD(q) = D(1 − e−a(q − q0))2

(5)

Here, q0 = 0.96131414 Å, D0 = 105.0 kcal/mol, and a = 2.40635 Å−1. The values of q0 and D0 are from ref 14, and the value of a was determined so as to reproduce the experimental vibrational OH stretch frequency of methanol in the gas phase.42 It should be noted that the value of a used here is slightly different from that used in ref 14, since the latter was determined for deuterated methanol. It should also be noted that we determine the hydroxyl stretch potential parameters from a calculation performed on methanol, rather than on the tetrol molecule, in order to make sure that the parameters are not affected by Hbonding with neighboring hydroxyls. More specifically, since the influence of H-bonding with neighboring hydroxyls is being taken into account within the mixed quantum-classical MD simulations, accounting for them also in the potential parameters would have amounted to double counting. Two methods for determining the partial charges of the antiand syn-tetrol molecules were tested, namely, RESP43 and AM1-BCC.44,45 Starting from the optimal geometries reported by Vöhringer and co-workers,39 we used the Antechamber

II. METHODS A. Mixed Quantum-Classical Molecular Dynamics. The mixed quantum-classical methodology used here is similar to that employed in ref 14 and will therefore only be outlined briefly, with emphasis on new features associated with its application to tetrols. We consider a single anti- or syn-tetrol molecule dissolved in liquid CDCl3. One of the four hydroxyl stretches of the tetrol molecule is treated as quantum-mechanical, while all the remaining degrees of freedom (DOF), including the other three 16494



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Table 1. The RESP and AM1-BCC Partial Charges on the Four Hydroxyls and the Backbone Oxygen for anti-Tetrol and synTetrol (in Units of e) charges for anti-tetrol OH group first OH second OH third OH fourth OH backbone

charges for syn-tetrol

atom

RESP

AM1-BCC

RESP

AM1-BCC

O H O H O H O H O

−0.568557 0.336786 −0.625680 0.386681 −0.560418 0.349068 −0.539940 0.349348 −0.242807

−0.500640 0.342880 −0.509280 0.348400 −0.502400 0.346080 −0.506480 0.346080 −0.346240

−0.535549 0.322442 −0.528679 0.363810 −0.523394 0.357673 −0.557190 0.347418 −0.206852

−0.493600 0.339600 −0.502560 0.342880 −0.500560 0.344080 −0.505440 0.346480 −0.343760

constant γ = 1.0 ps, and the Berendsen algorithm52 for pressure coupling with a pressure relaxation time of 0.2 ps. The resulting dimensions of the cubic simulation boxes (in Å) are 32.1680342, 32.4017020, 32.2514920, and 32.2407640 for anti-tetrol/RESP, syn-tetrol/RESP, anti-tetrol/AM1-BCC, and syn-tetrol/RESP, respectively. After an additional 200 ps constant volume and constant temperature (300 K) equilibration run, initial configurations were collected every 2 ps. For each initial configuration, a classical equilibration run was performed at a constant temperature of 300 K, for 200 ps, assigning the initial velocities from the Maxwell distribution, with a constraint on the dihedral angle (defined by the four atoms marked by the gray area in Figure 1). This was done by imposing a harmonic potential of the form V = k(ψ − ψ0)2. Here, k = 30.0 kcal/mol/rad2 and ψ0 = 60°, −60°, and 180° corresponding to the three local minima in the potential of mean force obtained from the free energy calculation (see below). It was verified that the constraint does not affect the results by comparing results obtained from averaging over segments of unrestrained trajectories where no conformational transitions took place to results obtained from restrained simulations of similar length. The equilibration run with classical force fields was followed by a 35 ps constant temperature equilibration mixed quantumclassical run using the Berendsen weak coupling algorithm.52 50 ps mixed quantum-classical constant volume and constant energy production runs were then carried out at the abovementioned constrained dihedral angles. The time step for all the classical and mixed quantumclassical MD runs was 1.0 fs. The cutoff radius for the nonbonding interaction was set at 10 Å. The long-range electrostatic interactions were calculated on the basis of the particle mesh Ewald method.53,54 Finally, analysis of H-bonding structure and dynamics was based on the following definition of a H bond: (1) O···H distance less than 2.65 Å and (2) O···H−O angle greater than 120° (“···” denotes the hydrogen bond). D. Free Energy Calculation. Preliminary simulations have shown that the H-bonding in this system is sensitive to conformational changes associated with the dihedral angle between the fourth hydroxyl and the backbone oxygen (indicated by the gray area in Figure 1). The probability distributions as a function of dihedral angle were calculated using replica exchange molecular dynamics (REMD),55−57 using 16 replicas at 16 different temperatures (300, 314, 329, 345, 361, 378, 396, 414, 434, 455, 476, 499, 522, 547, 573, and 600 K). Exchange between the adjacent temperatures was attempted every 100 time steps. The success ratio of

