Ab Initio Classical Molecular Dynamics Research Articles

Applicability of the Thawed Gaussian Wavepacket Dynamics to the Calculation of Vibronic Spectra of Molecules with Double-Well Potential Energy Surfaces.

Simulating vibrationally resolved electronic spectra of anharmonic systems, especially those involving double-well potential energy surfaces, often requires expensive quantum dynamics methods. Here, we explore the applicability and limitations of the recently proposed single-Hessian thawed Gaussian approximation for the simulation of spectra of systems with double-well potentials, including 1,2,4,5-tetrafluorobenzene, ammonia, phosphine, and arsine. This semiclassical wavepacket approach is shown to be more robust and to provide more accurate spectra than the conventional harmonic approximation. Specifically, we identify two cases in which the Gaussian wavepacket method is especially useful due to the breakdown of the harmonic approximation: (i) when the nuclear wavepacket is initially at the top of the potential barrier but delocalized over both wells, e.g., along a low-frequency mode, and (ii) when the wavepacket has enough energy to classically go over the low potential energy barrier connecting the two wells. The method is efficient and requires only a single classical ab initio molecular dynamics trajectory, in addition to the data required to compute the harmonic spectra. We also present an improved algorithm for computing the wavepacket autocorrelation function, which guarantees that the evaluated correlation function is continuous for arbitrary size of the time step.

Static and Dynamic Correlations in Water: Comparison of Classical Ab Initio Molecular Dynamics at Elevated Temperature with Path Integral Simulations at Ambient Temperature.

It is a common practice in ab initio molecular dynamics (AIMD) simulations of water to use an elevated temperature to overcome the overstructuring and slow diffusion predicted by most current density functional theory (DFT) models. The simulation results obtained in this distinct thermodynamic state are then compared with experimental data at ambient temperature based on the rationale that a higher temperature effectively recovers nuclear quantum effects (NQEs) that are missing in the classical AIMD simulations. In this work, we systematically examine the foundation of this assumption for several DFT models as well as for the many-body MB-pol model. We find for the cases studied that a higher temperature does not correctly mimic NQEs at room temperature, which is especially manifest in significantly different three-molecule correlations as well as hydrogen bond dynamics. In many of these cases, the effects of NQEs are the opposite of the effects of carrying out the simulations at an elevated temperature.

Nuclear quantum and H/D isotope effects on three‐centered bonding diborane: Path integral molecular dynamics simulations

AbstractNuclear quantum and H/D isotope effects of bridging and terminal hydrogen atoms of diborane (B2H6) molecules were systematically studied by classical ab initio molecular dynamics (CLMD) and ab initio path integral molecular dynamics (PIMD) simulations with BHandHLYP/6‐31++G** level of theory at room temperature (298.15 K). Calculated results clearly show that H/D isotope effect appears in the distribution of hydrogen (deuterium) of B2H6 (B2D6). Geometry of B2H6 also plays a significant role in the nuclear quantum effect proved by PIMD simulations, but slightly deviated from its equilibrium structure when simulated via CLMD simulation. The bond lengths between boron atoms R (B1 … B2) and the bridging hydrogen atoms RHH (HB1 … HB2) of the B2H6 molecule obtained from PIMD simulations are slightly longer than those of the deuterated form of the diborane (B2D6) molecule. The principal component analysis (PCA) was also employed to distinguish the important modes of bridging hydrogen as related to the nuclear quantum and H/D isotope effects. The highest level of contribution obtained from PCA of PIMD simulations is bending, while various mixed vibrations with less contribution were also found. Therefore, the nuclear quantum and H/D isotope effects need to be taken into account for a better understanding of diborane geometry.

Approximate Quantum Dynamics using Ab Initio Classical Separable Potentials: Spectroscopic Applications.

Algorithms for quantum molecular dynamics simulations that directly use ab initio methods have many potential applications. In this article, the ab initio classical separable potentials (AICSP) method is proposed as the basis for approximate algorithms of this type. The AICSP method assumes separability of the total time-dependent wave function of the nuclei and employs mean-field potentials that govern the dynamics of each degree of freedom. In the proposed approach, the mean-field potentials are determined by classical ab initio molecular dynamics simulations. The nuclear wave function can thus be propagated in time using the effective potentials generated "on the fly". As a test of the method for realistic systems, calculations of the stationary anharmonic frequencies of hydrogen stretching modes were carried out for several polyatomic systems, including three amino acids and the guanine-cytosine pair of nucleobases. Good agreement with experiments was found. The method scales very favorably with the number of vibrational modes and should be applicable for very large molecules, e.g., peptides. The method should also be applicable for properties such as vibrational line widths and line shapes. Work in these directions is underway.

Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory.

Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost.

Protonated water dimer on benzene: standing Eigen or crouching Zundel?

Protonated water clusters that are hydrogen-bonded to a neutral benzene molecule are a reductionist model for protons at hydrophobic surfaces, which are of fundamental importance in biological energy transduction processes. Of particular interest is the protonated water dimer ("Zundel ion") on benzene, whose gas-phase messenger IR spectrum has been previously interpreted in terms of an asymmetric binding of the protonated water dimer to the benzene ring through a single water molecule. This "standing Eigen" isomer has a hydronium core. We have found an alternative "crouching Zundel" isomer, which attaches to the benzene ring symmetrically via both of its water molecules. When Ar-tagged, it has an IR spectrum in much better agreement with experiment than the standing Eigen isomer, particularly at the lower frequencies. These conclusions are based on static harmonic (and anharmonic) normal-mode analysis using density functional theory with various (dispersion corrected) functionals and particularly on dynamic anharmonic spectra obtained from the dipole autocorrelation functions from classical ab initio molecular dynamics with the BLYP, PBE, and B3LYP functionals. Possible implications to protons on water/organic-phase interfaces are discussed.

Velocity-changing collisions in pure H2 and H2-Ar mixture.

We show how to effectively introduce a proper description of the velocity-changing collisions into the model of isolated molecular transition for the case of self- and Ar-perturbed H2. We demonstrate that the billiard-ball (BB) approximation of the H2-H2 and H2-Ar potentials gives an accurate description of the velocity-changing collisions. The BB model results are compared with ab initio classical molecular dynamics simulations. It is shown that the BB model correctly reproduces not only the principal properties such as frequencies of velocity-changing collisions or collision kernels, but also other characteristics of H2-H2 and H2-Ar gas kinetics like rate of speed-changing collisions. Finally, we present line-shape measurement of the Q(1) line of the first overtone band of self-perturbed H2. We quantify the systematic errors of line-shape analysis caused by the use of oversimplified description of velocity-changing collisions. These conclusions will have significant impact on recent rapidly developing ultra-accurate metrology based on Doppler-limited spectroscopic measurements such as Doppler-width thermometry, atmosphere monitoring, Boltzmann constant determination, or transition position and intensity determination for fundamental studies.

Ab Initio Path Integral Molecular Dynamics Study of the Nuclear Quantum Effect on Out-of-Plane Ring Deformation of Hydrogen Maleate Anion.

Ab initio path integral molecular dynamics (PIMD) simulation was performed to understand the nuclear quantum effect on the out-of-plane ring deformation of hydrogen maleate anion and investigate the existence of a stable structure with ring deformation, which was suggested in experimental observation (Fillaux et al., Chem. Phys. 1999, 120, 387-403). The isotope effect and the temperature effect are studied as well. We first investigated the nuclear quantum effect on the proton transfer. In static calculation and classical ab initio molecular dynamics simulations, the proton in the hydrogen bond is localized to either oxygen atom. On the other hand, the proton is located at the center of two oxygen atoms in quantum ab initio PIMD simulations. The nuclear quantum effect washes out the barrier of proton transfer. We next examined the nuclear quantum effect on the motion of hydrogen maleate anion. Principal component analysis revealed that the out-of-plane ring bending modes have dominant contribution to the entire molecular motion. In quantum ab initio PIMD simulations, structures with ring deformation were the global minimum for the deuterated isotope at 300 K. We analyzed the out-of-plane ring bending mode further and found that there are three minima along a ring distortion mode. We successfully found a stable structure with ring deformation of hydrogen maleate for the first time, to our knowledge, using theoretical calculation. The structures with ring deformation found in quantum simulation of the deuterated isotope allowed the proton transfer to occur more frequently than the planar structure. Static ab initio electronic structure calculation found that the structures with ring deformation have very small proton transfer barrier compared to the planar structure. We suggest that the "proton transfer driven" mechanism is the origin of stabilization for the structure with out-of-plane ring deformation.

