Car-Parrinello and path integral molecular dynamics study of the hydrogen bond in the chloroacetic acid dimer system

We have studied the double proton transfer (DPT) reaction in the cyclic dimer of chloroacetic acid using both classical and path integral Car-Parrinello molecular dynamics. We also attempt to quantify the errors in the potential energy surface that arise from the use of a pure density functional. In the classical dynamics a clear reaction mechanism can be identified, where asynchronized DPT arises due to coupling between the O-H stretching oscillator and several low energy intermolecular vibrational modes. This mechanism is considerably altered when quantum tunneling is permitted in the simulation. The introduction of path integrals leads to considerable changes in the thermally averaged molecular geometry, leading to shorter and more centered hydrogen bond linkages.     

A quantum equation of motion for chemical reaction systems on an adiabatic double-well potential surface in solution based on the framework of mixed quantum-classical molecular dynamics

We present a quantum equation of motion for chemical reaction systems on an adiabatic double-well potential surface in solution in the framework of mixed quantum-classical molecular dynamics, where the reactant and product states are explicitly defined by dividing the double-well potential into the reactant and product wells. The equation can describe quantum reaction processes such as tunneling and thermal excitation and relaxation assisted by the solvent. Fluctuations of the zero-point energy level, the height of the barrier, and the curvature of the well are all included in the equation. Here, the equation was combined with the surface hopping technique in order to describe the motion of the classical solvent. Applying the present method to model systems, we show two numerical examples in order to demonstrate the potential power of the present method. The first example is a proton transfer by tunneling where the high-energy product state was stabilized very rapidly by solvation. The second example shows a thermal activation mechanism, i.e., the initial vibrational excitation in the reactant well followed by the reacting transition above the barrier and the final vibrational relaxation in the product well.     

Theoretical studies of the N2O van der Waals dimer: ab initio potential energy surface, intermolecular vibrations and rotational transition frequencies

Theoretical studies of the potential energy surface and bound states were performed for the N(2)O dimer. A four-dimensional intermolecular potential energy surface (PES) was constructed at the CCSD(T) level with aug-cc-pVTZ basis set supplemented with bond functions. Three co-planar local minima were found on this surface. They correspond to a nonpolar isomer with slipped-antiparallel planar structure and two equivalent polar isomers with slipped-parallel planar structures. The nonpolar isomer is energetically more stable than the polar ones by 162 cm(-1). To assign the fundamental vibrational frequencies for both isomers, more than 150 vibrational bound states were calculated based on this PES. The orientation of the nodal surface of the wave functions plays an important role in the assignment of disrotation and conrotation vibrational modes. The calculated vibrational frequencies are in good agreement with the available experimental data. We have also found a quantum tunneling effect between the two equivalent polar structures in the higher vibrational excited states. Rotational transition frequencies of the polar structure were also calculated. The accuracy of the PES is validated by the good agreement between theoretical and experimental results for the transition frequencies and spectroscopic parameters.     

Blueshift and intramolecular tunneling of NH3 umbrella mode in 4He n clusters

We present diffusion Monte Carlo calculations of the ground and first excited vibrational states of NH(3) (4)He(n) for n< or =40. We use the potential energy surface developed by one of us [M. P. Hodges and R. J. Wheatley, J. Chem. Phys. 114, 8836 (2001)], which includes the umbrella mode coordinate of NH(3). Using quantum Monte Carlo calculations of excited states, we show that this potential is able to reproduce qualitatively the experimentally observed effects of the helium environment, namely, a blueshift of the umbrella mode frequency and a reduction of the tunneling splittings in ground and first excited vibrational states of the molecule. These basic features are found to result regardless of whether dynamical approximations or exact calculations are employed.     

New ab initio potential energy surface and the vibration-rotation-tunneling levels of (H2O)2 and (D2O)2

We report a new full-dimensional potential energy surface (PES) for the water dimer, based on fitting energies at roughly 30,000 configurations obtained with the coupled-cluster single and double, and perturbative treatment of triple excitations method using an augmented, correlation consistent, polarized triple zeta basis set. A global dipole moment surface based on Moller-Plesset perturbation theory results at these configurations is also reported. The PES is used in rigorous quantum calculations of intermolecular vibrational frequencies, tunneling splittings, and rotational constants for (H2O)2 and (D2O)2, using the rigid monomer approximation. Agreement with experiment is excellent and is at the highest level reported to date. The validity of this approximation is examined by comparing tunneling barriers within that model with those from fully relaxed calculations.     