program in the AMBER package to obtain the RESP and AM1BCC charges for the anti- and syn-tetrol molecules. The RESP partial charges were determined on the basis of an ab initio calculation of the electrostatic potential at the HF/6-31G* level. The AM1-BCC method is semiempirical and based on AM1 population charges corrected to emulate electrostatic potential at the HF/6-31G* level.44,45 The correction is calculated by the additive bond charge correction (BCC) method of Bayly et al.44 The parameter set describing the BCCs was determined by consensus fitting to the HF/6-31G* electrostatic potentials of a training set of more than 2700 molecules.45 In addition to the partial charges, polarizability was included via the point dipole model as implemented within the AMBER polarizable force fields.46,47 A scale factor of 0.8 has been applied to both RESP and AM1-BCC charges to compensate for the increased electrostatic interaction due to the inclusion of polarizability. Table 1 shows the partial charges on the hydroxyls and the backbone oxygen as obtained via the RESP and AM1-BCC methods. It should be noted that both methods predict that the negative charge on the backbone oxygen is smaller than that on the hydroxyl oxygens. The hydroxyl oxygen partial charges obtained via RESP are seen to be more negative than these obtained via AM1-BCC. In contrast, the negative charge on the backbone oxygen as obtained via RESP is less negative than that obtained via AM1-BCC. As we will show below, these seemingly subtle differences have a significant effect on molecular structure as well as on its spectroscopic signature. In implementing the polarizable force fields, we employed a damping procedure to take into account the effect of reduced dipolar interaction when two atoms are close to each other due to repulsive interaction of overlapping electron clouds.48,49 The detailed expressions used to account for damping were given in ref 14. The values of the parameters used in this work are the same as those used in our previous work on methanol/CCl4.14 The remaining force field parameters, including van der Waals interactions and intramolecular potential function, were obtained from the AMBER ff02pol.r1 and GAFF force fields.50,51 C. Molecular Dynamics Simulations. Simulations were performed with a single anti- or syn-tetrol molecule and 247 chloroform molecules in the simulation box. The size of the simulation box was determined by a 200 ps constant temperature run, during which the system was heated from 0 to 300 K, followed by a 800 ps constant pressure and constant temperature equilibration run at 300 K and 1 atm, using Langevin dynamics for temperature coupling with the coupling 16495



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dihedral angles (60°, −60°, 180°), respectively. Thus, the ONIOM QM/MM calculations for 100 snapshot structures were done for a total of 48 different cases. Finally, error bars in the plots of the free energy and the IR absorption spectra were obtained by dividing the data set into four subsets and calculating the corresponding standard deviations.

temperature exchange was 19%, on average. The value of the dihedral angle was written after every 100 time steps, and immediately before attempting the temperature exchange. It should be noted that the replica exchange simulations were carried out within the framework of purely classical MD. E. IR Absorption Spectrum. Within the mixed quantumclassical treatment, the IR absorption spectrum can be calculated based on the following formula:58 3

4

I(ω) = Re ∑ pψ j=1

j

∑∫ i=1

0

∞

dtJψ(i)(t ) j

III. RESULTS AND DISCUSSION A. Conformational Analysis. The chemical structures of the anti- and syn-tetrol are shown in Figure 1. In the case of syn-tetrol, the four hydroxyls are oriented in a manner favorable for forming H-bonds, whereas in the case of anti-tetrol they are not. In addition, we have found that both molecules can assume three distinctive conformations with respect to the dihedral angle ψ, and that the conformation impacts H-bond structure (see below). The calculated probability densities of the dihedral angle, ψ, as obtained from REMD simulations at 300 K are shown in

exp(iωt ) (6)

