Quantum molecular dynamics of hydrogen bonded complexes of rigid molecules using the semiclassical initial value representation in Cartesian coordinates

Semiclassical initial value representation calculations are performed for the constrained water dimer in Cartesian coordinates. The study represents the first application of a previously reported method [Issak and Roy, J. Chem. Phys. 123, 084103 (2005); 126, 024111 (2007)] to a molecular cluster. Bound state energies are calculated for a dimer of rigid water molecules (H2O)2 as well as its deuterated form (D2O)2. The results show that the approach fares well with respect to accuracy in capturing quantum effects in intermolecular interactions.     

Geometric constraints in semiclassical initial value representation calculations in Cartesian coordinates: excited states

The authors show that a recently proposed approach [J. Chem. Phys. 123, 084103 (2005)] for the inclusion of geometric constraints in semiclassical initial value representation calculations can be used to obtain excited states of weakly bound complexes. Sample calculations are performed for free and constrained rare gas clusters. The results show that the proposed approach allows the evaluation of excited states with reasonable accuracy when compared to exact basis set calculations.     

Geometric constraints in semiclassical initial value representation calculations in Cartesian coordinates: accurate reduction in zero-point energy

An approach for the inclusion of geometric constraints in semiclassical initial value representation calculations is introduced. An important aspect of the approach is that Cartesian coordinates are used throughout. We devised an algorithm for the constrained sampling of initial conditions through the use of multivariate Gaussian distribution based on a projected Hessian. We also propose an approach for the constrained evaluation of the so-called Herman-Kluk prefactor in its exact log-derivative form. Sample calculations are performed for free and constrained rare-gas trimers. The results show that the proposed approach provides an accurate evaluation of the reduction in zero-point energy. Exact basis set calculations are used to assess the accuracy of the semiclassical results. Since Cartesian coordinates are used, the approach is general and applicable to a variety of molecular and atomic systems.     

Semiclassical initial value representation study of internal conversion rates

Internal conversion is an inherently quantum mechanical process. To date, "on the fly" computation of internal conversion rates is limited to harmonic approximations, which would seem to be especially unsuitable, given that the typical transition to the ground electronic state occurs at energies which are far from the harmonic limit. It is thus of interest to study the applicability of the semiclassial initial value representation (SCIVR) approach which is in principle amenable to on the fly studies even with "many" degrees of freedom. In this paper we study the applicability of the Herman-Kluk (HK) SCIVR to a model system with two coupled and anharmonic degrees of freedom. We find that (a) the HK SCIVR is a good approximation to the exact quantum dynamics; (b) computation of the first order correction to the HK-SCIVR approximation corroborates the accuracy; (c) by studying a large parameter range, we find that the harmonic approximation is mostly unsatisfactory; and (d) for the specific model used, the coupling between the modes was found to be relatively unimportant. These results imply that the HK-SCIVR methodology is a good candidate for on the fly studies of internal conversion processes of "large" molecules.     

Semiclassical initial value treatment of correlation functions

Two semiclassical, initial value representation (IVR) treatments are presented for the correlation function psi(f) e-iHt/h psi(i), where psi(i) and psi(f), are energy eigenfunctions of a "zero-order" Hamiltonian describing an arbitrary, integrable, vibrational system. These wave functions are treated semiclassically so that quantum calculations and numerical integrations over these states are unnecessary. While one of the new approximations describes the correlation function as an integral over all phase space variables of the system, in a manner similar to most existing IVR treatments, the second approximation describes the correlation function as an integral over only half of the phase space variables (i.e., the angle variables for the initial system). The relationship of these treatments to the conventional Herman-Kluk approximation for correlation functions is discussed. The accuracy and convergence of these treatments are tested by calculations of absorption spectra for model systems having up to 18 degrees of freedom, using Monte Carlo techniques to perform the multidimensional phase space integrations. Both treatments are found to be capable of producing spectra of excited, anharmonic states that agree well with quantum results. Although generally less accurate than full phase space or Herman-Kluk treatments, the half phase space method is found to require far fewer trajectories to achieve convergence. In addition, this number is observed to increase much more slowly with the system size than it does for the former methods, making the half-phase space technique a very promising method for the treatment of large systems.     

High-performance transformation of protein structure representation from internal to Cartesian coordinates

We present a highly parallel algorithm to convert internal coordinates of a polymeric molecule into Cartesian coordinates. Traditionally, converting the structures of polymers (e.g., proteins) from internal to Cartesian coordinates has been performed serially, due to an inherent linear dependency along the polymer chain. We show this dependency can be removed using a tree-based concatenation of coordinate transforms between segments, and then parallelized efficiently on graphics processing units (GPUs). The conversion algorithm is applicable to protein engineering and fitting protein structures to experimental data, and we observe an order of magnitude speedup using parallel processing on a GPU compared to serial execution on a CPU.     

