Cis-->trans, trans-->cis isomerizations and N-O bond dissociation of nitrous acid (HONO) on an ab initio potential surface obtained by novelty sampling and feed-forward neural network fitting

The isomerization and dissociation dynamics of HONO are investigated on an ab initio potential surface obtained by fitting the results of electronic structure calculations at 21 584 configurations by using previously described novelty sampling and feed-forward neural network (NN) methods. The electronic structure calculations are executed by using GAUSSIAN 98 with a 6-311G(d) basis set at the MP4(SDQ) level of accuracy. The average absolute error of the NN fits varies from 0.012 eV (1.22 kJ mol(-1)) to 0.017 eV (1.64 kJ mol(-1)). The average computation time for a HONO trajectory using a single NN surface is approximately 4.8 s. These computation times compare very favorably with those required by other methods primarily because the NN fitting needs to be executed only one time rather than at every integration point. If the average result obtained from a committee of NNs is employed at each point rather than a single NN, increased fitting accuracy can be achieved at the expense of increased computational requirements. In the present investigation, we find that a committee comprising five NN potentials reduces the average absolute interpolation error to 0.0111 eV (1.07 kJ mol(-1)). Cis-trans isomerization rates with total energy of 1.70 eV (including zero point energy) have been computed for a variety of different initial distributions of the internal energy. In contrast to results previously reported by using an empirical potential, where cis-->trans to trans-->cis rate coefficient ratios at 1.70 eV total energy were found to lie in the range of 2.0-12.9 depending on the vibration mode excited, these ratios on the ab initio NN potential lie in the range of 0.63-1.94. It is suggested that this result is a reflection of much larger intramode coupling terms present in the ab initio potential surface. A direct consequence of this increased coupling is a significant decrease in the mode specific rate enhancement when compared to results obtained by using empirical surfaces. All isomerizations are found to be first order in accordance with the results reported by using empirical potentials. The dissociation rate to NO+OH has been investigated at internal HONO energies of 3.10 and 3.30 eV for different distributions of this energy among the six vibrational modes of HONO. These dissociations are also found to be first order. The computed dissociation rate coefficients exhibit only modest mode specific rate enhancement that is significantly smaller than that obtained on an empirical surface because of the much larger mode couplings present on the ab initio surface.     

Ab initio rate constants from hyperspherical quantum scattering: application to H + CH4 --> H2 + CH3

A general and practical procedure is described for calculating rate constants for chemical reactions using a minimal number of ab initio calculations and quantum-dynamical computations. The method exploits a smooth interpolating functional developed in the hyperspherical representation. This functional is built from two Morse functions and depends on a relatively small number of parameters with respect to conventional functionals developed to date. Thus only a small number of ab initio points needs to be computed. The method is applied to the H + CH4 --> H2 + CH3 reaction. The quantum scattering calculations are performed treating explicitly the bonds being broken and formed. All the degrees of freedom except the breaking and forming bonds are optimized ab initio and harmonic vibrational frequencies and zero-point energies for them are calculated at the MP2(full) level with a cc-pVTZ basis set. Single point energies are calculated at a higher level of theory with the same basis set, namely CCSD(T, full). We report state-to-state cross sections and thermal rate constants for the title reaction and make comparisons with previous results. The calculated rate constants are in good agreement with experiments.     

An interaction potential between an alanine zwitterion and a water molecule based on ab initio calculations

Interaction energies between an alanine zwitterion and a water molecule at 150 different positions and orientations have been calculated using the ab initio method with the minimal basis set and employing the counterpoise method to eliminate the basis set superposition error. Dispersion energies are estimated using the Slater–Kirkwood formula. Out of a total of 150 computed interaction energies, 140 whose SCF interaction energies are below 5 kcal/mol have been fitted with a summation of atom-atom pair potentials in the form of the Lennard–Jones potential plus an electrostatic term. The standard deviation for this fitting is 0.49 kcal/mol. A sampling scheme regarding geometrical configurations is presented. Twenty rays are uniformly drawn from the origin of coordinates, a floatable division with equal ratios is made along each ray, and one of 60 orientations is randomly taken as the orientation of a water molecule. A nonlinear fitting method is used with a restriction on the sign change of fitting coefficients.     