Here, i = 1, 2, 3, 4 denotes the four hydroxyls (see Figure 1), {ψ1 = 60°, ψ2 = −60°, ψ3 = 180°} are the three values of the dihedral angle ψ that define stable conformations, {pψ1, pψ2, pψ3} are the probabilities of those conformations, and Jψ(i)(t ) = e−t /2T1⟨μ01(t )μ10 (0) exp[−i j

∫0

t

dτω10(i)(τ )]⟩ψj (7)

where ⟨···⟩ψj =

∫ dQ 0 ∫ dP0

exp[−βH0(Q 0, P0) + Vψj(Q 0)]

···

Z0, ψj

(8)

with μ01(t) being the transition dipole moment, Vψj(Q0) the harmonic restraining potential for the dihedral angle ψ to the value ψj, H0(Q0, P0) = KB(P0) + E0(Q0), and Z0,ψj = ∫ dQ0 ∫ dP0 exp[−βH0(Q0, P0) + Vψj(Q0)] the classical bath Hamiltonian and partition function for a given conformation when the quantum hydroxyl is in its ground vibrational state. (Q0, P0) represents the initial coordinates and momenta of the (i) bath DOF, ω(i) 10 (t) ≡ ω10 (Qt) is the transition frequency, and Qt represents the bath configuration after evolving for a period of time t on the adiabatic ground surface. Finally, T1 is the lifetime of the first-excited state, which we set to T1 = 0.5 ps, corresponding to the lifetime of the hydroxyl in a methanol/ CCl4 mixture.15 The transition dipole moment, μ01(t), is given by μ10 (t ) = μ′⟨Ψ1(Q t)|q|̂ Ψ0(Q t⟩

Figure 2. Representative structures of the three conformations of antiand syn-tetrol.

(9)

where

μ′ =

∂μ ∂q

q = q0

(10) 59

We use QM/MM (based on the ONIOM method as implemented in the Gaussian 09 package60 and including all the molecules in the simulation box) in order to calculate μ′ for 100 randomly chosen configurations taken from equilibrium ground state mixed quantum-classical MD simulations. In these simulations, the QM part corresponds to the tetrol molecule, treated at the DFT/B3LYP/6-31+G(d) level, while the MM part corresponds to the solvent molecules, using nonpolarizable AMBER force fields. We establish a linear map that correlates μ′ with the electric field along the hydroxyl stretch. Since we are interested in calculating ∂μ/∂q for each local hydroxyl stretch, we assumed that the remaining three hydroxyls are deuterated. We implemented this procedure for each of the four hydroxyls in anti- and syn-tetrol, with the RESP and AM1-BCC charge model, and for each of the three

Figure 3. Probability distribution of the dihedral angle for anti- and syn-tetrol molecules with RESP or AM1-BCC charges.

Figure 3. The corresponding populations of the three conformers are listed in Table 2. Interestingly, the populations differ between the anti and syn configurations and depend strongly on whether RESP or AM1-BCC is used for assigning partial charges. As we will show below, the propensity of the 16496



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corresponding to the anti and syn, RESP and AM1-BCC, the three conformations and the four hydroxyls. However, in practice, we found that the effective number of maps can be reduced to eight. More specifically, for a given choice between anti and syn and RESP and AM1-BCC, the maps for hydroxyls 1, 2, and 3 coincided, whereas hydroxyl 4 required a separate map at some conformations. More specifically: • For the anti-tetrol within RESP, the fourth hydroxyl in the ψ = −60° conformation required a separate map. • For the anti-tetrol within AM1-BCC, the fourth hydroxyl in the ψ = 60°, −60° conformations required a separate map. • For the syn-tetrol within RESP or AM1-BCC, the fourth hydroxyl in the ψ = 60° conformation required a separate map. As we will show below, conformations which require a different map for hydroxyl 4 correspond to the formation of a stronger H-bond with the backbone oxygen atom. C. H-Bond Structure. The H-bonding patterns can be rather sensitive to the molecular structure (anti vs syn), conformation (ψ = 60°, −60°, 180°), and partial charge assignments (RESP vs AM1-BCC). The analysis of these patterns is facilitated by introducing the symbol A → B to denote H-bond between hydroxyls A (as donor) and B (as acceptor), and the symbol A| |B to denote the case where hydroxyls A and B are not H-bonded. Tables 4−7 show the