Semiclassical initial value series representation in the continuum limit: application to vibrational relaxation

A recently formulated continuum limit semiclassical initial value series representation (SCIVR) of the quantum dynamics of dissipative systems is applied to the study of vibrational relaxation of model harmonic and anharmonic oscillator systems. As is well known, the classical dynamics of dissipative systems may be described in terms of a generalized Langevin equation. The continuum limit SCIVR uses the Langevin trajectories as input, albeit with a quantum noise rather than a classical noise. Combining this development with the forward-backward form of the prefactor-free propagator leads to a tractable scheme for computing quantum thermal correlation functions. Here we present the first implementation of this continuum limit SCIVR series method to study two model problems of vibrational relaxation. Simulations of the dissipative harmonic oscillator system over a wide range of parameters demonstrate that at most only the first two terms in the SCIVR series are needed for convergence of the correlation function. The methodology is then applied to the vibrational relaxation of a dissipative Morse oscillator. Here, too, the SCIVR series converges rapidly as the first two terms are sufficient to provide the quantum mechanical relaxation with an estimated accuracy on the order of a few percent. The results in this case are compared with computations obtained using the classical Wigner approximation for the relaxation dynamics.     

NMR relaxation study of a hydrogen bonded complex

Spin-lattice relaxation times T₁ were measured over a large frequency region for H and D nuclei in the hydrogen bonded complex of trichloroacetic acid and dimethylsulphoxide. The measured relaxation times T₁ can be ascribed to the motion of the complex as a whole with a negligible contribution from the association—dissociation process.     

Quantum initial value representation simulation of water trimer far infrared absorption spectrum

We extend the technique of quantum propagation on a grid of trajectory guided coupled coherent states to simulate experimental absorption spectra. The approach involves calculating the thermally averaged dipole moment autocorrelation function by means of quantum propagation in imaginary time. The method is tested on simulation of the far infrared spectrum of water trimer based on a three-dimensional model potential. Results are in good agreement with experiment and with other calculations.     

Real time correlation function in a single phase space integral beyond the linearized semiclassical initial value representation

It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSC-IVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the Wigner functions corresponding to the two operators. The difference is that the trajectories involved in the LSC-IVR evolve classically, i.e., according to the classical equations of motion, while in the exact theory they evolve according to generalized equations of motion that are derived here. Approximations to the exact equations of motion are then introduced to achieve practical methods that are applicable to complex (i.e., large) molecular systems. Four such methods are proposed in the paper--the full Wigner dynamics (full WD) and the second order WD based on "Wigner trajectories" [H. W. Lee and M. D. Scully, J. Chem. Phys. 77, 4604 (1982)] and the full Donoso-Martens dynamics (full DMD) and the second order DMD based on "Donoso-Martens trajectories" [A. Donoso and C. C. Martens, Phys. Rev. Lett. 8722, 223202 (2001)]--all of which can be viewed as generalizations of the original LSC-IVR method. Numerical tests of the four versions of this new approach are made for two anharmonic model problems, and for each the momentum autocorrelation function (i.e., operators linear in coordinate or momentum operators) and the force autocorrelation function (nonlinear operators) have been calculated. These four new approximate treatments are indeed seen to be significant improvements to the original LSC-IVR approximation.     

Influence of a polar near-neighbor on incipient proton transfer in a strongly hydrogen bonded complex

