Expansion Potential Energy Surface Research Articles

Adaptive density-guided approach to double incremental potential energy surface construction

We present a combination of the recently developed double incremental expansion of potential energy surfaces with the well-established adaptive density-guided approach to grid construction. This unique methodology is based on the use of an incremental expansion for potential energy surfaces, known as n-mode expansion; an incremental many-body representation of the electronic energy; and an efficient vibrational density-guided approach to automated determination of grid dimensions and granularity. The reliability of the method is validated calculating potential energy surfaces and obtaining fundamental excitation energies for three moderate-size chain-like molecular systems. The use of our methodology leads to considerable computational savings for potential energy surface construction compared to standard approaches while maintaining a high level of accuracy in the resulting potential energy surfaces. Additional investigations indicate that our method can be applied to covalently bound and strongly interacting molecular systems, even though these cases are known to be very unfavorable for fragmentation schemes. We therefore conclude that the presented methodology is a robust and flexible approach to potential energy surface construction, which introduces considerable computational savings without compromising the accuracy of vibrational spectra calculations.

Globally accurate potential energy surface for PH2 + (11 A′) by using the switching function formalism

As an intermediate product of phosphorus compounds in astrophysical chemistry, has great significance in research on the systems. However, as a basis for studying its reaction mechanisms, lacks an accurate global potential energy surface (PES) and related dynamic reports. In this investigation, based on a multi-reference configuration interaction approach with Davidson correction, an accurate global many-body expansion PES for in its ground state was reported by fitting extensive ab initio energies, as calculated with the correlation-consistent basis set aug-cc-pVQZ. Meanwhile, the switching function formalism was adopted to explain and distinguish the transformation between and in one-body energy terms, which ensured the correct dissociation channel in the reaction process of . The topographical characteristics of the title system PES were meticulously contrasted with those in other literature reports, which were consistent with previous experimental and theoretical values. Subsequently, the time-dependent wave packet approach was adopted to calculate the reaction probability and integral cross-section for the reaction to verify the accuracy of the new PES. This dynamics study may help to further explain the thermochemical reactions of phosphorus-containing molecules in interstellar media.

Isotope Effect of the Stereodynamics for the Reactions N(<sup>4</sup>S)+HD→NH+D and N(<sup>4</sup>S)+HD→ND+H

Quasi-classical trajectory calculations have been employed to investigate the influence of isotope effect on the stereodynamics of the title reactions N(4S)+HD→NH+D and N(4S)+HD→ND+H on the 4A" double many-body expansion (DMBE) potential energy surface (PES) newly constructed by L. A. Poveda et al. [Phys. Chem. Chem. Phys. 7 (2005) 2867]. The generalized polarization-dependent differential cross sections (PDDCSs) and the three angular distributions of P(θr), P(φr) and P(θr,φr) are presented and discussed. It is revealed isotope effect exert a substantial influence on the product polarizations.

Linear-scaling generation of potential energy surfaces using a double incremental expansion

We present a combination of the incremental expansion of potential energy surfaces (PESs), known as n-mode expansion, with the incremental evaluation of the electronic energy in a many-body approach. The application of semi-local coordinates in this context allows the generation of PESs in a very cost-efficient way. For this, we employ the recently introduced flexible adaptation of local coordinates of nuclei (FALCON) coordinates. By introducing an additional transformation step, concerning only a fraction of the vibrational degrees of freedom, we can achieve linear scaling of the accumulated cost of the single point calculations required in the PES generation. Numerical examples of these double incremental approaches for oligo-phenyl examples show fast convergence with respect to the maximum number of simultaneously treated fragments and only a modest error introduced by the additional transformation step. The approach, presented here, represents a major step towards the applicability of vibrational wave function methods to sizable, covalently bound systems.

QUASI-CLASSICAL TRAJECTORY STUDY OF THE REACTION N + NH (v = 0–3, j=0) → N2 + H

The quasi-classical trajectory (QCT) calculations have been carried out for the reaction N + NH (v = 0–3, j=0) → N2 + H on the ground state of double many-body expansion (DMBE) potential energy surface [Caridade, PJSB, Poveda LA, Rodrigues SPJ, Varandas AJC, J Phys Chem A111:1172, 2007]. The influence of reagent vibrational excitation on reaction probability for total angular momentum J = 0 and integral cross section (ICS) at collision energies ranging from 0.1 eV to 1.0 eV has been investigated. The reaction probability tends to decrease with increasing collision energy and increase with the rising of initial vibration state, although some fluctuations appear. The ICS declines monotonously with the increase of collision energy and v. The product rotational alignment factor 〈P2(j′•k)〉 has also been calculated, and its value has a declining trend with the increase of collision energy. In spite of that, the results still show that the product is highly aligned. In addition, the vibrational excitation effect on the product polarization has also been studied. All the distributions of P(ϕr), P(θr), and the generalized polarization dependent differential cross sections indicate dependent behaviors on v.

Accurate ab-Initio-Based Single-Sheeted DMBE Potential-Energy Surface for Ground-State N2O

A global accurate double-many-body expansion potential-energy surface is reported for the electronic ground state of N(2)O. The new form is shown to accurately mimic the ab-initio points calculated at the multireference configuration interaction level using the aug-cc-pVTZ basis set and the full-valence-complete-active-space wave function as reference. To improve the calculated raw energies, they have been extrapolated to the completed basis set limit and most importantly to the full configuration-interaction limit by correcting semiempirically the calculated dynamical correlation with the double-many-body expansion-scaled external correlation method. The topographical features of the novel potential-energy surface were examined in detail and compared with those of other potential functions available in the literature. Good agreement with the experimental data is observed.