Table 2. The Subpopulations of the Different Conformers for anti-Tetrol and syn-Tetrol with RESP and AM1-BCC Partial Charges anti-tetrol

syn-tetrol

ψ

RESP

AM1-BCC

RESP

AM1-BCC

60 −60 180

0.29 ± 0.04 0.30 ± 0.03 0.40 ± 0.05

0.13 ± 0.05 0.80 ± 0.06 0.07 ± 0.02

0.81 ± 0.02 0.15 ± 0.01 0.04 ± 0.02

0.96 ± 0.01 0.03 ± 0.01 0.01 ± 0.01

fourth hydroxyl to form a H-bond with the backbone oxygen (as a donor) and with the third hydroxyl (as an acceptor) are seen to be particularly sensitive to the conformation as well as to the method of assigning partial charges.

Table 4. H-Bond Pattens for anti-Tetrol with RESP Chargesa

Figure 4. Linear maps for dipole derivatives as a function of the electric field on the OH bond of the tetrol molecules with RESP and AM1-BCC charge model. “H4” stands for the fourth hydroxyl, and the number that follows is the dihedral angle ψ.

Table 3. Fitting Parameters for the Dipole Derivative Maps Shown in Figure 4 in the Form of μ′ = a + bx, Where x Is the Electric Field along the OH Bond in Units of e/a02 and μ′ Is in Units of Debye Å−1 amu−1/2 a a OH4, −60° others OH4, 60° others OH4, 60° and −60° others OH4, 60° others

anti(RESP) 4.238495 4.755816 syn(RESP) 2.849346 4.238778 anti(AM1-BCC) 1.635278 2.500315 syn(AM1-BCC) −1.187148 2.358437

a

anti/RESP

ψ = 60°

1 → 2 → 3 → 4| |O 1 ← 2 ← 3 ← 4| |O 1 ← 2 ← 3| |4| |O 1| |2 ← 3 ← 4| |O 1 ← 2| |3 → 4 → O 1 ← 2| |3 ← 4| |O 1 ← 2| |3 → 4| |O

4.0 8.8

4.8 47.9 13.3

ψ = −60°

ψ = 180° 5.9 30.2 11.1 5.8

88.4 33.8

The largest population for each conformation is shown in boldface.

various possible H-bond patterns observed in our simulations, as well as the corresponding subpopulations. It should be noted that H-bonding patterns with subpopulations below 4.0% have been assumed small enough to be left out of these tables.

b 1259.991761 491.818245

Table 5. H-Bond Patterns for anti-Tetrol with AM1-BCC Chargesa

1112.679737 595.102465

anti/AM1-BCC 1 1 1 1 1 1 1 1 1 1 1 1

887.621448 589.829220 982.654359 643.547686

a

OH4 denotes the fourth hydroxyl, and the number following it is the value of the dihedral angle ψ that indicates the conformation.

B. Non-Condon Effects. Figure 4 shows the linear maps that correlate μ′ and the electric field along the hydroxyl stretch. The corresponding fitting parameters are shown in Table 3. In principle, 48 different linear maps are needed,

a

16497

→ → ← → ← → ← → ← ← ← ←

2→3→4→O 2 → 3 → 4| |O 2 ← 3 ← 4| |O 2 → 3| |4 → O 2 ← 3| |4 → O 2| |3 → 4 → O 2| |3 → 4 → O 2 → 3| |4| |O 2 ← 3| |4| |O 2| |3 ← 4| |O 2| |3| |4 → O 2| |3| |4| |O

ψ = 60°

ψ = −60°

16.6 11.7 12.8

49.5

4.6 5.6 4.3 12.6

ψ = 180°

36.7 6.8 9.1 6.0 17.1 28.9 12.3 5.3

6.2

12.0

The largest population for each conformation is shown in boldface. dx.doi.org/10.1021/jp4080724 | J. Phys. Chem. B 2013, 117, 16493−16505


