Molecular potential-energy surfaces by interpolation: Further refinements

A moving interpolation technique which provides an accurate representation of potential energy surfaces for polyatomic molecules is presented. The method uses the ab initio energy, energy gradient, and second derivatives calculated at dynamically important configurations. The interpolant of the energy and its derivatives converges to the exact value with increasing number of data. A procedure is given for finding the optimum configurations at which ab initio calculations are performed. The method is demonstrated by application to the six-dimensional surface of a diatomic plus diatomic reaction.

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.

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.

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.

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

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.

Linear scaling methods for density-functional theory (DFT) simulations are formulated in terms of localised orbitals in real-space, rather than the delocalised eigenstates of conventional approaches. In local-orbital methods, relative to conventional DFT, desirable properties can be lost to some extent, such as the translational invariance of the total energy of a system with respect to small displacements and the smoothness of the potential energy surface. This has repercussions for calculating accurate ionic forces and geometries. In this work we present results from \textsc{onetep}, our linear scaling method based on localised orbitals in real-space. The use of psinc functions for the underlying basis set and on-the-fly optimisation of the localised orbitals results in smooth potential energy surfaces that are consistent with ionic forces calculated using the Hellmann-Feynman theorem. This enables accurate geometry optimisation to be performed. Results for surface reconstructions in silicon are presented, along with three example systems demonstrating the performance of a quasi-Newton geometry optimisation algorithm: an organic zwitterion, a point defect in an ionic crystal, and a semiconductor nanostructure.

Towards efficient refinement of molecular potential energy surfaces: Ammonia as a case study

The room temperature conversion of gaseous methanol to carbon monoxide and hydrogen on a polycrystalline Au film at ambient pressure has been triggered and characterized by oxygen K-edge excitation and vibrationally resolved resonant inelastic X-ray scattering. The rate-limiting first methanol dehydrogenation step is driven by ultrafast O-H dissociation and deprotonation of O K-edge excited CH3OH. The Au surface further dehydrogenates the CH3O+ photoradical created by X-rays via electron transfer from the Au surface. With vibrationally resolved resonant inelastic X-ray scattering, we trace the CO molecular potential energy surface along the C-O coordinate. The CO bond softens, and the C-O stretch frequency changes from 2250 to 2065 cm-1 at a CO chemisorption energy of 38-58 kJ/mol. This constitutes weak chemisorption as compared to the transition metals but also stronger bonding than the physisorbed CO species on single-crystal Au surfaces. In liquid methanol, the recombination of the CH3O+ photoradical created by X-rays with protons quenches this conversion.

Symmetry Rules for Chemical Reactions: Orbital Topology and Elementary Processes. By R. G. Pearson. Pp. ix + 548. (Wiley-Interscience, New York and London, 1976.) $31; £17.50.

The ground states of MH2, HMHe+ and MHe2(2+) (M = Mg, Ca) have been investigated using relativistically-corrected CCSD(T), IC-MRCI and IC-MRCI+Q, in conjunction with ANO-RCC (Mg, Ca) and aug-cc-pVQZ (H, He) basis sets. The ground states of all magnesium species are predicted to be linear, in agreement with predicted trends. Conversely, HCaHe+ and CaHe2(2+) were determined to be quasi-linear species, with linear-inversion barriers of ca. 115 and 3 cm(-1), respectively. For CaH2, a stationary point on the molecular potential energy surface corresponding to a non-linear equilibrium structure was not observed. Trends in bonding, dissociative potential well-depths and spectroscopic constants for these species have been considered with regards to isoelectronic and isovalent reasoning. These trends are consistent with helium and hydrogen forming electrostatic and covalent bonds with the metal ion, respectively.

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

The treatment of the solvation charges using Gaussian functions in the polarizable continuum model results in a smooth potential energy surface. These charges are placed on top of the surface of the solute cavity. In this article, we study the effect of the solute cavity (van der Waals-type or solvent-excluded surface-type) using the Gaussian charge scheme within the framework of the conductor-like polarizable continuum model on (a) the accuracy and computational cost of the self-consistent field (SCF) energy and its gradient and on (b) the calculation of free energies of solvation. For that purpose, we have considered a large set of systems ranging from few atoms to more than 200 atoms in different solvents. Our results at the DFT level using the B3LYP functional and the def2-TZVP basis set show that the choice of the solute cavity does neither affect the accuracy nor the cost of calculations for small systems (< 100 atoms). For larger systems, the use of a vdW-type cavity is recommended, as it prevents small oscillations in the gradient (present when using a SES-type cavity), which affect the convergence of the SCF energy gradient. Regarding the free energies of solvation, we consider a solvent-dependent probe sphere to construct the solvent-accessible surface area required to calculate the nonelectrostatic contribution to the free energy of solvation. For this part, our results for a large set of organic molecules in different solvents agree with available experimental data with an accuracy lower than 1 kcal/mol for both polar and nonpolar solvents.

A heterogeneous conductorlike solvation model (conductorlike screening model/conductorlike polarizable continuum model) that uses different local effective dielectrics for different portions of the solute cavity surface is implemented for quantum chemical Hartree-Fock and Kohn-Sham methods. A variational treatment is used to form the heterogeneous solvation operator, so a simple analytic expression of the energy gradients, which are vital for geometry optimization and molecular dynamics simulation, is derived and implemented. Using the new Fixed Points with Variable Areas surface tessellation scheme, continuous and smooth potential energy surfaces as well as analytic gradients are obtained for this heterogeneous model. Application of the heterogeneous solvation model to a realistic quantum model consisting of 101 atoms for the type-1 Cu center in rusticyanin shows that the desolvation due to protein burial can likely raise the reduction potential by approximately 200 mV and, including the heterogeneity in geometry optimization, can likely affect the results by approximately 2 kcal/mol or approximately 70 mV.