Dissociation of H2NCH Dication in a Strong Laser Field

Ab initio classical molecular dynamics calculations have been used to simulate the dissociation of H(2)NCH(2+) in a strong laser field. The frequencies of the continuous oscillating electric field were chosen to be ω = 0.02, 0.06, and 0.18 au (2280, 760, and 253 nm, respectively). The field had a maximum strength of 0.03 au (3.2 × 10(13) W cm(-2)) and was aligned with the CN bond. Trajectories were started with 100 kcal/mol of vibrational energy above zero point and were integrated for up to 600 fs at the B3LYP/6-311G(d,p) level of theory. A total of 200 trajectories were calculated for each of the three different frequencies and without a field. Two dissociation channels are observed: HNCH(+) + H(+) and H(2)NC(+) + H(+). About one-half to two-thirds of the H(+) dissociations occurred directly, while the remaining indirect dissociations occurred at a slower rate with extensive migration of H(+) between C and N. The laser field increased the initial dissociation rate by a factor of ca. 1.4 and decreased the half-life by a factor of ca. 0.75. The effects were similar at each of the three frequencies. The HNCH(+) to H(2)NC(+) branching ratio decreased from 10.6:1 in the absence of the field to an average of 8.4:1 in the laser field. The changes in the rates and branching ratios can be attributed to the laser field lowering the reaction barriers as a result of a difference in polarizability of the reactant and transition states.

Ab Initio Molecular Dynamics with Dual Basis Set Methods

On-the-fly, ab initio classical molecular dynamics are demonstrated with an underlying dual basis set potential energy surface. Dual-basis self-consistent field (Hartree-Fock and density functional theory) and resolution-of-the-identity second-order Møller-Plesset perturbation theory (RI-MP2) dynamics are tested for small systems, including the water dimer. The resulting dynamics are shown to be faithful representations of their single-basis analogues for individual trajectories, as well as vibrational spectra. Computational cost savings of 58% are demonstrated for SCF methods, even relative to Fock-extrapolated dynamics, and savings are further increased to 71% with RI-MP2. Notably, these timings outperform an idealized estimate of extended-Lagrangian molecular dynamics. The method is subsequently demonstrated on the vibrational absorption spectrum of two NO(+)(H₂O)₃ isomers and is shown to recover the significant width of the shared-proton bands observed experimentally.

Accelerated ab initio molecular dynamics with response equation extrapolation

Polynomial extrapolation of response (‘ z-vector’) elements is shown to reduce the cost of correlated-wavefunction, classical ab initio molecular dynamics. Demonstrations with resolution-of-the-identity Møller–Plesset perturbation theory (RI-MP2) show that the number of response equation iterations is reduced by a factor of 2–3, thereby enabling accelerated MP2 dynamics. Coupled with previously demonstrated Fock matrix extrapolation, the combined iterative SCF and z-vector calculations are reduced to a minority share of the total calculation. Though demonstrated for MP2, these methods can also be generalized to higher levels of electron correlation or excited state methods.

Quantum Effects on Vibrational and Electronic Spectra of Hydrazine Studied by “On-the-Fly” ab Initio Ring Polymer Molecular Dynamics

Structural and spectroscopic properties of hydrazine, H(2)N-NH(2), it being a floppy or fluxional molecule in a vacuum, are investigated by means of ab initio molecular dynamics, ab initio path integral molecular dynamics, and ab initio ring polymer molecular dynamics simulations in conjunction with "on-the-fly" MP2 and CIS(D) electronic structure calculations. Whereas the former method relies on the classical approximation of nuclear motion, quantum effects on structure and dynamics are taken into account at finite temperatures by ab initio path integral and ab initio ring polymer molecular dynamics, respectively. It is shown that quantum-mechanical fluctuation effects of the nuclei, in addition to their purely thermal activation, cause significant configurational fluctuations due to strongly anharmonic vibrations and thus increase the explored regions on the Born-Oppenheimer potential energy surface at room temperature. Including these effects, in turn, leads to significant improvements in the computed spectra compared to stick spectra obtained at the equilibrium structure by means of harmonic normal-mode analysis, as well as by classical ab initio molecular dynamics. This family of methods, combining electronic structure with path integrals, offers a powerful and general computational approach not only to molecular structure determination of floppy or fluxional molecules, but also to evaluation of their electronic and vibrational spectra.