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Table 6. H-Bond Patterns for syn-Tetrol with RESP Chargesa

a

syn/RESP

ψ = 60°

ψ = −60°

1→2→3→4→O 1 → 2 → 3 → 4| |O 1 ← 2 ← 3 ← 4| |O 1| |2 → 3 → 4 → O 1| |2 → 3 → 4| |O

83.0

11.8 70.3

ψ = 180° 66.1 18.2

15.4 13.5

12.5


Table 7. H-Bond Patterns for syn-Tetrol with AM1-BCC Chargesa

a

syn/AM1-BCC

ψ = 60°

ψ = −60°

1→2→3→4→O 1 → 2 → 3 → 4| |O 1 ← 2 ← 3 ← 4| |O

98.8

16.0 79.2

ψ = 180° 88.2 10.3


D. Infrared Absorption Spectra. Figures 5−8 show the IR spectra for anti- and syn-tetrol with RESP and AM1-BCC charges, as calculated for each hydroxyl and at each conformation (left), as well as the corresponding conformational averages (right). In analyzing these spectra, it is useful to

Figure 6. Same as Figure 5 but for anti-tetrol with AM1-BCC charges.

classify the hydroxyls according to their participation in Hbonds: • not H-bonded (α) • H-bond acceptor (β) • H-bond donor (γ) • simultaneous H-bond donor and acceptor (δ) As in methanol/CCl4 mixtures, the transition frequency distributions of the α and β subpopulations are found to be narrow and to overlap, thereby giving rise to a single narrow band. The transition frequency distributions of the γ and δ subpopulations are found to be broader and to partially overlap, thereby giving rise to a single broad band which is red-shifted relative to the αβ band. 1. anti-Tetrol with RESP Charges. The spectra of the first hydroxyl is characterized by a prominent narrow feature at 3645 cm−1, originating from the majority β 2 →1 subpopulation where this hydroxyl plays the role of H-bond acceptor. The smaller and broader red-shifted feature originates from the smaller γ 1 → 2 subpopulation. The different relative intensities of these two features at different conformations reflect the conformational sensitivity of the H-bonding patterns. The spectra of the second hydroxyl consist of one prominent feature centered at 3430 cm−1, which is rather insensitive to the conformation. This feature can be traced back to the majority 2 → 1 subpopulation where this hydroxyl plays the role of Hbond donor. Whether or not the second hydroxyl can be classified as γ or δ, that is, play the role of donor or

Figure 5. IR spectra for anti-tetrol with RESP charges, as calculated for each hydroxyl and at each conformation (left), as well as the conformationally averaged spectra (right). 16498



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Figure 7. Same as Figure 5 but for syn-tetrol with RESP charges.

Figure 8. Same as Figure 5 but for syn-tetrol with AM1-BCC charges.

simultaneous roles as H-bond donor and acceptor, has a relatively minor effect on the spectra. Unlike the second hydroxyl, the spectra of the third hydroxyl are very sensitive to the conformation. For ψ = 60°, the spectrum consists of contributions from β, γ, and δ subpopulations. For ψ = −60°, the spectrum is dominated by the γ subpopulation. For ψ = 180°, the spectrum consists of a large δ feature and a smaller β feature. The spectra of the fourth hydroxyl are even more sensitive to the conformation. For ψ = 60 and 180°, this hydroxyl plays the role of H-bond donor in forming a H-bond with the third hydroxyl. However, for ψ = −60°, the fourth hydroxyl plays the role of H-bond donor in forming a H-bond with the backbone oxygen. The fact that the negative RESP partial charge on the backbone oxygen is much smaller compared to the other oxygens, and therefore blue-shifts and narrows the spectrum at ψ = −60°. The larger H-bond donor subpopulation at ψ = 180° also red-shifts and broadens the spectrum for ψ = 180° in comparison to ψ = 60°. Finally, the higher intensity of the spectrum at ψ = −60° can be traced back to the stronger nonCondon effects for the fourth hydroxyl at the ψ = −60° conformation (see Figure 4). Since there is no one dominant conformation in the case of anti-tetrol with RESP charges, the averaged spectra represent a mixture of the corresponding three conformation-specific spectra (see right column of Figure 5). 2. anti-Tetrol with AM1-BCC Charges. The spectra of the first hydroxyl are seen to be the most sensitive to the choice of

