Automatic generation of force fields and property surfaces for use in variational vibrational calculations of anharmonic vibrational energies and zero-point vibrational averaged properties

An automatic and general procedure for the calculation of geometrical derivatives of the energy and general property surfaces for molecular systems is developed and implemented. General expressions for an n-mode representation are derived, where the n-mode representation includes only the couplings between n or less degrees of freedom. The general expressions are specialized to derivative force fields and property surfaces, and a scheme for calculation of the numerical derivatives is implemented. The implementation is interfaced to electronic structure programs and may be used for both ground and excited electronic states. The implementation is done in the context of a vibrational structure program and can be used in combination with vibrational self-consistent field (VSCF), vibrational configuration interaction (VCI), vibrational Moller-Plesset, and vibrational coupled cluster calculations of anharmonic wave functions and calculation of vibrational averaged properties at the VSCF and VCI levels. Sample calculations are presented for fundamental vibrational energies and vibrationally averaged dipole moments and frequency dependent polarizabilities and hyperpolarizabilities of water and formaldehyde.     

Full dimensional quantum calculations of vibrational energies of N-methyl acetamide

We report quantum calculations of vibrational states of trans N-methyl acetamide (H3C-HNCO-CH3) in full dimensionality using the code MULTIMODE. In this code, the full potential is represented as a hierarchical sum of n-mode potentials in the normal coordinates. All 30 one- and 435 two-mode potentials are included in the sum, as well as a restricted set of 10 three-mode potentials corresponding to the experimentally probed amide band. The electronic energies on the various n-mode grids are obtained using ab initio M?ller-Plesset perturbation theory with a triple-zeta quality, correlation-consistent basis set. Convergence tests of the low-lying vibrational eigenvalues of the amide band show that this limited three-mode representation of the full potential yields well converged results that are in excellent agreement with experiment. The infrared spectrum in the region of the amide bands is calculated and also agrees well with experiment.     

Interpolating moving least-squares methods for fitting potential energy surfaces: computing high-density potential energy surface data from low-density ab initio data points

A highly accurate and efficient method for molecular global potential energy surface (PES) construction and fitting is demonstrated. An interpolating-moving-least-squares (IMLS)-based method is developed using low-density ab initio Hessian values to compute high-density PES parameters suitable for accurate and efficient PES representation. The method is automated and flexible so that a PES can be optimally generated for classical trajectories, spectroscopy, or other applications. Two important bottlenecks for fitting PESs are addressed. First, high accuracy is obtained using a minimal density of ab initio points, thus overcoming the bottleneck of ab initio point generation faced in applications of modified-Shepard-based methods. Second, high efficiency is also possible (suitable when a huge number of potential energy and gradient evaluations are required during a trajectory calculation). This overcomes the bottleneck in high-order IMLS-based methods, i.e., the high cost/accuracy ratio for potential energy evaluations. The result is a set of hybrid IMLS methods in which high-order IMLS is used with low-density ab initio Hessian data to compute a dense grid of points at which the energy, Hessian, or even high-order IMLS fitting parameters are stored. A series of hybrid methods is then possible as these data can be used for neural network fitting, modified-Shepard interpolation, or approximate IMLS. Results that are indicative of the accuracy, efficiency, and scalability are presented for one-dimensional model potentials as well as for three-dimensional (HCN) and six-dimensional (HOOH) molecular PESs.     

A hierarchical construction scheme for accurate potential energy surface generation: an application to the F+H2 reaction

We present a hierarchical construction scheme for accurate ab initio potential energy surface generation. The scheme is based on the observation that when molecular configuration changes, the variation in the potential energy difference between different ab initio methods is much smaller than the variation for potential energy itself. This means that it is easier to numerically represent energy difference to achieve a desired accuracy. Because the computational cost for ab initio calculations increases very rapidly with the accuracy, one can gain substantial saving in computational time by constructing a high accurate potential energy surface as a sum of a low accurate surface based on extensive ab initio data points and an energy difference surface for high and low accuracy ab initio methods based on much fewer data points. The new scheme was applied to construct an accurate ground potential energy surface for the FH(2) system using the coupled-cluster method and a very large basis set. The constructed potential energy surface is found to be more accurate on describing the resonance states in the FH(2) and FHD systems than the existing surfaces.     