Quantum algorithm for obtaining the energy spectrum of molecular systems

Simulating a quantum system is more efficient on a quantum computer than on a classical computer. The time required for solving the Schr?dinger equation to obtain molecular energies has been demonstrated to scale polynomially with system size on a quantum computer, in contrast to the well-known result of exponential scaling on a classical computer. In this paper, we present a quantum algorithm to obtain the energy spectrum of molecular systems based on the multiconfigurational self-consistent field (MCSCF) wave function. By using a MCSCF wave function as the initial guess, the excited states are accessible. Entire potential energy surfaces of molecules can be studied more efficiently than if the simpler Hartree-Fock guess was employed. We show that a small increase of the MCSCF space can dramatically increase the success probability of the quantum algorithm, even in regions of the potential energy surface that are far from the equilibrium geometry. For the treatment of larger systems, a multi-reference configuration interaction approach is suggested. We demonstrate that such an algorithm can be used to obtain the energy spectrum of the water molecule.     

Nuclear quantum effects on an enzyme-catalyzed reaction with reaction path potential: proton transfer in triosephosphate isomerase

Nuclear quantum mechanical effects have been examined for the proton transfer reaction catalyzed by triosephosphate isomerase, with the normal mode centroid path integral molecular dynamics based on the potential energy surface from the recently developed reaction path potential method. In the simulation, the primary and secondary hydrogens and the C and O atoms involving bond forming and bond breaking were treated quantum mechanically, while all other atoms were dealt classical mechanically. The quantum mechanical activation free energy and the primary kinetic isotope effects were examined. Because of the quantum mechanical effects in the proton transfer, the activation free energy was reduced by 2.3 kcal/mol in comparison with the classical one, which accelerates the rate of proton transfer by a factor of 47.5. The primary kinetic isotope effects of kH/kD and kH/kT were estimated to be 4.65 and 9.97, respectively, which are in agreement with the experimental value of 4+/-0.3 and 9. The corresponding Swain-Schadd exponent was predicted to be 3.01, less than the semiclassical limit value of 3.34, indicating that the quantum mechanical effects mainly arise from quantum vibrational motion rather than tunneling. The reaction path potential, in conjunction with the normal mode centroid molecular dynamics, is shown to be an efficient computational tool for investigating the quantum effects on enzymatic reactions involving proton transfer.     

Does ℏ play a role in multidimensional spectroscopy? Reduced hierarchy equations of motion approach to molecular vibrations

To investigate the role of quantum effects in vibrational spectroscopies, we have carried out numerically exact calculations of linear and nonlinear response functions for an anharmonic potential system nonlinearly coupled to a harmonic oscillator bath. Although one cannot carry out the quantum calculations of the response functions with full molecular dynamics (MD) simulations for a realistic system which consists of many molecules, it is possible to grasp the essence of the quantum effects on the vibrational spectra by employing a model Hamiltonian that describes an intra- or intermolecular vibrational motion in a condensed phase. The present model fully includes vibrational relaxation, while the stochastic model often used to simulate infrared spectra does not. We have employed the reduced quantum hierarchy equations of motion approach in the Wigner space representation to deal with nonperturbative, non-Markovian, and nonsecular system-bath interactions. Taking the classical limit of the hierarchy equations of motion, we have obtained the classical equations of motion that describe the classical dynamics under the same physical conditions as in the quantum case. By comparing the classical and quantum mechanically calculated linear and multidimensional spectra, we found that the profiles of spectra for a fast modulation case were similar, but different for a slow modulation case. In both the classical and quantum cases, we identified the resonant oscillation peak in the spectra, but the quantum peak shifted to the red compared with the classical one if the potential is anharmonic. The prominent quantum effect is the 1-2 transition peak, which appears only in the quantum mechanically calculated spectra as a result of anharmonicity in the potential or nonlinearity of the system-bath coupling. While the contribution of the 1-2 transition is negligible in the fast modulation case, it becomes important in the slow modulation case as long as the amplitude of the frequency fluctuation is small. Thus, we observed a distinct difference between the classical and quantum mechanically calculated multidimensional spectra in the slow modulation case where spectral diffusion plays a role. This fact indicates that one may not reproduce the experimentally obtained multidimensional spectrum for high-frequency vibrational modes based on classical molecular dynamics simulations if the modulation that arises from surrounding molecules is weak and slow. A practical way to overcome the difference between the classical and quantum simulations was discussed.     