Rotational spectroscopy and ab initio calculations have been used to characterize the complexes H(3)N-HF and H(3)N-HF-HF in the gas phase. H(3)N-HF is a C(3v) symmetric, hydrogen bonded system with an NF distance of 2.640(21) A and an N...H hydrogen bond length of 1.693(42) A. The H(3)N-HF-HF complex, on the other hand, forms a six-membered HN-HF-HF ring, in which both the linear hydrogen bond in the H(3)N-HF moiety and the F-H-F angle of (HF)(2) are perturbed relative to those in the corresponding dimers. The N...F and F...F distances in the trimer are 2.4509(74) A and 2.651(11) A, respectively. The N...H hydrogen bond length in H(3)N-HF-HF is 1.488(12) A, a value which is 0.205(54) A shorter than that in H(3)N-HF. Similarly, the F...F distance, 2.651(11) A, is 0.13(2) A shorter than that in (HF)(2). Counterpoise-corrected geometry optimizations are presented, which are in good agreement with the experimental structures for both the dimer and trimer, and further characterize small, but significant, changes in the NH(3) and HF subunits upon complexation. Analysis of internal rotation in the spectrum of H(3)N-HF-HF gives the potential barrier for internal rotation of the NH(3) unit, V(3), to be 118(2) cm(-1). Ab initio calculations reproduce this number to within 10% if the monomer units and the molecular frame are allowed to fully relax as the internal rotation takes place. The binding energies of H(3)N-HF and H(3)N-HF-HF, calculated at the MP2/aug-cc-pVTZ level and corrected for basis set superposition error are 12.3 and 22.0 kcal/mol, respectively. Additional energy calculations have been performed to explore the lowest frequency vibration of H(3)N-HF-HF, a ring-opening motion that increases the NFF angle. The addition of one HF molecule to H(3)N-HF represents the first step of microsolvation of a hydrogen bonded complex and the results of this study demonstrate that a single, polar near-neighbor has a significant influence on the extent of proton transfer across the hydrogen bond. As measured using the proton-transfer parameter rho(PT), previously defined by Kurnig and Scheiner [Int. J. Quantum Chem., Quantum Biol. Symp. 1987, 14, 47], the degree of proton transfer in H(3)N-HF-HF is greater than that in either (CH(3))(3)N-HF or H(3)N-HCl but less than that in (CH(3))(3)N-HCl.     

Using a nondirect product discrete variable representation for angular coordinates to compute vibrational levels of polyatomic molecules

In this paper we test a nondirect product discrete variable representation (DVR) method for solving the bend vibration problem and compare it with well-established direct product DVR and finite basis representation approaches.     

Solvent dependent assembly and disassembly of a hydrogen bonded helical structure in a Co-Mo bimetallic complex

The effect of solvent on the assembly and disassembly of a hydrogen bonded helical structure in a bimetallic cobalt complex of a molybdenum-containing metalloligand and their spontaneous resolution has been demonstrated.     

Onset of hydrogen bonded collective network of water in 1,4-dioxane

We have studied the evolution of water hydrogen bonded collective network dynamics in mixtures of 1,4-dioxane (Dx) as the mole fraction of water (X(w)) increases from 0.005 to 0.54. The inter- and intramolecular vibrations of water have been observed using terahertz time domain spectroscopy (THz-TDS) in the frequency range 0.4-1.4 THz (13-47 cm(-1)) and Fourier transform infrared (FTIR) spectroscopy in the far-infrared (30-650 cm(-1)) and mid-infrared (3000-3700 cm(-1)) regions. These results have been correlated with the reactivity of water in these mixtures as determined by kinetic studies of the solvolysis reaction of benzoyl chloride (BzCl). Our studies show an onset of intermolecular hydrogen bonded water network dynamics beyond X(w) ≥ 0.1. At the same concentration, we observe a rapid increase of the rate constant of solvolysis of BzCl in water-Dx mixtures. Our results establish a correlation between the onset of collective hydrogen bonded network with the solvation dynamics and the activity of clustered water.     

Large amplitude vibration in polyatomic molecules. I. A polar representation of orthogonal relative coordinates

A general expression for the rovib kinetic energy operator in a system of orthogonal internal coordinates is derived for arbitrary amplitudes of motion. Plots of the molecular potential in such coordinates serve to determine coordinate subsets in which the potential approaches separability. A revision of previous theory for the three-body problem is presented. A rovib hamiltonian for non-branched four-atom molecules (such as C₂H₂) is derived. Certain features of application to polyatomic (five-atom) molecules are considered.     

The electronic structure of the 1:1 hydrogen bonded complex of hydroperoxy radical with water in gaseous phase

The electronic structure of the three possible configurations HOO'…H₂O hydrogen bonded systems, with full geometry optimization is studied using the semi-empirical UHF-INDO method. In the models proposed, individual molecules undergo hindered rotation and oscillatory translational motion. The linear model is predicted to be far more stable than the other structures. For this structure the calculated stabilisation energy and geometry follow the same trend as that found in the Hamilton and Naleway calculations [1]. Ionization potentials, net charges and spin redistribution are discussed in the terms of reactivity.     

On the possible catalysis by single water molecules of gas-phase hydrogen abstraction reactions by OH radicals

The gas phase hydrogen abstraction reaction between OH and CY(2)XH, where X = H, F, OH, or NH(2) and Y = H, CH(3) or F, in the absence and presence of a single water molecule is investigated using both density function theory, B3LYP, and explicitly correlated coupled cluster theory, CCSD(T)-F12. We find that a single water molecule could have a catalytic effect at low temperatures possible in laboratory experiments, but does not seem to catalyze these reactions at 298 K, and will not play a role under relevant atmospheric conditions.