AbInitio Theory for Accurate Spectroscopic Constants and Molecular Properties

Abstract

Having access to highly accurate potential energy surfaces (PESs) is a prerequisite for the ab initio calculation of accurate spectroscopic constants and molecular properties. The construction of such surfaces, however, is a formidable task. It not only requires solving of the time‐independent, nonrelativistic, clamped‐nuclei, electronic Schrödinger equation of the molecular n ‐electron system at the highest possible level of approximation, but it also requires inclusion of small energy terms that are often neglected at other occasions. Such terms are, for example, due to nonadiabatic and relativistic effects (scalar and nonscalar). Nevertheless, the largest sources of error in calculating PESs are most often due to the inadequate description of the nonrelativistic electronic wave function of the molecular n ‐electron system in the Born–Oppenheimer approximation. This article is concerned with these sources of error, which are related to the truncation of the one‐electron basis set of atomic functions and to the incomplete expansion of the wave function in a basis of n ‐electron functions. In particular, these errors diminish only extremely slowly with the extension of the one‐electron basis set when the wave function is expanded in terms of n ‐electron functions that are (antisymmetrized) products of one‐electron functions (orbitals). Coupled‐cluster theory in conjunction with explicitly correlated two‐electron geminals (instead of the more commonly used products of two orbitals) appears to be a promising approach toward obtaining an adequate description of the clamped‐nuclei, nonrelativistic electronic wave function and, thus, for the calculation of highly accurate PESs, from which accurate spectroscopic constants and molecular properties may be obtained.

Ab initio instanton rate theory made efficient using Gaussian process regression

“…For electronic structures where the independent particle model is qualitatively correct, electronic energies computed at the basis set limit CCSD(T) level of theory are expected to be accurate to better than 1 kcal/mol for reaction barriers, 0.1 pm for structures and 5 cm −1 for harmonic vibrational wavenumbers. 43 Until relatively recently, the cost associated with using the large basis sets traditionally required to access the basis set limit has prevented this high level of theory from being routinely used in quantum dynamics simulations, which typically require many thousands of energy evaluations. With the maturation of modern F12 explicitly correlated theory, 44 near basis set limit CCSD(T) energies can now be computed using small (triple-zeta) orbital basis, at a cost only 15% larger than a traditional CCSD(T)/TZ calculation, and quantum dynamics studies can be performed using near basis set limit CCSD(T) Born-Oppenheimer potential energy surfaces on a routine basis.…”

Global Analytical Potential Energy Surfaces for High‐resolution Molecular Spectroscopy and Reaction Dynamics

“…In the Born-Oppenheimer approximation, the first step is to solve the molecular Schrödinger equation for the electronic states at fixed nuclear geometries. This procedure is based on first principles and is carried out in many modern computer codes for ab initio calculations (see also Yamaguchi and Schaefer 2011: Analytic Derivative Methods in Molecular Electronic Structure Theory: A New Dimension to Quantum Chemistry and its Applications to Spectroscopy; Tew et al 2011 Wörner and Merkt 2011: Fundamentals of Electronic Spectroscopy, this handbook). Despite the great advances made in computer technology since the early days of quantum mechanics, traditional ab initio calculations can yield only approximate values of electronic energies because many-electron molecular systems are highly correlated (Löwdin 1959).…”

“…The drawback of the original R12-method by Kutzelnigg and Klopper (1991) is the computational cost. More recently, a nonlinear variant of this method, the F12-method (CCSD(T)-F12 (Adler et al 2007), MP2-F12 (Werner et al 2007)), has been used to derive accurate potential energy functions for a series of diatomic molecules including elements of the third row (Yousaf and Peterson 2008) at a cost that is lower by a factor of 2, when compared to the original method (see also Tew et al 2011: Ab Initio Theory for Accurate Spectroscopic Constants and Molecular Properties, this handbook).…”

Fundamentals of Rotation–Vibration Spectra

“…Spectroscopy,Tew et al 2011: Ab Initio Theory for Accurate Spectroscopic Constants and Molecular Properties and Breidung and Thiel 2011: Prediction of Vibrational Spectra from Ab Initio Theory, this handbook.…”