Quantum dynamics of hydride transfer catalyzed by bimetallic electrophilic catalysis: synchronous motion of Mg(2+) and H(-) in xylose isomerase

Xylose isomerase exhibits a bridged-bimetallic active-site motif in which the substrate is bound to two metals connected by a glutamate bridge, and X-ray crystallographic studies suggest that metal movement is involved in the hydride transfer rate-controlling catalytic step. Here we report classical/quantal dynamical simulations of this step that provide new insight into the metal motion. The potential energy surface is calculated by treating xylose with semiempirical molecular orbital theory augmented by a simple valence bond potential and the rest of the system by molecular mechanics. The rate constant for the hydride-transfer step was calculated by ensemble-averaged dynamical simulations including both variational transition-state theory for determination of the statistically averaged dynamical bottleneck and optimized multidimensional tunneling calculations. The dynamics calculations include 25 317 atoms, with quantized vibrational free energy in 89 active-site degrees of freedom, and with 32 atoms moving through static secondary zone transition-state configurations in the quantum tunneling simulation. Our simulations show that the average Mg-Mg distance R increases monotonically as a function of the hydride-transfer progress variable z. The range of the average R along the reaction path is consistent with the X-ray structure, thus providing a dynamical demonstration of the postulated role of Mg in catalysis. We also predicted the primary deuterium kinetic isotope effect (KIE) for the chemical step. We calculated a KIE of 3.8 for xylose at 298 K, which is consistent with somewhat smaller experimentally observed KIEs for glucose substrate at higher temperatures. More than half of our KIE is due to tunneling; neglecting quantum effects on the reaction coordinate reduces the calculated KIE to 1.8.     

Concerted hydrogen exchange tunneling in formic acid dimer

The effect of conformational relaxation on the quantum dynamics of the hydrogen exchange tunneling is studied in the D2h subspace of formic acid dimer. The fully coupled quantum dynamics in up to six dimensions are derived for potential energy hypersurfaces interpolated directly from hybrid density functional calculations with and without geometry relaxation. For a calculated electronic barrier height of 35.0 kJ/mol the vibrational ground state shows a tunneling splitting of 0.0013 cm(-1). The results support the vibrational assignment of Madeja and Havenith [J. Chem. Phys. 2002, 117, 7162-7168]. Fully coupled ro-vibrational calculations demonstrate the compatibility of experimentally observed inertia defects with in-plane hydrogen exchange tunneling dynamics in formic acid dimer.     

A surface hopping method for chemical reaction dynamics in solution described by diabatic representation: an analysis of tunneling and thermal activation

We present a surface hopping method for chemical reaction in solution based on diabatic representation, where quantum mechanical time evolution of the vibrational state of the reacting nuclei as well as the reaction-related electronic state of the system are traced simultaneously together with the classical motion of the solvent. The method is effective in describing the system where decoherence between reactant and product states is rapid. The diabatic representation can also give a clear picture for the reaction mechanism, e.g., thermal activation mechanism and a tunneling one. An idea of molecular orbital theory has been applied to evaluate the solvent contribution to the electronic coupling which determines the rate of reactive transition between the reactant and product potential surfaces. We applied the method to a model system which can describe complex chemical reaction of the real system. Two numerical examples are presented in order to demonstrate the applicability of the present method, where the first example traces a chemical reaction proceeded by thermal activation mechanism and the second examines tunneling mechanism mimicking a proton transfer reaction.     

A new ab initio potential energy surface for studying vibrational relaxation in NO(v) + NO collisions

A new ab initio potential energy surface for the ground state of the NO-NO system has been calculated within a reduced dimensionality model. We find an unusually large vibrational dependence of the interaction potential which explains previous spectroscopic observations. The potential can be used to model vibrational energy transfer, and here we perform quantum scattering calculations of the vibrational relaxation of NO(v). We show that the vibrational relaxation for v = 1 is 4 orders of magnitude larger than that for the related O(2)(v) + O(2) system without having to invoke nonadiabatic mechanisms as had been suggested in the past. For highly vibrationally excited states, we predict a strong dependence of the rates on the vibrational quantum number as has been observed experimentally, although there remain important quantitative differences. The importance of a chemically bound isomer on the relaxation mechanism is analyzed, and we conclude it does not play a role for the values of v considered in the experiment. Finally, the intriguing negative temperature dependence of the vibrational relaxation rate constants observed in experiments was studied using an statistical model to include the presence of many asymptotically degenerate spin-orbit states.     