the method of assigning partial charges (RESP vs AM1-BCC). More specifically, with AM1-BCC charges: • The ψ = 180° conformation is dominated by β 2 → 1 Hbonding, thereby giving rise to a prominent narrow high frequency band. • The ψ = −60° conformation is dominated by the γδ 1 → 2 H-bonding, thereby giving rise to a prominent broad low frequency band. • The ψ = 60° conformation exhibits a mixture of β 2 → 1 and γδ 1 → 2 H-bonding, with similar weights, thereby giving rise to both features. This should be contrasted to the anti-tetrol with RESP charges, which is dominated by the β 2 → 1 band, and where the relative size of the γδ 1 → 2 band is actually largest for the ψ = 180° conformation and smallest for the ψ = −60° conformation. The spectra of the second hydroxyl reflect the opposite trend to those of the first hydroxyl. The lack of a high frequency narrow band can be attributed to the fact that the second hydroxyl serves as a H-bond donor to hydroxyl 3 when it plays the role of H-bond acceptor to hydroxyl 1, which corresponds to a minimal β subpopulation. The spectra of the third hydroxyl are dominated by the low frequency broad γδ band, which reflects the fact that this hydroxyl often plays the role of H-bond donor to either the second or third hydroxyl. The majority δ 2 → 3 → 4 subpopulation for the ψ = −60° conformation makes the spectrum in this case broader and more red-shifted in 16499



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Figure 9. The calculated spectra of anti-tetrol with RESP charges for each of the three conformations and a comparison of the corresponding conformational average to the experimental absorption spectrum.

Figure 10. Same as Figure 9 but for anti-tetrol with AM1-BCC charges.

comparison to the ψ = 60° and ψ = 180° conformations, where the γ and β subpopulations are more prominent. The spectra of the fourth hydroxyl are very sensitive to conformation. The ψ = −60° conformation is dominated by Hbonding to backbone oxygen. Interestingly, the corresponding band red shifts and broadens when the partial charges are changed from RESP to AM1-BCC, which can be attributed to

the significantly more negative AM1-BCC charge of the backbone oxygen. Finally, averaged spectra in this case are seen to be dominated by the ψ = −60° conformation. This should be contrasted with the case of the RESP charges where the relative populations of the three conformations are comparable, so that 16500



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Figure 11. Same as Figure 9 but for syn-tetrol with RESP charges.

Figure 12. Same as Figure 9 but for syn-tetrol with AM1-BCC charges.

this case are oriented favorably for forming H-bonds. As a result, the 1 → 2 → 3 → 4 → O H-bonding pattern is dominant in both cases. The main difference between RESP and AM1-BCC can be traced back to the significantly more negative AM1-BCC backbone oxygen, which leads to a broader and more red-shifted band of the fourth hydroxyl, and less negative AM1-BCC first hydroxyl oxygen, which leads to a lower subpopulation where this hydroxyl is an H-bond

the averaged spectra represent a mixture of the corresponding three conformation-specific spectra. 3. syn-Tetrol with RESP and AM1-BCC Charges. The spectra for syn-tetrol are considerably simpler and less structured than those of anti-tetrol. The differences between the RESP and AM1-BCC charges are also smaller in this case, and the dominant conformation is ψ = 60° in both cases. These observations can be traced back to the fact that the hydroxyls in 16501



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RESP charges reproduced the small peak at ∼3620 cm−1, the broad peak acquired a bimodal structure which is inconsistent with experiment. This discrepancy can be traced back to the smaller charge on the fourth hydroxyl (compared to the other hydroxyls), which leads to a smaller H-bond-induced red-shift. The fact that this less-red-shifted peak is further enhanced by non-Condon effects in the ψ = −60° conformation then gave rise to an unphysical peak at ∼3520 cm−1. The unphysical peak at ∼3510 cm−1 in the case of syn-tetrol with the RESP charges can be explained in the same manner. In contrast, using the AM1-BCC charges, the prominent low frequency broad peak can be reproduced rather well in both syn-tetrol and anti-tetrol. However, the smaller high frequency peak at ∼3620 cm−1 is not well reproduced with AM1-BCC charges. This suggests that the AM1-BCC charges overestimate the extent of H-bonding. In summary, the aforementioned comparison with experiment suggests that using AM1-BCC charges better captures the spectral signature of H-bonding. This is manifested by the significantly better agreement with experiment in the case of syn-tetrol, which is the more H-bonded species. Since selfconsistency requires that the same method for assigning partial charges is used for syn-tetrol and anti-tetrol, AM1-BCC charges therefore appear to be more consistent with experiment, overall.

