An efficient and numerically stable procedure for generating sextic force fields in normal mode coordinates

Abstract

In this paper, we outline a general, scalable, and black-box approach for calculating high-order strongly coupled force fields in rectilinear normal mode coordinates, based upon constructing low order expansions in curvilinear coordinates with naturally limited mode-mode coupling, and then transforming between coordinate sets analytically. The optimal balance between accuracy and efficiency is achieved by transforming from 3 mode representation quartic force fields in curvilinear normal mode coordinates to 4 mode representation sextic force fields in rectilinear normal modes. Using this reduced mode-representation strategy introduces an error of only 1 cm(-1) in fundamental frequencies, on average, across a sizable test set of molecules. We demonstrate that if it is feasible to generate an initial semi-quartic force field in curvilinear normal mode coordinates from ab initio data, then the subsequent coordinate transformation procedure will be relatively fast with modest memory demands. This procedure facilitates solving the nuclear vibrational problem, as all required integrals can be evaluated analytically. Our coordinate transformation code is implemented within the extensible PyPES library program package, at http://sourceforge.net/projects/pypes-lib-ext/.

Accuracy and Interpretability: The Devil and the Holy Grail. New Routes across Old Boundaries in Computational Spectroscopy

“…The method also involves an efficient and numerically stable procedure for generating sextic force fields in normal mode coordinates. 259 A remarkable example of the performance of the VCI approach is provided by the joint experimental-theoretical investigation of the gas-phase vibrational spectrum of azidoacetylene 260 (see panel M, Figure 1), which is dominated by strong couplings. As already pointed out, a mandatory prerequisite is the accurate determination of the PES, whose representation was provided in terms of grid points, with the multi-mode expansion of the PES truncated after the 3D contributions (i.e., up to triple-mode coupling terms included), with the energies being calculated at the explicitly correlated CCSD(T)-F12a level in conjunction with a triple-ζ basis set.…”

“…According to the benchmark study of ref , with the exception of those cases showing highly anharmonic and highly coupled modes, this approach is expected to recover fundamental frequencies with maximum errors lower than 5 cm –1 . The method also involves an efficient and numerically stable procedure for generating sextic force fields in normal mode coordinates …”

Dinitrogen as a Sensor for Metastable Carboxylic Acid Dimers and a Weak Hydrogen Bond Benchmarking Tool

“…Only a combination of accurate electronic structure theory and vibrational treatment − promises to provide the right answers for the right reason. To combine the two ingredients, an analytical representation of the Born–Oppenheimer potential energy hypersurface is typically needed ,− unless a perturbative treatment of vibrational anharmonicity based on local force constants may be considered sufficient. The latter is conceivable for the hydrogen-bonded complex of formic acid and a single nitrogen molecule, whereas addition of a second nitrogen or a methyl rotor is likely to stretch the limits of perturbation theory.…”

Evaluating the anharmonicity contributions to the molecular excited state internal conversion rates with finite temperature TD-DMRG

“…For large systems, the high-order Taylor expansion of the PES at the equilibrium geometry is often used to calculate the anharmonic frequencies. 51,52 However, it is known that high-order Taylor expansion often has artificial "holes" on PES, which is disastrous for the variational approaches such as DMRG.…”