Molecular dynamics investigations of the dissociation of SiO2 on an ab initio potential energy surface obtained using neural network methods

The neural network (NN) procedure to interpolate ab initio data for the purpose of molecular dynamics (MD) simulations has been tested on the SiO(2) system. Unlike other similar NN studies, here, we studied the dissociation of SiO(2) without the initial use of any empirical potential. During the dissociation of SiO(2) into Si+O or Si+O(2), the spin multiplicity of the system changes from singlet to triplet in the first reaction and from singlet to pentet in the second. This paper employs four potential surfaces. The first is a NN fit [NN(STP)] to a database comprising the lowest of the singlet, triplet, and pentet energies obtained from density functional calculations in 6673 nuclear configurations. The other three potential surfaces are obtained from NN fits to the singlet, triplet, and pentet-state energies. The dissociation dynamics on the singlet-state and NN(STP) surfaces are reported. The results obtained using the singlet surface correspond to those expected if the reaction were to occur adiabatically. The dynamics on the NN(STP) surface represent those expected if the reaction follows a minimum-energy pathway. This study on a small system demonstrates the application of NNs for MD studies using ab initio data when the spin multiplicity of the system changes during the dissociation process.     

Ab initio vibrational predissociation dynamics of He-I2(B) complex

Three-dimensional quantum mechanical calculations on the vibrational predissociation dynamics of HeI2 B state complex are performed using a potential energy surface accurately fitted to unrestricted open-shell coupled cluster ab initio data, further enabling extrapolation for large I2 bond lengths. A Lanczos iterative method with an optimized complex absorbing potential is used to determine energies and lifetimes of the vibrationally predissociating He,I2(B,v') complex for v'相似文献   

On the use of optimal internal vibrational coordinates for symmetrical bent triatomic molecules

The use of generalized internal coordinates for the variational calculation of excited vibrational states of symmetrical bent triatomic molecules is considered with applications to the SO2, O3, NO2, and H2O molecules. These coordinates depend on two external parameters which can be properly optimized. We propose a simple analytical method to determine the optimal internal coordinates for this kind of molecules based on the minimization with respect to the external parameters of the zero-point energy, assuming only quadratic terms in the Hamiltonian and no quadratic coupling between the optimal coordinates. The optimal values of the parameters thus obtained are shown to agree quite well with those that minimize the sum of a number of unconverged energies of the lowest vibrational states, computed variationally using a small basis function set. The unconverged variational calculation uses a basis set consisting of the eigenfunctions of the uncoupled anharmonic internal coordinate Hamiltonian. Variational calculations of the excited vibrational states for the four molecules considered carried out with an increasing number of basis functions, also evidence the excellent convergence properties of the optimal internal coordinates versus those provided by other normal and local coordinate systems.     

Polarizable Atomic Multipole-based Molecular Mechanics for Organic Molecules

An empirical potential based on permanent atomic multipoles and atomic induced dipoles is reported for alkanes, alcohols, amines, sulfides, aldehydes, carboxylic acids, amides, aromatics and other small organic molecules. Permanent atomic multipole moments through quadrupole moments have been derived from gas phase ab initio molecular orbital calculations. The van der Waals parameters are obtained by fitting to gas phase homodimer QM energies and structures, as well as experimental densities and heats of vaporization of neat liquids. As a validation, the hydrogen bonding energies and structures of gas phase heterodimers with water are evaluated using the resulting potential. For 32 homo- and heterodimers, the association energy agrees with ab initio results to within 0.4 kcal/mol. The RMS deviation of hydrogen bond distance from QM optimized geometry is less than 0.06 ?. In addition, liquid self-diffusion and static dielectric constants computed from molecular dynamics simulation are consistent with experimental values. The force field is also used to compute the solvation free energy of 27 compounds not included in the parameterization process, with a RMS error of 0.69 kcal/mol. The results obtained in this study suggest the AMOEBA force field performs well across different environments and phases. The key algorithms involved in the electrostatic model and a protocol for developing parameters are detailed to facilitate extension to additional molecular systems.     

