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.     

Ground state structures and excited state dynamics of pyrrole-water complexes: ab initio excited state molecular dynamics simulations

Structures of the ground state pyrrole-(H2O)n clusters are investigated using ab initio calculations. The charge-transfer driven femtosecond scale dynamics are studied with excited state ab initio molecular dynamics simulations employing the complete-active-space self-consistent-field method for pyrrole-(H2O)n clusters. Upon the excitation of these clusters, the charge density is located over the farthest water molecule which is repelled by the depleted pi-electron cloud of pyrrole ring, resulting in a highly polarized complex. For pyrrole-(H2O), the charge transfer is maximized (up to 0.34 a.u.) around approximately 100 fs and then oscillates. For pyrrole-(H2O)2, the initial charge transfer occurs through the space between the pyrrole and the pi H-bonded water molecule and then the charge transfer takes place from this water molecule to the sigma H-bonded water molecule. The total charge transfer from the pyrrole to the water molecules is maximized (up to 0.53 a.u.) around approximately 100 fs.     

Structure and ultrafast dynamics of liquid water: a quantum mechanics/molecular mechanics molecular dynamics simulations study

A quantum mechanics/molecular mechanics molecular dynamics simulation was performed for liquid water to investigate structural and dynamical properties of this peculiar liquid. The most important region containing a central reference molecule and all nearest surrounding molecules (first coordination shell) was treated by Hartree-Fock (HF), post-Hartree-Fock [second-order Moller-Plesset perturbation theory (MP2)], and hybrid density functional B3LYP [Becke's three parameter functional (B3) with the correlation functional of Lee, Yang, and Parr (LYP)] methods. In addition, another HF-level simulation (2HF) included the full second coordination shell. Site to site interactions between oxygen-oxygen, oxygen-hydrogen, and hydrogen-hydrogen atoms of all ab initio methods were compared to experimental data. The absence of a second peak and the appearance of a shoulder instead in the gO-O graph obtained from the 2HF simulation is notable, as this feature has been observed so far only for pressurized or heated water. Dynamical data show that the 2HF procedure compensates some of the deficiency of the HF one-shell simulation, reducing the difference between correlated (MP2) and HF results. B3LYP apparently leads to too rigid structures and thus to an artificial slow down of the dynamics.     

Determination of molecular vibrational state energies using the ab initio semiclassical initial value representation: application to formaldehyde

We have demonstrated the use of ab initio molecular dynamics (AIMD) trajectories to compute the vibrational energy levels of molecular systems in the context of the semiclassical initial value representation (SC-IVR). A relatively low level of electronic structure theory (HF/3-21G) was used in this proof-of-principle study. Formaldehyde was used as a test case for the determination of accurate excited vibrational states. The AIMD-SC-IVR vibrational energies have been compared to those from curvilinear and rectilinear vibrational self-consistent field/vibrational configuration interaction with perturbation selected interactions-second-order perturbation theory (VSCF/VCIPSI-PT2) and correlation-corrected vibrational self-consistent field (cc-VSCF) methods. The survival amplitudes were obtained from selecting different reference wavefunctions using only a single set of molecular dynamics trajectories. We conclude that our approach is a further step in making the SC-IVR method a practical tool for first-principles quantum dynamics simulations.     

Direct assessment of quantum nuclear effects on hydrogen bond strength by constrained-centroid ab initio path integral molecular dynamics

The impact of quantum nuclear effects on hydrogen (H-) bond strength has been inferred in earlier work from bond lengths obtained from path integral molecular dynamics (PIMD) simulations. To obtain a direct quantitative assessment of such effects, we use constrained-centroid PIMD simulations to calculate the free energy changes upon breaking the H-bonds in dimers of HF and water. Comparing ab initio simulations performed using PIMD and classical nucleus molecular dynamics (MD), we find smaller dissociation free energies with the PIMD method. Specifically, at 50 K, the H-bond in (HF)(2) is about 30% weaker when quantum nuclear effects are included, while that in (H(2)O)(2) is about 15% weaker. In a complementary set of simulations, we compare unconstrained PIMD and classical nucleus MD simulations to assess the influence of quantum nuclei on the structures of these systems. We find increased heavy atom distances, indicating weakening of the H-bond consistent with that observed by direct calculation of the free energies of dissociation.     

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 M?ller-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(+)(H?O)? isomers and is shown to recover the significant width of the shared-proton bands observed experimentally.     

Hybrid approach for ab initio molecular dynamics simulation combining energy density analysis and short-time Fourier transform: energy transfer spectrogram

We propose a new analysis technique for specifying molecular vibrational modes related with intramolecular and/or intermolecular energy transfer in ab initio molecular dynamics simulation of chemical reaction. The technique combines the short-time Fourier transform method with energy density analysis, which partitions the quantum chemical potential energy in the system into atomic contributions. The image obtained by the combined scheme, termed an energy transfer spectrogram (ETS), enables us to understand the dynamics of energy transfer by time-frequency representation. The time change of the local energy is quite important in chemical reactions. In order to assess the performance of the ETS, its application to the collision reaction between two carbon dioxide molecules is shown.     

