Molecular potential energy surfaces by interpolation

The use of ab initio quantum chemical methods to aid in the interpretation of resonance Raman spectra is illustrated with examples where the resonant electronic absorption spectra are unstructured. In such cases only the gradient of the excited electronic state potential energy surface at the ground electronic state geometry is important in determining the upper state dynamics that are relevant to the Raman scattering process. The use of ab initio methods for which analytic gradients are available permits application to large molecular systems and to cluster models of molecules in solution. This procedure eliminates possible ambiguities in the empirical interpretation of resonance Raman spectra. These same ab initio methods may be used to provide descriptions of the ground-state normal modes and the effect of isotopic substitution on the form of the normal modes. © 1998 John Wiley & Sons Ltd.

TheoReTS – An information system for theoretical spectra based on variational predictions from molecular potential energy and dipole moment surfaces

A new method for the representation of potential energy surfaces (PESs) based on the p version of the finite element method is presented and applied to the PES of the [COH2]+ system in order to study the C++H2O-->[COH]++H reaction through the quasiclassical trajectory method. Benchmark ab initio computations have been performed on the most relevant stationary points of the PES through a procedure that incorporates basis set extrapolations, the contribution of the core correlation energy, and scalar relativistic corrections. The electronic structure method employed to compute the many points needed to construct the PES is a hybrid density functional approach of the B3LYP type with geometry-dependent parameters, which improves dramatically the performance with respect of the B3LYP method. The trajectory computations shed light on the behavior of the COH2+ complex formed in the collision. At a fixed relative translational energy of 0.62 eV, which corresponds to the crossed beam experiments [D. M. Sonnenfroh et al., J. Chem. Phys. 83, 3985 (1985)], the complex dissociates significantly into the reactants (37%). However, the behavior for a thermal sampling at T=300 K is significantly different because only 9% of the trajectories where capture occurs lead to dissociation into the reactants. The latter kind of behavior is coherent with the view that simple ion-molecule reactions proceed quite often at the capture rate provided it is corrected by the fraction of the electronic states which, being nearly degenerate for the reactants, become attractive at short distances. For both T=300 K and crossed beam conditions, the trajectory computations indicate that COH2+ is the critical intermediate, in agreement with a recent work [Y. Ishikawa et al., Chem. Phys. Lett. 370, 490 (2003)] and in contrast with the interpretation of the crossed beam experiments. Besides, virtually all trajectories generate COH++H (>99%), but a significant proportion of the isoformyl cation is formed with enough vibrational energy as to surmount the COH+-HCO+ isomerization barrier, about 37% at T=300 K.

We propose a method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing. The method is useful for studies involving large numbers of PES evaluations, such as the search for local minima, transition states, or integration. We apply this method for estimating zero point energies and frequencies of molecules using a three step approach. In the first step, we interpret the PES as a sparse tensor on polynomial basis and determine its entries by a compressed sensing based algorithm using only a few PES evaluations. Then, we implement a rank reduction strategy to compress this tensor in a suitable low-rank canonical tensor format using standard tensor compression tools. This allows representing a high dimensional PES as a small sum of products of one dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate the product of sparse canonical low-rank representation of PES and Green’s function in the second-order diagrammatic vibrational many-body Green’s function theory (XVH2) for estimation of zero-point energies and frequencies. Numerical tests on molecules considered in this work suggest a more efficient scaling of computational cost with molecular size as compared to other methods.

The full configuration interaction quantum Monte Carlo (FCIQMC) is a state-of-the-art stochastic electronic structure method, providing a methodology to compute FCI-level state energies of molecular systems within a quantum chemical basis. However, especially to probe dynamics at the FCIQMC level, it is necessary to devise more efficient schemes to produce nuclear forces and potential energy surfaces (PES) from FCIQMC. In this work, we derive the general formula for nuclear forces from FCIQMC, and clarify different contributions of the total force. This method to obtain FCIQMC forces eliminates previous restrictions and can be used with frozen core approximation and free selection of orbitals, making it promising for more efficient nuclear forces calculations. After some numerical checks of this procedure on the binding curve of N2 molecule, we use the FCIQMC energy and force to obtain the full-dimensional ground state PES of the water molecule via Gaussian processes regression. The new water FCIQMC PES can be used as the basis for H2O ground state nuclear dynamics, structure optimization, and rotation-vibrational spectrum calculation.