acceptor. As expected, the averaged spectra in both cases are dominated by the ψ = 60° conformation. 4. Comparison to Experiment. Figure 9 shows the calculated spectra of anti-tetrol with RESP charges for each of the three conformations, and a comparison of the corresponding conformational average to the experimental absorption spectrum.39 It should be noted that all three conformations contribute significantly to the conformational average in this case. The main discrepancy between the calculated and experimental spectrum corresponds to the peak at 3525 cm−1, which appears in the calculated spectrum, but not in the experimental one. This peak can be traced back to the large 3 → 4 → O δ peak in the ψ = −60° conformation (see Figure 5). The red-shift of this peak is smaller than other δ peaks because of the smaller negative RESP charge of the backbone oxygen. At the same time, the intensity of this peak is amplified by the enhanced non-Condon effect for the fourth hydroxyl. Figure 10 shows the calculated spectra of anti-tetrol with AM1-BCC charges for each of the three conformations and a comparison of the corresponding conformational average to the experimental absorption spectrum. Unlike the RESP case, the ψ = −60° conformation is dominant in this case (80%). The main discrepancy between the calculated and experimental spectrum corresponds to the αβ peak, which is smaller in the calculated spectrum compared to the experimental one. This can be traced back to an overall enhancement of H-bonding compared to RESP. Figure 11 shows the calculated spectra of syn-tetrol with RESP charges for each of the three conformations and a comparison of the corresponding conformational average to the experimental absorption spectrum. The fact that the ψ = 60° conformation carries 81% of the population implies that it dominates the spectrum in this case. The major discrepancy between the experimental and calculated spectra has to do with the fact that, while the former is dominated by the low frequency broad peak, the latter is bimodal. While the width of the calculated low frequency peak is very similar to the width of the dominant experimental peak, the peak position is redshifted by about 50 cm−1 in comparison to experiment. The calculated high frequency peak centered at 3510 cm−1, which originates from the strong δ peak of the fourth hydroxyl (see Figure 7), appears to have no experimental counterpart. Figure 12 shows the calculated spectra of syn-tetrol with AM1-BCC charges for each of the three conformations and a comparison of the corresponding conformational average to the experimental absorption spectrum. Here too, the ψ = 60° is dominant (96%). However, unlike the RESP case, the agreement with experiment is excellent. More specifically, the calculated spectrum corresponds to a single broad feature that agrees with the corresponding experimental feature both in terms of peak position and width. The difference between the RESP and AM1-BCC spectra can be traced back to the contribution from the fourth hydroxyl, which is broader and more red-shifted when AM1-BCC charges are used. The discrepancies between the experimental and calculated spectra and between the calculated spectra with different partial charges demonstrate the high sensitivity of H-bonding and its resulting spectral signature to the model parameters. More specifically, the experimental spectra for anti-tetrol consist of a prominent broad peak at 3470 cm−1 and a smaller narrow peak at 3620 cm−1. However, the calculated results have failed to reproduce both of the peaks. For anti-tetrol, while using the