Ab initio Ehrenfest dynamics

We present an ab initio direct Ehrenfest dynamics scheme using a three time-step integrator. The three different time steps are implemented with nuclear velocity Verlet, nuclear-position-coupled midpoint Fock integrator, and time-dependent Hartree-Fock with a modified midpoint and unitary transformation algorithm. The computational cost of the ab initio direct Ehrenfest dynamics presented here is found to be only a factor of 2-4 larger than that of Born-Oppenheimer (BO) dynamics. As an example, we compute the vibration of the NaCl molecule and the intramolecular torsional motion of H2C=NH2+ by Ehrenfest dynamics compared with BO dynamics. For the vibration of NaCl with an initial kinetic energy of 1.16 eV, Ehrenfest dynamics converges to BO dynamics with the same vibrational frequency. The intramolecular rotation of H2C=NH2+ produces significant electronic excitation in the Ehrenfest trajectory. The amount of nonadiabaticity, suggested by the amplitude of the coherent progression of the excited and ground electronic states, is observed to be directly related to the strength of the electron-nuclear coupling. Such nonadiabaticity is seen to have a significant effect on the dynamics compared with the adiabatic approximation.     

Energy-flow dynamics in the molecular channel of propanal photodissociation, C2H5CHO --> C2H6 + CO: direct ab initio molecular dynamics study

Direct ab initio molecular dynamics calculations have been carried out for the molecular channel of the photodissociation of propanal, C2H5CHO --> C2H6 + CO, at the RMP2(full)/cc-pVDZ level of ab initio molecular orbital theory. The initial conditions were generated using the microcanonical sampling to put the excess energy randomly into all vibrational modes of the TS. Starting from the TS, a total of approximately 700 trajectories were numerically integrated for 100 fs. The obtained final energy distributions for the C2H6 and CO fragments and their relative translational motion were found to be quite similar to those obtained for the acetaldehyde reaction, CH3CHO --> CH4 + CO, in our previous study (Chem. Phys. Lett. 2006, 421, 549) despite the fact that the number of degree of freedom for C2H6 is larger than that for CH4. The coupling between the intrinsic reaction coordinate and one of the generalized normal modes orthogonal to it was predicted substantially strong around s = 1.4 amu(1/2) bohr, and it is expected that the energy flow out of C2H6 proceeds through this coupling. However, the obtained energy distributions strongly suggest that the coupling among the modes in C2H6 is quite small and the intramolecular energy redistribution does not occur efficiently in this molecule.     

FTIR and FT-Raman spectra, molecular geometry, vibrational assignments, first-order hyperpolarizability, ab initio and DFT calculations for 3,4-dimethoxybenzonitrile

Quantum chemical calculations of energies, geometrical structure and vibrational wave numbers of 3,4-dimethoxybenzonitrile (DMBN) were carried out by the ab initio Hartree-Fock (HF) and density functional theory (DFT) with complete relaxation in the potential energy surface using 6-311++G(d,p) basis set. The computed values of frequencies are scaled using a suitable scale factor to yield good coherence with the observed values. Making use of the recorded data, the complete vibrational assignments are made and analysis of the observed fundamental bands of molecule is carried out. The geometries and normal modes of vibrations obtained from ab initio HF and B3LYP calculations are in good agreement with the experimentally observed data. The electric dipole moment (μ) and the first hyperpolarizability (β) values of the investigated molecule have been computed using ab initio quantum mechanical calculations. The calculated HOMO and LUMO energies show that charge transfer occur within the molecule. The theoretical FTIR and FT-Raman spectra for the title molecule have been constructed.     

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

Nuclear 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 R_HH (H_B1 … H_B2) 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.     

Constrained dynamics and extraction of normal modes from ab initio molecular dynamics: application to ammonia

We present a methodology for extracting phonon data from ab initio Born-Oppenheimer molecular dynamics calculations of molecular crystals. Conventional ab initio phonon methods based on perturbations are difficult to apply to lattice modes because the perturbation energy is dominated by intramolecular modes. We use constrained molecular dynamics to eliminate the effect of bond bends and stretches and then show how trajectories can be used to isolate and define in particular, the eigenvalues and eigenvectors of modes irrespective of their symmetry or wave vector. This is done by k-point and frequency filtering and projection onto plane wave states. The method is applied to crystalline ammonia: the constrained molecular dynamics allows a significant speed-up without affecting structural or vibrational modes. All Gamma point lattice modes are isolated: the frequencies are in agreement with previous studies; however, the mode assignments are different.     