The molecular potential energy surface and vibrational energy levels of methyl fluoride. Part II

New analytical bending and stretching, ground electronic state, potential energy surfaces for CH(3)F are reported. The surfaces are expressed in bond-length, bond-angle internal coordinates. The four-dimensional stretching surface is an accurate, least squares fit to over 2000 symmetrically unique ab initio points calculated at the CCSD(T) level. Similarly, the five-dimensional bending surface is a fit to over 1200 symmetrically unique ab initio points. This is an important first stage towards a full nine-dimensional potential energy surface for the prototype CH(3)F molecule. Using these surfaces, highly excited stretching and (separately) bending vibrational energy levels of CH(3)F are calculated variationally using a finite basis representation method. The method uses the exact vibrational kinetic energy operator derived for XY(3)Z systems by Manson and Law (preceding paper, Part I, Phys. Chem. Chem. Phys., 2006, 8, DOI: 10.1039/b603106d). We use the full C(3v) symmetry and the computer codes are designed to use an arbitrary potential energy function. Ultimately, these results will be used to design a compact basis for fully coupled stretch-bend calculations of the vibrational energy levels of the CH(3)F system.     

Efficient correlation-corrected vibrational self-consistent field computation of OH-stretch frequencies using a low-scaling algorithm

The authors present a new computational scheme to perform accurate and fast direct correlation-corrected vibrational self-consistent field (CC-VSCF) computations for a selected number of vibrational modes, which is aimed at predicting a few vibrations in large molecular systems. The method is based on a systematic selection of vibrational mode-mode coupling terms, leading to the direct ab initio construction of a sparse potential energy surface. The computational scaling of the CC-VSCF computation on the generated surface is then further reduced by using a screening procedure for the correlation-correction contributions. The proposed method is applied to the computation of the OH-stretch frequency of five aliphatic alcohols. The authors investigate the influence of different pseudopotential and all-electron basis sets on the quality of the correlated potential energy surfaces computed and on the OH-stretch frequencies calculated for each surface. With the help of these test systems, the authors show that their method offers a computational scaling that is two orders of magnitude lower than a standard CC-VSCF method and that it is of equal accuracy.     

Spin-orbit coupled potential energy surfaces and properties using effective relativistic coupling by asymptotic representation

A new method has been reported recently [H. Ndome, R. Welsch, and W. Eisfeld, J. Chem. Phys. 136, 034103 (2012)] that allows the efficient generation of fully coupled potential energy surfaces (PESs) including derivative and spin-orbit (SO) coupling. The method is based on the diabatic asymptotic representation of the molecular fine structure states and an effective relativistic coupling operator and therefore is called effective relativistic coupling by asymptotic representation (ERCAR). The resulting diabatic spin-orbit coupling matrix is constant and the geometry dependence of the coupling between the eigenstates is accounted for by the diabatization. This approach allows to generate an analytical model for the fully coupled PESs without performing any ab initio SO calculations (except perhaps for the atoms) and thus is very efficient. In the present work, we study the performance of this new method for the example of hydrogen iodide as a well-established test case. Details of the diabatization and the accuracy of the results are investigated in comparison to reference ab initio calculations. The energies of the adiabatic fine structure states are reproduced in excellent agreement with reference ab initio data. It is shown that the accuracy of the ERCAR approach mainly depends on the quality of the underlying ab initio data. This is also the case for dissociation and vibrational level energies, which are influenced by the SO coupling. A method is presented how one-electron operators and the corresponding properties can be evaluated in the framework of the ERCAR approach. This allows the computation of dipole and transition moments of the fine structure states in good agreement with ab initio data. The new method is shown to be very promising for the construction of fully coupled PESs for more complex polyatomic systems to be used in quantum dynamics studies.     

Theoretical investigation of the He-I2(E3Πg) ion-pair state: ab initio intermolecular potential and vibrational levels

We present a theoretical study on the potential energy surface and vibrational bound states of the E electronic excited state of the HeI(2) van der Waals system. The interaction energies are computed using accurate ab initio methods and large basis sets. Relativistic small-core effective core potentials in conjunction with a quintuple-zeta quality basis set are employed for the heavy iodine atoms in multireference configuration interaction calculations for the (3)A' and (3)A" states. For the representation of the potential energy surface we used a general interpolation technique for constructing potential surfaces from ab initio data based on the reproducing kernel Hilbert space method. The surface presents global and local minima for T-shaped configurations with well-depths of 33.2 and 4.6 cm(-1), respectively. Vibrational energies and states are computed through variational quantum mechanical calculations. We found that the binding energy of the HeI(2)(E) T-shaped isomer is 16.85 cm(-1), in excellent agreement with recent experimental measurements. In lieu of more experimental data we also report our predictions on higher vibrational levels and we analyze the influence of the underlying surface on them. This is the first attempt to represent the potential surface of such a highly excited electronic state of a van der Waals complex, and it demonstrates the capability of the ab initio technology to provide accurate results for carrying out reliable studies to model experimental data.     