IV. CONCLUDING REMARKS Mixed quantum-classical simulations can provide a powerful tool for modeling H-bond structure in liquid solution and interpreting its signature on IR spectra. In a series of previous papers, we have demonstrated this in the case of intermolecular H-bonding in methanol/CCl4 mixtures. In the present paper, we have extended the methodology to the case of intramolecular H-bond structure of poly alcohols dissolved in an aprotic solvent. The mixed quantum-classical methodology employed here treats one hydroxyl at a time quantum-mechanically, while the rest are treated classically, as opposed to treating all hydroxyls quantum-mechanically as a vibrational excitonic system.39 However, it should be noted that line broadening due to interactions with the other hydroxyls is accounted for within the framework of our mixed quantum-classical treatment, and that this broadening is larger than the gaps between the excitonic energy levels.39 Furthermore, the ability of this localmode approach to capture the experimental IR absorption spectrum of syn-tetrol, where all four hydroxyls are H-bonded to each other, suggests that the line shapes are dominated by classical thermal solvent fluctuations, rather than by the intrinsic width of the excitonic band. The fact that the discrepancies between the experimental and calculated spectra are more significant in the less H-bonded anti-tetrol also suggest that these discrepancies are likely due to inaccuracies in the force fields rather than the inadequacy of the local mode approach. However, we cannot rule out the possibility that some of the discrepancies between the calculated and experimental spectra result from limitations of the local-mode approach employed here. Indeed, accounting for coupling between local modes has been recently observed to give rise to a significant spectral signature on the vibrational absorption spectrum of liquid water.61 Extending such studies to alcohols within the mixed quantum classical formulation of optical response employed here would clearly be highly desirable. The main conclusions of the present study can be summarized as follows: 16502



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• Extensive conformational analysis of syn- and anti-tetrol was performed in order to determine the dominant conformations, the distribution among them, and its sensitivity to the method for assigning partial charges (RESP vs AM1-BCC). In addition, a detailed analysis on H-bond structure in anti- and syn-tetrol molecule was performed. Three different conformations were identified, which differ with respect to the dihedral angle ψ between the fourth hydroxyl and the backbone oxygen. The H-bond structure was shown to be strongly conformation-dependent, and the relative population of the different conformations was shown to be highly sensitive to the choice of method of assigning partial charges. • The signature of the method of assigning partial charges and conformational distribution on the IR absorption spectra was analyzed in detail. The important role of non-Condon effects was elucidated, and the spectral signature of H-bonding was mapped in detail and explained in terms of the underlying H-bonding structure. It should be noted that, although the hydroxyl stretches are treated as local, the interaction between them is accounted for within our quantum-classical scheme. In this context, it should be noted that the local mode representation is easier to implement in practice in light of the fact that the relative orientations between the hydroxyl stretches and the degree of H-bonding between them continuously change with time. • One of our goals was to compare the ability of two well established methods for assigning partial charges (RESP and AM1-BCC) to reproduce the IR absorption spectra of the hydroxyl stretch in the system under study. It is possible that using the partial charges as fitting parameters may have led to better agreement with experiment. However, the calculated spectra for syntetrol obtained with the AM1-BCC charges are in good quantitative agreement with experiment. They are also clearly in better agreement with experiment than those obtained with RESP charges. Since syn-tetrol is the more H-bonded species, this suggests that AM1-BCC charges represent a better choice than RESP charges for capturing the spectral signature of H-bonding. It should be noted however that both AM1-BCC and RESP charges seem unable to fully capture the spectra of antitetrol. We attribute this to the more complex and fragile nature of H-bonding in this species, which results in a spectral signature which is more sensitive to the model parameters. However, we feel that the agreement is fair, especially when one takes into account the fact that no adjustable parameters were used. We also believe that self-consistency requires that the same method for assigning partial charges is used for syn-tetrol and antitetrol. This suggests that the AM1-BCC charges represent a better choice for modeling the IR spectra of the hydroxyl stretches in this system. Finally, it should be noted that, while the absorption IR spectrum of the hydroxyl stretch is highly sensitive to Hbonding structure when the hydroxyl is in the ground vibrational state, it contains no information on H-bonding in excited vibrational states and is also relatively insensitive to Hbond dynamics. However, one of the main advantages of our mixed quantum-classical methodology is that it can be extended

to excited states in a straightforward manner. Work on extending the study presented herein to excited states and thereby elucidating the non-equilibrium H-bond dynamics probed via time-resolved nonlinear IR spectroscopy is currently underway and will be reported in a future publication.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 734-763-8012. Fax: 734647-4865. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This project was supported by the National Science Foundation through grant CHE-1111495. The authors would like to thank Professor Peter Vöhringer for helpful conversations.

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REFERENCES

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A Mixed Quantum-Classical Molecular Dynamics Study of anti-Tetrol

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