Quantum wave packet ab initio molecular dynamics: an approach to study quantum dynamics in large systems

A methodology to efficiently conduct simultaneous dynamics of electrons and nuclei is presented. The approach involves quantum wave packet dynamics using an accurate banded, sparse and Toeplitz representation for the discrete free propagator, in conjunction with ab initio molecular dynamics treatment of the electronic and classical nuclear degree of freedom. The latter may be achieved either by using atom-centered density-matrix propagation or by using Born-Oppenheimer dynamics. The two components of the methodology, namely, quantum dynamics and ab initio molecular dynamics, are harnessed together using a time-dependent self-consistent field-like coupling procedure. The quantum wave packet dynamics is made computationally robust by using adaptive grids to achieve optimized sampling. One notable feature of the approach is that important quantum dynamical effects including zero-point effects, tunneling, as well as over-barrier reflections are treated accurately. The electronic degrees of freedom are simultaneously handled at accurate levels of density functional theory, including hybrid or gradient corrected approximations. Benchmark calculations are provided for proton transfer systems and the dynamics results are compared with exact calculations to determine the accuracy of the approach.     

Thermal Gaussian molecular dynamics for quantum dynamics simulations of many-body systems: application to liquid para-hydrogen

A new method, here called thermal Gaussian molecular dynamics (TGMD), for simulating the dynamics of quantum many-body systems has recently been introduced [I. Georgescu and V. A. Mandelshtam, Phys. Rev. B 82, 094305 (2010)]. As in the centroid molecular dynamics (CMD), in TGMD the N-body quantum system is mapped to an N-body classical system. The associated both effective Hamiltonian and effective force are computed within the variational Gaussian wave-packet approximation. The TGMD is exact for the high-temperature limit, accurate for short times, and preserves the quantum canonical distribution. For a harmonic potential and any form of operator A?, it provides exact time correlation functions C(AB)(t) at least for the case of B, a linear combination of the position, x, and momentum, p, operators. While conceptually similar to CMD and other quantum molecular dynamics approaches, the great advantage of TGMD is its computational efficiency. We introduce the many-body implementation and demonstrate it on the benchmark problem of calculating the velocity time auto-correlation function for liquid para-hydrogen, using a system of up to N = 2592 particles.     

Water mediated proton transfer in a mesostructured aluminosilicate framework: an ab initio molecular dynamics study

The proton transfer process mediated by water molecules adsorbed in an aluminosilicate framework has been studied using ab initio molecular dynamics simulations. This investigation has been carried out using a quasi-one-dimensional model simulating the mesoporous aluminosilicate channel structures. The effects of both the water loading and temperature of the system have been considered. At low coverage (one water molecule per acid site), the hydroxonium ion (H(3)O)(+) is found to be a transition state, in agreement with earlier studies on zeolites. At a higher water coverage (two water molecules per acid site), the (H(5)O(2))(+) species and the hydrogen bonded "neutral complex" structure are both found to be stable complexes at finite temperatures. The vibrational frequency spectrum is simulated by performing a Fourier transform of the velocity autocorrelation function (VAF), and the peak positions in the VAF are compared with IR measurements and zero-temperature calculations.     

Mixed quantum-classical molecular dynamics simulation of vibrational relaxation of ions in an electrostatic field

The vibrational relaxation of ions in low-density gases under the action of an electrostatic field is reproduced through a molecular dynamics simulation method. The vibration is treated though quantum mechanics and the remaining degrees of freedom are considered classical. The procedure is tested through comparison against analytic results for a two-dimensional quantum model and by studying energy exchange during binary ion-atom collisions. Finally, the method has been applied successfully to the calculation of the mobility and the vibrational relaxation rate of O2+ in Kr as a function of the mean collision energy using a model interaction potential that reproduces the potential minimum of a previously known ab initio potential surface. The calculation of the steady mean vibrational motion of the ions in (flow) drift tubes seems straightforward, though at the expense of large amounts of computer time.     

Ab initio molecular dynamics approach to tunneling splitting in polyatomic molecules

An ab initio molecular dynamics approach is combined with the semiclassical tunneling method of Makri and Miller, which is applied to estimations of tunneling splitting in the umbrella inversion of ammonia and the intramolecular hydrogen transfer in malonaldehyde. In the application to malonaldehyde, effects of multidimensionality are examined by assigning quantum zero-point energies only to significant vibrational modes and changing the amount of energy given to other degrees of freedom. The calculated tunneling splitting values are in good agreement with the corresponding experimental values for both molecules.     

An implemented potential of non-rigid water molecules for molecular dynamics simulations

The central force model for a water molecule is corrected by adding a three-body term. The present potential fits both an accurate ab initio potential energy surface and the fundamental vibrational frequencies of gas-phase water. The three-body terms allow us to reproduce the gas-phase IR spectrum by molecular dynamics simulations. Some problems connected with MD simulations of IR spectra are discussed.