Ab initio potential-energy surfaces for complex, multichannel systems using modified novelty sampling and feedforward neural networks

A neural network/trajectory approach is presented for the development of accurate potential-energy hypersurfaces that can be utilized to conduct ab initio molecular dynamics (AIMD) and Monte Carlo studies of gas-phase chemical reactions, nanometric cutting, and nanotribology, and of a variety of mechanical properties of importance in potential microelectromechanical systems applications. The method is sufficiently robust that it can be applied to a wide range of polyatomic systems. The overall method integrates ab initio electronic structure calculations with importance sampling techniques that permit the critical regions of configuration space to be determined. The computed ab initio energies and gradients are then accurately interpolated using neural networks (NN) rather than arbitrary parametrized analytical functional forms, moving interpolation or least-squares methods. The sampling method involves a tight integration of molecular dynamics calculations with neural networks that employ early stopping and regularization procedures to improve network performance and test for convergence. The procedure can be initiated using an empirical potential surface or direct dynamics. The accuracy and interpolation power of the method has been tested for two cases, the global potential surface for vinyl bromide undergoing unimolecular decomposition via four different reaction channels and nanometric cutting of silicon. The results show that the sampling methods permit the important regions of configuration space to be easily and rapidly identified, that convergence of the NN fit to the ab initio electronic structure database can be easily monitored, and that the interpolation accuracy of the NN fits is excellent, even for systems involving five atoms or more. The method permits a substantial computational speed and accuracy advantage over existing methods, is robust, and relatively easy to implement.     

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.     

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.     

Accurate ab initio determination of the adiabatic potential energy function and the Born-Oppenheimer breakdown corrections for the electronic ground state of LiH isotopologues

High level ab initio potential energy functions have been constructed for LiH in order to predict vibrational levels up to dissociation. After careful tests of the parameters of the calculation, the final adiabatic potential energy function has been composed from: (a) an ab initio nonrelativistic potential obtained at the multireference configuration interaction with singles and doubles level including a size-extensivity correction and quintuple-sextuple ζ extrapolations of the basis, (b) a mass-velocity-Darwin relativistic correction, and (c) a diagonal Born-Oppenheimer (BO) correction. Finally, nonadiabatic effects have also been considered by including a nonadiabatic correction to the kinetic energy operator of the nuclei. This correction is calculated from nonadiabatic matrix elements between the ground and excited electronic states. The calculated vibrational levels have been compared with those obtained from the experimental data [J. A. Coxon and C. S. Dickinson, J. Chem. Phys. 134, 9378 (2004)]. It was found that the calculated BO potential results in vibrational levels which have root mean square (rms) deviations of about 6-7 cm(-1) for LiH and ～3 cm(-1) for LiD. With all the above mentioned corrections accounted for, the rms deviation falls down to ～1 cm(-1). These results represent a drastic improvement over previous theoretical predictions of vibrational levels for all isotopologues of LiH.     

A systematic investigation of the ground state potential energy surface of H3+

Based on different ab initio electronic structure calculations (CI-R12 and Gaussian Geminals) of the Born-Oppenheimer electronic energy E(BO) of H(3)(+) from high to highest quality, we build up a potential energy surface which represents a highly reliable form of the topology of the whole potential region, locally and globally. We use the CI-R12 method in order to get within reasonable CPU-time a relatively dense grid of energy points. We demonstrate that CI-R12 is good enough to give an accurate surface, i.e., Gaussian Geminals are not absolutely necessary. For different types of potential energy surface fits, we performed variational calculations of all bound vibrational states, including resonances above the dissociation limit, for total angular momentum J = 0. We clarify the differences between different fits of the energy to various functional forms of the potential surface. Small rms-values (<1 cm(-1)) of the fit do not provide precise information about the interpolatory behaviour of the fit functions.     

Theoretical studies of the tunneling splitting of malonaldehyde using the multiconfiguration time-dependent Hartree approach

Full dimensional multi-configuration time-dependent Hartree calculations of the zero point energy and the tunneling splitting of malonaldehyde using a recently published potential energy surface [Y. Wang, B. J. Braams, J. M. Bowman, S. Carter, and D. P. Tew, J. Chem. Phys. 128, 224314 (2008)] are reported. The potential energy surface has been approximated by a modified version of the n-mode representation and careful convergence check has been performed to ensure accurate results. The obtained value for the splitting (23.4 cm(-1)) is in acceptable agreement with the experimental value of 21.583 cm(-1). The computed zero-point-energy is 14,670 cm(-1) which is lower than previous results of Wang et al., but likely to be about 4 cm(-1) too low because of shortcomings of the n-mode representation of the potential. The energies reported in this abstract contain a correction to account for neglected vibrational angular momentum terms.     