A nested molecule-independent neural network approach for high-quality potential fits

It is shown that neural networks (NNs) are efficient and effective tools for fitting potential energy surfaces. For H2O, a simple NN approach works very well. To fit surfaces for HOOH and H2CO, we develop a nested neural network technique in which we first fit an approximate NN potential and then use another NN to fit the difference of the true potential and the approximate potential. The root-mean-square error (RMSE) of the H2O surface is 1 cm(-1). For the 6-D HOOH and H2CO surfaces, the nested approach does almost as well attaining a RMSE of 2 cm(-1). The quality of the NN surfaces is verified by calculating vibrational spectra. For all three molecules, most of the low-lying levels are within 1 cm(-1) of the exact results. On the basis of these results, we propose that the nested NN approach be considered a method of choice for both simple potentials, for which it is relatively easy to guess a good fitting function, and complicated (e.g., double well) potentials for which it is much harder to deduce an appropriate fitting function. The number of fitting parameters is only moderately larger for the 6-D than for the 3-D potentials, and for all three molecules, decreasing the desired RMSE increases only slightly the number of required fitting parameters (nodes). NN methods, and in particular the nested approach we propose, should be good universal potential fitting tools.     

Interpolating moving least-squares methods for fitting potential energy surfaces: a strategy for efficient automatic data point placement in high dimensions

An accurate and efficient method for automated molecular global potential energy surface (PES) construction and fitting is demonstrated. An interpolating moving least-squares (IMLS) method is developed with the flexibility to fit various ab initio data: (1) energies, (2) energies and gradients, or (3) energies, gradients, and Hessian data. The method is automated and flexible so that a PES can be optimally generated for trajectories, spectroscopy, or other applications. High efficiency is achieved by employing local IMLS in which fitting coefficients are stored at a limited number of expansion points, thus eliminating the need to perform weighted least-squares fits each time the potential is evaluated. An automatic point selection scheme based on the difference in two successive orders of IMLS fits is used to determine where new ab initio data need to be calculated for the most efficient fitting of the PES. A simple scan of the coordinate is shown to work well to identify these maxima in one dimension, but this search strategy scales poorly with dimension. We demonstrate the efficacy of using conjugate gradient minimizations on the difference surface to locate optimal data point placement in high dimensions. Results that are indicative of the accuracy, efficiency, and scalability are presented for a one-dimensional model potential (Morse) as well as for three-dimensional (HCN), six-dimensional (HOOH), and nine-dimensional (CH4) molecular PESs.     

Potential energy functions of polyatomic molecules

A direct method is proposed for determining polyatomic potential energy functions, expressed in terms of normal coordinates, which yield a given set of vibrational excitation energies. The method is a modification of the semiclassical technique for computing vibrational energy levels of Percival and Pomphrey. The technique is used to derive potential functions for the NO₂, SO₂ and ClO₂ molecules. With these potentials twenty two higher vibrational excitations energies have been predicted for these molecules and these results differ from the experimental values by at most 3 cm^?1. The computed potential functions are not unique despite the apparent accuracy of the vibrational energy levels. Comparison with the RKR method indicates that the present method must be extended to include rotational perturbations.     

Searching for globally optimal functional forms for interatomic potentials using genetic programming with parallel tempering

Molecular dynamics and other molecular simulation methods rely on a potential energy function, based only on the relative coordinates of the atomic nuclei. Such a function, called a force field, approximately represents the electronic structure interactions of a condensed matter system. Developing such approximate functions and fitting their parameters remains an arduous, time-consuming process, relying on expert physical intuition. To address this problem, a functional programming methodology was developed that may enable automated discovery of entirely new force-field functional forms, while simultaneously fitting parameter values. The method uses a combination of genetic programming, Metropolis Monte Carlo importance sampling and parallel tempering, to efficiently search a large space of candidate functional forms and parameters. The methodology was tested using a nontrivial problem with a well-defined globally optimal solution: a small set of atomic configurations was generated and the energy of each configuration was calculated using the Lennard-Jones pair potential. Starting with a population of random functions, our fully automated, massively parallel implementation of the method reproducibly discovered the original Lennard-Jones pair potential by searching for several hours on 100 processors, sampling only a minuscule portion of the total search space. This result indicates that, with further improvement, the method may be suitable for unsupervised development of more accurate force fields with completely new functional forms.     