This paper introduces a fully symmetrized Hamiltonian formalism designed for description of vibrational motion in ammonia (and any XH3 molecule). A major feature of our approach is the introduction of complex basis vibrational wavefunctions in product form, satisfying the complex symmetry species (CSS) of the molecular symmetric top point group (D 3h). The described formalism for ammonia is an adaptation of the approach, previously developed and applied to benzene, based on the CSS of the point group D 6h. The molecular potential energy surface (PES) is presented in the form of a Taylor series expansion around the planar equilibrium state. Using the described formalism, calculations have been carried out on the vibrational overtone and combination levels in 14NH3 up to vibrational excitation energies corresponding to the fourth N-H stretch overtone. The results from the calculations are adjusted to experimentally measured data, in order to determine the values of the harmonic and some anharmonic force constants of the molecular PES.

A molecular potential energy surface may be approximately described in terms of the energy, energy gradients, and second derivatives at a discrete set of points along a reaction path. The accuracy of this approach is limited, in part, by the level of ab initio theory that can be employed to obtain energy gradients and second derivatives. A method is derived and demonstrated whereby the energy surface can be scaled to achieve a greater degree of accuracy, using a set of energies calculated at a higher level of ab initio theory.

In this paper, we discuss the applications of spherical and hyperspherical harmonics expansions for potential energy surfaces for intermolecular interactions, focusing on four- and five-body problems. Case studies include diatomic-molecule–diatomic-molecule systems, floppy-molecule–rare-gas-atom cases, atom–triatomic, and nonlinear-molecule–linear-molecule systems. Among these systems, the important ones regarding water interaction with atoms and diatomic molecules are presented here to illustrate the use of spherical and hyperspherical coordinates and harmonics for weakly interacting systems. The interaction potential representation involves the distance between the centers of mass of the two molecules and a set of angles that defines the mutual orientation of the molecules, whose geometries are assumed to be either ‘frozen’ in their equilibrium configurations or to vary according to specific large-amplitude modes. The potential energy surfaces in the given examples of water–hydrogen, nitrogen and oxygen interactions are generated at the CCSD(T)/aug-cc-pVTZ level. Comparisons to the theoretical and experimental results of recent works for these and similar systems are presented.

A new method for the expansion of potential energy surfaces has been developed exploiting the peculiar properties of Hahn polynomials, a class of orthogonal polynomials of a discrete variable which generalize 3j vector coupling coefficients of angular momentum algebra. The method has been tested for the Hénon–Heiles potential, a typical model for coupled oscillators, and applied to the representation of the potential energy surface of malonaldehyde, a prototype system for intramolecular proton transfer in polyatomic molecules. The representation is obtained by fitting the polynomial expansion to a set of points calculated by the density functional theory method on a hyperspherical effective three-center coordinate system, in view of perspective quantum dynamical calculations of the proton transfer process.

Preface 1. Overview: Accurate Description of Low-Lying Electronic States and Potential Energy Surfaces 2. Simultaneous Account of Dynamic and Nondynamic Correlations Based on Complementarity of CI and CC Approaches 3. Method of Moments of Coupled-Cluster Equations: A New Theoretical Framework for Designing Black-Box Approaches for Molecular Potential Energy Surfaces 4. The Photoelectron Spectrum of the NO3 Radical Revisited: A Theoretical Investigation of Potential Energy Surfaces and Conical Intersections 5. Coupled Cluster Methods for Bond-Breaking 6. State-Specific Multireference Coupled Cluster-Based Methods for Potential Energy Surfaces and Their Approximate Variants 7. The Excited and Ion States of Allene 8. Hamiltonian Matrix Elements for the Table-CI Method Using Genealogical Configuration State Functions 9. Jacob's Ladder for Time-Dependent Density-Functional Theory: Some Rungs on the Way to Photochemical Heaven 10. Spectral Theory of Chemical Bonding 11. Comparison of CaF, ZnF, CaO, and ZnO: Their Anions and Cations in Their Ground and Low-Lying Excited States 12. The X1(2(3/2) and X2(2(1/2) Potentials of the Halogen Monoxides: A Comparison of RKR and Ab Initio Results 13. Symmetry in Spin-Orbit Coupling 14. Non-Adiabatic Bending Dissociation of OCS Induced by Orbital Unlocking 15. Electronic Structure and Dynamics in the O4 System 16. Model Studies of Intersystem Crossing Effects in the O + H2 Reaction 17. The Challenge of High-Resolution Dynamics: Rotationally Mediated Unimolecular Dissociation of HOCl 18. The Electronic Adiabatic-to-Diabatic Transformation Matrix and the Irreducible Representation of the Rotation Group 19. Spectroscopic Determination of Potential Energy Surfaces for the Out-of-Plane Ring Vibrations of Indan and Related Molecules in Their S0 and S1 ((, (*) States 20. Semiclassical Time Evolution in the Forward-Backward Stationary-Phase Limit 21. Development and Application of an Ab Initio Methane-Water Potential for the Study of Phase Equilibria of Methane Hydrates Indexes Author Index Subject Index