Accurate ab initio‐based double many‐body expansion adiabatic potential energy surface for the 22 A′ state of NH2 by extrapolation to the complete basis set limit

AbstractAn accurate single‐sheeted double many‐body expansion potential energy surface (PES) is reported for the title system, which is suitable for dynamics and kinetics studies of the reactions N(2D) + H2(X1 Σ) ⇋ NH(b1 Σ+) + H(2S) and their isotopomeric variants. It is obtained using the aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets with extrapolation of the electron correlation energy to the complete basis set limit, plus extrapolation to the complete basis set limit of the complete‐active‐space self‐consistent field energy. A switching function formalism has been used to ensure the correct behavior at the NH(A3 Π) + H(2S) and NH(b1 Σ+) + H(2S) dissociation limits. The topographical features of the new global PES are examined in detail, and found to be in general good agreement with those calculated directly from the raw ab initio energies, as well as previous calculations from the literature. © 2012 Wiley Periodicals, Inc.

Towards automated multi-dimensional quantum dynamical investigations of double-minimum potentials: Principles and example applications

A multi-coordinate expansion of potential energy surfaces has been used to perform quantum dynamical calculations for reactions showing double-minimum potentials. Starting from the transition state, a fully automated algorithm for exploring the multi-dimensional potential energy surface represented by arbitrary internal or normal coordinates allows for an accurate description of the relevant regions for vibrational dynamics calculations. An interface to our multi-purpose quantum-dynamics program M rP ropa enables routine calculations for simple chemical reactions. Illustrative calculations involving potential energy surfaces obtained from explicitly-correlated coupled-cluster calculations, CCSD(T)-F12a, are provided for the tunneling splittings in the isotopologues of hydrogen peroxide and for reaction dynamics based on the enantiomeric inversion of PHDCl.

Theoretical study of the dynamics of the reaction C(3P)+CH(X2Π)

A theoretical study of the dynamics of the reaction C() + CH() using the quasi-classical trajectory (QCT) method has been performed based on the double many-body expansion (DMBE) potential energy surface (PES) [Phys. Chem. Chem. Phys. 2, 1693 (2000)]. The integral cross section, as well as the product rotational alignment factor ⟨p 2(j′ · k)⟩ and four polarization-dependent differential cross sections (PDDCSs), i.e. and were studied. Furthermore, the distribution of the dihedral angle and the distribution of the angle between k and j′ are discussed. The angular distribution of the product rotational vector was also calculated.

Multiresolution potential energy surfaces for vibrational state calculations

A compact and robust many-mode expansion of potential energy surfaces (PES) is presented for anharmonic vibrations of polyatomic molecules, where the individual many-mode terms are approximated with various different resolutions, i.e., electronic structure methods, basis sets, and functional forms. As functional forms, the following three representations have been explored: numerical values on a grid, cubic spline interpolation, and a Taylor expansion. A useful index is proposed which rapidly identifies important many-mode terms that warrant a high resolution. Applications to water and formaldehyde demonstrate that the present scheme can increase the efficiency of the PES computation by a factor of up to 11 with the errors in anharmonic vibrational frequencies being no worse than ~ 10cm−1.

Direct fit of extended Hartree–Fock approximate correlation energy model to spectroscopic data

Abstract By direct-fitting the parameters in the physically motivated extended Hartree–Fock approximate correlation energy model to spectroscopic data, potential curves have been obtained for a variety of diatomic systems that mimic the ro-vibrational data often within much less than 1 cm−1. The approach offers a simple, yet accurate, scheme for modeling the two-body terms that are the leading contributions in a cluster expansion of potential energy surfaces of larger dimensionality.

Automated calculation of fundamental frequencies: Application to AlH3 using the coupled-cluster singles-and-doubles with perturbative triples method

An automated scheme for calculating numerical derivatives of functions is presented and applied to the Taylor expansion of potential energy surfaces. The computational cost is reduced by invoking the symmetry properties of noncubic groups. The scheme is applied to the quartic force field of isotopomers of AlH3 by numerical differentiation of the CCSD(T) energy, using the cc-pCVQZ basis for the harmonic part of the potential and the cc-pCVTZ basis for the anharmonic part. From this force field, zero-order vibrational corrections to the geometry and the fundamental frequencies are calculated by second-order perturbation theory. The results are compared with experiment and previous calculations.

Representation of potential energy surfaces by discrete polynomials: proton transfer in malonaldehyde

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.

Virial theorem constraints on n-body terms of potential energy surfaces

The virial theorem for the n-body energy terms in a cluster expansion of potential energy surfaces has been investigated. Integral conditions on the uniform scaling cuts of the kinetic and potential components of the n-body energy term are reported. The corresponding relations for n-body energy terms of molecular fragments are also examined. A use of the integral relations as constraints on the model n-body functions is suggested. An example is presented for the ground state surface of Li 3.

The double many‐body expansion of potential energy surfaces from interacting 2S atoms

AbstractThe double many‐body expansion (DMBE) method has been applied to the many‐valued ground‐state potential energy surfaces from three and four interacting 2S atoms. New forms are suggested where the degeneracy manifold of the two Riemann sheets of the potential surface can be made identical to that predicted from the London equation that is correct to first‐order. Considerable flexibility can be introduced through adjustable coefficients to fit ab initio data, whereas the potential energy terms can be chosen to maintain the correct analytic properties at the conical intersection. Hence, the new forms may be used on the extrapolation of the potential energy from the lowest‐ to the upper‐Riemann sheets. Long‐range effects are semiempirically described from the general formalism of the DMBE method.