Full-dimensional quantum dynamics study of vinylidene-acetylene isomerization: a scheme using the normal mode Hamiltonian

Full-dimensional quantum dynamics calculations of vinylidene-acetylene isomerization are performed and the state-specific resonance decay lifetimes of vinylidene(-d(2)) are computed. The theoretical scheme is a combination of several methods: normal coordinates are chosen to describe the nuclear motion of vinylidene, with both the parity and permutation symmetry exploited; phase space optimization in combination with physical considerations is used to generate an efficient discrete variable representation; the reaction coordinate is defined by us according to the three most relevant normal coordinates, along which a kind of optimal complex absorbing potential is imposed; the preconditioned inexact spectral transform method combined with an efficient preconditioner is employed to extract the energies and lifetimes of vinylidene. The overall computation is efficient. The computed energy levels generally agree with experiment well, and several state-specific lifetimes are reported for the first time.     

Using redundant coordinates to represent potential energy surfaces with lower-dimensional functions

We propose a method for fitting potential energy surfaces with a sum of component functions of lower dimensionality. This form facilitates quantum dynamics calculations. We show that it is possible to reduce the dimensionality of the component functions by introducing new and redundant coordinates obtained with linear transformations. The transformations are obtained from a neural network. Different coordinates are used for different component functions and the new coordinates are determined as the potential is fitted. The quality of the fits and the generality of the method are illustrated by fitting reference potential surfaces of hydrogen peroxide and of the reaction OH+H(2)-->H(2)O+H.     

An overlap fitted chain of spheres exchange method

The "chain of spheres" (COS) algorithm, as part of the RIJCOSX SCF procedure, approximates the exchange term by performing analytic integration with respect to the coordinates of only one of the two electrons, whereas for the remaining coordinates, integration is carried out numerically. In the present work, we attempt to enhance the efficiency of the method by minimizing numerical errors in the COS procedure. The main idea is based on the work of Friesner and consists of finding a fitting matrix, Q, which leads the numerical and analytically evaluated overlap matrices to coincide. Using Q, the evaluation of exchange integrals can indeed be improved. Improved results and timings are obtained with the present default grid setup for both single point calculations and geometry optimizations. The fitting procedure results in a reduction of grid sizes necessary for achieving chemical accuracy. We demonstrate this by testing a number of grids and comparing results to the fully analytic and the earlier COS approximations. This turns out to be favourable for total and reaction energies, for which chemical accuracy can now be reached with a corresponding ~30% speedup over the original RIJCOSX procedure for single point energies. Results are slightly less favourable for the accuracy of geometry optimizations, but the procedure is still shown to yield geometries with errors well below the method inherent errors of the employed theoretical framework.     

Density functional theory study on molecular structure and vibrational IR spectra of isocytosine

Density functional theory with the combined Becke3-LYP exchange-correlation energy functional [DFT(B3-LYP) method] using the 6-31G(d, p) basis set is applied to predict molecular parameters (geometries, rotational constants, dipole moments) and vibrational IR spectra (harmonic wavenumbers, absolute intensities) of six tautomers of the isocytosine molecule. The results are compared with the corresponding data calculated at the conventional ab initio Hartree-Fock (HF) level using the same basis set and with available experimental data. Calculations show that (a) three amino tautomers are slightly nonplanar species with, evidently, a distorted amino group, (b) the DFT (B3-LYP)/6-31G(d, p) method predicts better molecular parameters, than do the HF calculations, and (c) the DFT(B3-LYP)-calculated vibrational IR spectra of isocytosine agree well with the available recorded IR spectra, and they show marked improvement over the IR spectra predicted at the HF/6-31G(d, p) level. Tautomeric stabilities of isocytosine are discussed on the basis of computed electronic energies by the DFT(B3-LYP) and ab initio approaches [including the MP2 and MP4(SDQ) calculations of electronic energies] and predicted zero-point vibrational energies by DFT(B3-LYP) and HF methods. This relative energies at 0 K of the tautomeric forms of isocytosine predicted by both conventional ab initio and DFT(B3-LYP) methods correlate well with the experimental data, showing the predominance of the aminohydroxy tautomer of isocytosine for an isolated molecule. © 1997 John Wiley & Sons, Inc.     