K. C. Thompson and M. A. Collins, J. Chem. Soc., Faraday Trans., 1997, 93, 871 DOI: 10.1039/A606038B

A general interpolation method for constructing smooth molecular potential energy surfaces (PES’s) from ab initio data are proposed within the framework of the reproducing kernel Hilbert space and the inverse problem theory. The general expression for an a posteriori error bound of the constructed PES is derived. It is shown that the method yields globally smooth potential energy surfaces that are continuous and possess derivatives up to second order or higher. Moreover, the method is amenable to correct symmetry properties and asymptotic behavior of the molecular system. Finally, the method is generic and can be easily extended from low dimensional problems involving two and three atoms to high dimensional problems involving four or more atoms. Basic properties of the method are illustrated by the construction of a one-dimensional potential energy curve of the He–He van der Waals dimer using the exact quantum Monte Carlo calculations of Anderson et al. [J. Chem. Phys. 99, 345 (1993)], a two-dimensional potential energy surface of the HeCO van der Waals molecule using recent ab initio calculations by Tao et al. [J. Chem. Phys. 101, 8680 (1994)], and a three-dimensional potential energy surface of the H+3 molecular ion using highly accurate ab initio calculations of Röhse et al. [J. Chem. Phys. 101, 2231 (1994)]. In the first two cases the constructed potentials clearly exhibit the correct asymptotic forms, while in the last case the constructed potential energy surface is in excellent agreement with that constructed by Röhse et al. using a low order polynomial fitting procedure.

In Z-dependent perturbation theory, the lowest-order wave functions for a polyatomic molecule are not only independent of the nuclear charges, but also of the total number of nuclear centers and electrons in the molecule. The complexity of the problem is then determined by the highest order retained in the calculation. Choosing the simplest possible unperturbed Hamiltonian, we describe an n-electron, m-center polyatomic molecule as n ‘‘hydrogenic’’ electrons on a single center perturbed by electron–electron and electron–nucleus Coulomb interactions. With this H0, the first-order wave function for any polyatomic molecule will be a sum of products of hydrogenic orbitals with either two-electron, one-center or one-electron, two-center first-order wave functions. These first-order wave functions are obtained from calculations on He-like and H+2-like systems. Similarly, the nth-order wave function decouples so that the most complex terms are just the nth-order wave functions of all the p-electron, q-center subsystems (p+q=n+2) contained in the molecule. We illustrate applications of this method with some results, complete through third order in the energy, for H+3-like molecules. These are compared with accurate variational results available in the literature. We conclude that, through this order, this perturbation approach is capable of yielding results comparable in accuracy to variational calculations of moderate complexity. The ease and efficiency with which such results can be obtained suggests that this method would be useful for generating detailed potential energy surfaces for polyatomic molecules.

This review covers the multiconfiguration time‐dependent Hartree (MCTDH) method, which is a powerful and general algorithm for solving the time‐dependent Schrödinger equation. The formal derivation is discussed as well as applications of the method. Recent extensions of MCTDH are treated in brief, namely, MCTDHB and MCTDHF, for treating identical particles (bosons and fermions), and the very powerful multilayer (ML‐MCTDH) formalism. Compact representations of potential energy surfaces (PESs) are also discussed, as the representation of a PES becomes a major bottleneck when going to larger systems (nine or more dimensions) while employing a full‐dimensional, complicated, and nonseparable PES. As applications of MCTDH, we discuss the calculation of photoionization and photoexcitation spectra of the vibronically coupled systems butatriene and pyrazine, respectively, and the infra‐red spectrum of the Zundel cation (protonated water dimer) H5O+2. © 2011 John Wiley & Sons, Ltd.This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics

The floating occupation molecular orbital-complete active space configuration interaction (FOMO-CASCI) method is a promising alternative to the state-averaged complete active space self-consistent field (SA-CASSCF) method. We have formulated the analytic first derivative of FOMO-CASCI in a manner that is well-suited for a highly efficient implementation using graphical processing units (GPUs). Using this implementation, we demonstrate that FOMO-CASCI gradients are of similar computational expense to configuration interaction singles (CIS) or time-dependent density functional theory (TDDFT). In contrast to CIS and TDDFT, FOMO-CASCI can describe multireference character of the electronic wavefunction. We show that FOMO-CASCI compares very favorably to SA-CASSCF in its ability to describe molecular geometries and potential energy surfaces around minimum energy conical intersections. Finally, we apply FOMO-CASCI to the excited state hydrogen transfer reaction in methyl salicylate.