Six-dimensional quantum dynamics of H2 dissociative adsorption on the Pt(211) stepped surface

Results of experimental studies, and theoretical calculations utilizing classical trajectories, have shown that dissociation of H2 on the Pt(211) stepped surface is enhanced at low energies by a molecular trapping mechanism. Because quantum effects can play a large role at the low energies and long lifetimes that characterize molecular trapping, we have undertaken quantum dynamics calculations for this system, the first to treat all molecular degrees of freedom of a gas molecule reacting on a stepped metallic surface. The calculations show that molecular trapping persists in the quantum system, but only at much lower energies than experimentally seen, pointing to possible deficiencies in the potential energy surface. Classical and quasiclassical trajectory calculations on the same potential provide a reasonable picture of reaction overall, but many of the finer details are inaccurate, and certain classical reaction mechanisms are entirely invalid. We conclude that some skepticism should be shown toward any classical study for which long-lived trapping states play a role.     

Quantum wavepacket ab initio molecular dynamics: generalizations using an extended Lagrangian treatment of diabatic states coupled through multireference electronic structure

We present a generalization to our previously developed quantum wavepacket ab initio molecular dynamics (QWAIMD) method by using multiple diabatic electronic reduced single particle density matrices, propagated within an extended Lagrangian paradigm. The Slater determinantal wavefunctions associated with the density matrices utilized may be orthogonal or nonorthogonal with respect to each other. This generalization directly results from an analysis of the variance in electronic structure with quantum nuclear degrees of freedom. The diabatic electronic states are treated here as classical parametric variables and propagated simultaneously along with the quantum wavepacket and classical nuclei. Each electronic density matrix is constrained to be N-representable. Consequently two sets of new methods are derived: extended Lagrangian-QWAIMD (xLag-QWAIMD) and diabatic extended Lagrangian-QWAIMD (DxLag-QWAIMD). In both cases, the instantaneous potential energy surface for the quantum nuclear degrees of freedom is constructed from the diabatic states using an on-the-fly nonorthogonal multireference formalism. By introducing generalized grid-based electronic basis functions, we eliminate the basis set dependence on the quantum nucleus. Subsequent reuse of the two-electron integrals during the on-the-fly potential energy surface computation stage yields a substantial reduction in computational costs. Specifically, both xLag-QWAIMD and DxLag-QWAIMD turn out to be about two orders of magnitude faster than our previously developed time-dependent deterministic sampling implementation of QWAIMD. Energy conservation properties, accuracy of the associated potential surfaces, and vibrational properties are analyzed for a family of hydrogen bonded systems.     

Theoretical prediction on vibrational spectra of [Ar…Ar-H]~+

As a special substance between isolated molecules and condensed phase, clusters have drawn more and more attention by theoreticians and experimentalists. The protonated rare gas cluster is one kind of simplest clusters, which can be looked on as the simplest solution composed of the simplest solute, proton, and the simplest solvent, rare gas. The study on such a system can help us to know more about the complex condensed matter. However, the information for the molecular properties of protonat…     

Quantum study of Eley-Rideal reaction and collision induced desorption of hydrogen atoms on a graphite surface. I. H-chemisorbed case

Collision induced (CI) processes involving hydrogen atoms on a graphite surface are studied quantum mechanically within the rigid, flat surface approximation, using a time-dependent wave packet method. The Eley-Rideal (ER) reaction and collision induced desorption (CID) cross sections are obtained with the help of two propagations which use different sets of coordinates, a "product" and a "reagent" set. Several adsorbate-substrate initial states of the target H atom in the chemisorption well are considered, and CI processes are studied over a wide range of projectile energy. Results show that (i) the Eley-Rideal reaction is the major reactive outcome and (ii) CID cross sections do not exceed 4 A2 and present dynamic thresholds for low values of the target vibrational quantum number. ER cross sections show oscillations at high energies which cannot be reproduced by classical and quasiclassical trajectory calculations. They are related to the vibrational excitation of the reaction products, which is a rather steep decreasing function of the collision energy. This behavior causes a selective population of the low-lying vibrational states and allows the quantization of the product molecular states to manifest itself in a collisional observable. A peak structure in the CID cross section is also observed and is assigned to the selective population of metastable states of the transient molecular hydrogen.     