Explicitly correlated local second-order perturbation theory with a frozen geminal correlation factor

The recently introduced MP2-R122*A(loc) and LMP2-R122*A(loc) methods are modified to use a short-range correlation factor expanded as a fixed linear combination of Gaussian geminals. Density fitting is used to reduce the effort for integral evaluation, and local approximations are introduced to improve the scaling of the computational resources with molecular size. The MP2-F122*A(loc) correlation energies converge very rapidly with respect to the atomic orbital basis set size. Already with the aug-cc-pVTZ basis the correlation energies computed for a set of 21 small molecules are found to be within 0.5% of the MP2 basis set limit. Furthermore the short-range correlation factor leads to an improved convergence of the resolution of the identity, and eliminates problems with long-range errors in density fitting caused by the linear r12 factor. The DF-LMP2-F122*A(loc) method is applied to compute second-order correlation energies for molecules with up to 49 atoms and more than 1600 basis functions.     

Potential functions for alkali halide molecules

Repulsion and dispersion parameters for alkali–metal halide diatomic molecules were computed by ionic Rittner and truncated Rittner models with radial dependent repulsion terms. Experimental data on the bond energies, the equilibrium interionic distances, and the spectroscopic frequencies were employed for the purpose. The polarizabilities used were also computed from the experimental dipole moments of alkali–metal halides. The potential parameters obtained were compared with parameters from other sources and checked for consistency. The computed potential parameters of alkali–metal halide monomer molecules were used to predict the energetics and geometries for alkali–metal halide dimer molecules. The predicted values are in good agreement with experiment and other calculations indicating the consistency and reliability of the potential employed. Although the magnitude of repulsive and dispersive energy terms varies with potential functions employed, the difference between the two for a molecule is constant. The repulsive term is more sensitive than the attractive term. The uncertainty in the exponential repulsion results in an inaccurate representation of the attractive contribution. Introduction of the radial-dependent repulsion term changes the relative magnitudes of repulsive and dispersive parameters and hence the relative contribution to the total potential with monomers. But this has no significant effect on the energetics and geometries of the dimers.     

An SCF-CI method for determining the potential energy surface of a triatomic molecule

A self-consistent-field (SCF)-configuration interaction (CI) (SCF-CI) method for determining the potential energy surface of a triatomic molecule from the observed vibrational band origins has been suggested. By this method, the SCF-CI procedure in the internal coordinates is used to calculate the vibrational bond origins and their first derivatives with respect to parameters in the potential energy function using the exact vibrational Hamiltonian, and the optimizer LMF in the nonlinear-squares problem is employed to optimize parameters in the potential energy function. This approach is used to optimize the potential energy function of the water molecule. The standard deviation of this fitting to the 70 observed band origins is 1.154cm-1.     

Computational study of water and ammonia dimers with density functional theory methods

The structures and energies for the dimerization of water and ammonia molecules were computed with density functional theory (DFT) and ab initio methods. For all studies the same 6-311+G(2d,2p) basis set was used. Two linear hydrogen-bonded and cyclic ammonia dimer structures were computed and their relative stability is discussed. From the systematic studies, hybrid DFT methods were selected as reliable for computing the parameters of these types of van der Waals' complex.     

Computational study of the rovibrational spectrum of (OCS)2

In this paper, we report a new intermolecular potential energy surface and rovibrational transition frequencies and line strengths computed for the OCS dimer. The potential is made by fitting energies obtained from explicitly correlated coupled-cluster calculations and fit using an interpolating moving least squares method. The rovibrational Schroedinger equation is solved with a symmetry-adapted Lanczos algorithm and an uncoupled product basis set. All four intermolecular coordinates are included in the calculation. On the potential energy surface we find, previously unknown, cross-shaped isomers and also polar and non-polar isomers. The associated wavefunctions and energy levels are presented. To identify polar and cross states we use both calculations of line strengths and vibrational parent analysis. Calculated rotational constants differ from their experimental counterparts by less than 0.001 cm(-1).