Quantum Wavepacket Ab Initio Molecular Dynamics: An Approach for Computing Dynamically Averaged Vibrational Spectra Including Critical Nuclear Quantum Effects

We have introduced a computational methodology to study vibrational spectroscopy in clusters inclusive of critical nuclear quantum effects. This approach is based on the recently developed quantum wavepacket ab initio molecular dynamics method that combines quantum wavepacket dynamics with ab initio molecular dynamics. The computational efficiency of the dynamical procedure is drastically improved (by several orders of magnitude) through the utilization of wavelet-based techniques combined with the previously introduced time-dependent deterministic sampling procedure measure to achieve stable, picosecond length, quantum-classical dynamics of electrons and nuclei in clusters. The dynamical information is employed to construct a novel cumulative flux/velocity correlation function, where the wavepacket flux from the quantized particle is combined with classical nuclear velocities to obtain the vibrational density of states. The approach is demonstrated by computing the vibrational density of states of [Cl-H-Cl]-, inclusive of critical quantum nuclear effects, and our results are in good agreement with experiment. A general hierarchical procedure is also provided, based on electronic structure harmonic frequencies, classical ab initio molecular dynamics, computation of nuclear quantum-mechanical eigenstates, and employing quantum wavepacket ab initio dynamics to understand vibrational spectroscopy in hydrogen-bonded clusters that display large degrees of anharmonicities.

Ab initio molecular dynamics and wavepacket dynamics of highly charged fullerene cations produced with intense near-infrared laser pulses

We theoretically investigated the stability of highly charged C 60 z + cations produced with an ultrashort intense laser pulse of λ ∼ 1800 nm. We first review the results of our theoretical investigation of the stability of C 60 z + cations and report that C 60 z + cations up to z = 12 can be produced as a stable or quasistable (μs-order lifetime) intact parent cation. We next present the results of simulation as to how much vibrational energy is acquired by C 60 or C 60 z + through the interaction with an ultrashort intense pulse of λ = 1800 nm. This type of simulation was carried out by incorporating an ab initio classical molecular dynamics method into the framework of the time-dependent adiabatic state approach. The results indicate that large-amplitude vibration with energy of >20 eV is induced in the h g(1) mode of C 60 z + . C 60 or C 60 z + is mostly elongated along the field polarization direction, of which the motion can be described by using the time-dependent (TD) potential along the h g(1) coordinate. We also solved the corresponding TD Schrödinger equation to propagate the vibrational wavepacket on the TD potential. We found that the acquired vibrational energy is maximized at T p ∼ T vib/2, where T p is the pulse length and T vib is the vibrational period of the h g(1) mode. We show how the vibrational energy deposited in C 60 can be controlled by changing the pulse separation of a train of three pulses. We finally discuss the structure and dissociation of C 20 z + .

Ab initio centroid path integral molecular dynamics: application to vibrational dynamics of diatomic molecular systems.

An ab initio centroid molecular dynamics (CMD) method is developed by combining the CMD method with the ab initio molecular orbital method. The ab initio CMD method is applied to vibrational dynamics of diatomic molecules, H2 and HF. For the H2 molecule, the temperature dependence of the peak frequency of the vibrational spectral density is investigated. The results are compared with those obtained by the ab initio classical molecular dynamics method and exact quantum mechanical treatment. It is shown that the vibrational frequency obtained from the ab initio CMD approaches the exact first excitation frequency as the temperature lowers. For the HF molecule, the position autocorrelation function is also analyzed in detail. The present CMD method is shown to well reproduce the exact quantum result for the information on the vibrational properties of the system.

The infrared spectrum of the O⋯H⋯O fragment of H5O2+: Ab initio classical molecular dynamics and quantum 4D model calculations

The gas phase IR spectrum of the O⋯H⋯O fragment of H5O2+ and its deuterated analogue are calculated using ab initio classical molecular dynamics based on a MP2 potential energy surface. The assignment of the bands is made in terms of the quantum four-dimensional model calculations of anharmonic frequencies and intensities. Comparing low and high kinetic temperature simulations the importance of anharmonicities of the potential energy surface for understanding the vibrational band structure is highlighted. It is shown that any reasonable simulation of IR spectra of systems with very strong hydrogen bonds has to account for the dipole moment function beyond the linear approximation.

Simulation studies of liquid ammonia by classical ab initio, classical, and path-integral molecular dynamics

The structure of liquid ammonia at T=273 K has been studied using classical ab initio molecular dynamics, classical molecular dynamics, and the path-integral molecular dynamics methods. The three different types of calculation are employed to generate new insights into the ability of theoretical methods to model liquid ammonia effectively. Thus, the limitations of using classical nuclei, simple point charge models, small systems, and gradient corrected density functional theory are assessed through a comparison of the results of the different types of calculations to each other and recent experiments in a consistent manner. Briefly, the experimental intermolecular quantum structure is very well reproduced by the classical approximation while the intramolecular classical and quantum structures exhibit large deviations. The intermolecular ab initio partial radial structure factors of liquid ammonia and the associated radial distribution functions are in better agreement with experiment than the empirical models. However, the empirical models also perform reasonably well.