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.     

A heuristic potential function for intramolecular and intrasupermolecular chemical reactions

A heuristic fitting procedure to obtain an analytical potential function for describing a reactive potential energy surface in the neighborhood of the intrinsic reaction coordinate (IRC ) has been developed. For discussion, the pairwise potential function form, ∑a_nr^?n, is assumed in order to fit ab initio quantum mechanical calculations of intramolecular (or intrasupermolecular) interaction energies and its use is found advantageous because all the calculation can be carried out by the linear least squares method. Normal modes perpendicular to IRC are utilized to prepare an initial data base for the potential fitting in the neighborhood of IRC . Some trial molecular dynamics (MD ) simulations are performed in order to check the fitted potential function and, unless they lead to reasonable energies within the tolerance assumed, their results are utilized to construct an improved data base (the dynamic sampling). The present systematic optimization procedure has been applied to the proton transfer reaction of the formamidine–water (FW ) system. The normal mode analysis in both the transition state (TS ) and the stable state (SS ) regions suggests that the present fitted potential function can reproduce satisfactorily the Born–Oppenheimer (BO ) adiabatic surface obtained by ab initio molecular orbital (MO ) calculations. We conclude that our procedure works well for the chemical reaction molecular dynamics (CRMD ) simulation.     

First principles semiclassical calculations of vibrational eigenfunctions

Vibrational eigenfunctions are calculated on-the-fly using semiclassical methods in conjunction with ab initio density functional theory classical trajectories. Various semiclassical approximations based on the time-dependent representation of the eigenfunctions are tested on an analytical potential describing the chemisorption of CO on Cu(100). Then, first principles semiclassical vibrational eigenfunctions are calculated for the CO(2) molecule and its accuracy evaluated. The multiple coherent states initial value representations semiclassical method recently developed by us has shown with only six ab initio trajectories to evaluate eigenvalues and eigenfunctions at the accuracy level of thousands trajectory semiclassical initial value representation simulations.     

Nuclear quadrupole hyperfine structure in HC14N/H14NC and DC15N/D15NC isomerization: a diagnostic tool for characterizing vibrational localization

Large-amplitude molecular motions which occur during isomerization can cause significant changes in electronic structure. These variations in electronic properties can be used to identify vibrationally-excited eigenstates which are localized along the potential energy surface. This work demonstrates that nuclear quadrupole hyperfine interactions can be used as a diagnostic marker of progress along the isomerization path in both the HC14N/H14NC and DC15N/D15NC chemical systems. Ab initio calculations at the CCSD(T)/cc-pCVQZ level indicate that the hyperfine interaction is extremely sensitive to the chemical bonding of the quadrupolar 14N nucleus and can therefore be used to determine in which potential well the vibrational wavefunction is localized. A natural bonding orbital analysis along the isomerization path further demonstrates that hyperfine interactions arise from the asphericity of the electron density at the quadrupolar nucleus. Using the CCSD(T) potential surface, the quadrupole coupling constants of highly-excited vibrational states are computed from a one-dimensional internal coordinate path Hamiltonian. The excellent agreement between ab initio calculations and recent measurements demonstrates that nuclear quadrupole hyperfine structure can be used as a diagnostic tool for characterizing localized HCN and HNC vibrational states.     

Vibrational inelastic and charge transfer processes in H(+)+H2 system: an ab initio study

State-resolved differential cross sections, total and integral cross sections, average vibrational energy transfer, and the relative probabilities are computed for the H(+)+H2 system using the newly obtained ab initio potential energy surfaces at the full CI/cc-pVQZ level of accuracy which allow for both the direct vibrational inelastic and the charge transfer processes. The quantum dynamics is treated within the vibrational close-coupling infinite-order-sudden approximation approach using the two ab initio quasidiabatic potential energy surfaces. The computed collision attributes for both the processes are compared with the available state-to-state scattering experiments at E(c.m.)=20 eV. The results are in overall good agreement with most of the observed scattering features such as rainbow positions, integral cross sections, and relative vibrational energy transfers. A comparison with the earlier theoretical study carried out on the semiempirical surfaces (diatomics in molecules) is also made to illustrate the reliability of the potential energy surfaces used in the present work.