Vibrational interference effects in x-ray emission of a model water dimer: implications for the interpretation of the liquid spectrum

We apply the Kramers-Heisenberg formula to a model water dimer to discuss vibrational interference in the x-ray emission spectrum of the donor molecule for which the core-ionized potential energy surface is dissociative but bounded by the accepting molecule. A long core-hole lifetime leads to decay from Zundel-like, fully delocalized vibrational states in the intermediate potential without involvement of a specific dissociated component. Comparison is made to a model with an unbound intermediate state allowing dissociation to infinity which gives a sharp, fully dissociated feature, and a broad molecular peak at long core-hole life time. The implications of the vibrational interference effect on the liquid water spectrum are discussed and it is proposed that this mainly gives rise to an isotope-dependent asymmetrical broadening of the lone pair peak.     

An ab initio close-coupling calculation of the lower vibrational energies of the HCl dimer

We have previously determined an analytical ab initio six-dimensional potential energy surface for the HCl dimer, and in the present paper we use this potential, with the HCl bond lengths held fixed, in a full (four-dimensional) close-coupling calculation to determine the energies of the lowest 24 vibrational states. These vibrational states involve the intermolecular stretch ν₄, the trans-bend tunneling vibration ν₅, and the torsion ν₆. The highest of the 24 levels is the (ν₄ν₅ν₆)=(111) state, for which we calculate an energy of 200 cm⁻¹ above the (000) state. As well as determining tunneling energies up to 5ν₅=183 cm⁻¹, we determine ν₄=49 cm⁻¹, 2ν₄=93 cm⁻¹, 3ν₄=134 cm⁻¹, 4ν₄=172 cm⁻¹, ν₆=137 cm⁻¹ and ν₄+ν₆=178 cm⁻¹, together with tunneling energies in all these states. Making allowance for the HCl stretching zero-point energy we determine the dissociation energy D₀ as 390 cm⁻¹ on this analytical surface. We determine that below 300 cm⁻¹ there are 72 vibrational (J=K=0) states, and below dissociation there are 162 vibrational (J=K=0) states, for this potential surface.     

The importance of tunneling in the first hydrogenation step in ammonia synthesis over a Ru(0001) surface

The hydrogenation of nitrogen (N(ads)+H(ads)-->NH(ads)) on metal surfaces is an important step in ammonia catalysis. We investigate the reaction dynamics of this hydrogenation step by time independent scattering theory and variational transition state theory (VTST) including tunneling corrections. The potential energy surface is derived by hybrid density functional theory on a model cluster composed of 12 ruthenium atoms resembling a Ru(0001) surface. The scattering calculations are performed on a reduced dimensionality potential energy hypersurface, where two dimensions are treated explicitly and all others are included implicitly by the zero-point correction. The VTST calculations include quantum effects along the reaction coordinate by applying the small curvature tunneling scheme. Even at room temperature (where ruthenium already shows catalytic activity) we find rate enhancement by tunneling by a factor of approximately 70. Inspection of the reaction probabilities shows that the major contribution to reactivity comes from the vibrational ground state of the reactants into vibrationally excited product states. The reaction rates are higher than determined in previous studies, and are compatible with experimental overall rates for ammonia synthesis.     

The dissociative chemisorption of methane on Ni(100): reaction path description of mode-selective chemistry

We derive a model for the dissociative chemisorption of methane on a Ni(100) surface, based on the reaction path Hamiltonian, that includes all 15 molecular degrees of freedom within the harmonic approximation. The total wavefunction is expanded in the adiabatic vibrational states of the molecule, and close-coupled equations are derived for wave packets propagating on vibrationally adiabatic potential energy surfaces, with non-adiabatic couplings linking these states to each other. Vibrational excitation of an incident molecule is shown to significantly enhance the reactivity, if the molecule can undergo transitions to states of lower vibrational energy, with the excess energy converted into motion along the reaction path. Sudden models are used to average over surface impact site and lattice vibrations. Computed dissociative sticking probabilities are in good agreement with experiment, with respect to both magnitude and variation with energy. The ν(1) vibration is shown to have the largest efficacy for promoting reaction, due to its strong non-adiabatic coupling to the ground state, and a significant softening of the vibration at the transition state. Most of the reactivity at 475 K is shown to result from thermally assisted over-the-barrier processes, and not tunneling.