Adaptive vibrational configuration interaction (A-VCI): A posteriori error estimation to efficiently compute anharmonic IR spectra

Abstract

A new variational algorithm called adaptive vibrational configuration interaction (A-VCI) intended for the resolution of the vibrational Schrödinger equation was developed. The main advantage of this approach is to efficiently reduce the dimension of the active space generated into the configuration interaction (CI) process. Here, we assume that the Hamiltonian writes as a sum of products of operators. This adaptive algorithm was developed with the use of three correlated conditions, i.e., a suitable starting space, a criterion for convergence, and a procedure to expand the approximate space. The velocity of the algorithm was increased with the use of a posteriori error estimator (residue) to select the most relevant direction to increase the space. Two examples have been selected for benchmark. In the case of H2CO, we mainly study the performance of A-VCI algorithm: comparison with the variation-perturbation method, choice of the initial space, and residual contributions. For CH3CN, we compare the A-VCI results with a computed reference spectrum using the same potential energy surface and for an active space reduced by about 90%.

Using an expanding nondirect product harmonic basis with an iterative eigensolver to compute vibrational energy levels with as many as seven atoms

“…5 When the PES is a sum of products (SOP) it is now possible to solve the vibrational Schroedinger equation numerically for molecules with about 10 atoms. [6][7][8][9][10][11] Such calculations, often called variational, fully account for the effects of coupling and anharmonicity. When zeroth-order levels are close (resonances), perturbation theory works poorly.…”

“…32,39,41 (2) has been used in many recent papers. 11,[42][43][44][45][46][47][48][49] It is most straightforward to use a predetermined pruning condition. If the harmonic frequencies of all the coordinates are similar, then a product harmonic oscillator basis (HOB) can be effectively pruned by retaining only basis functions for which…”

Dual vibration configuration interaction (DVCI). An efficient factorization of molecular Hamiltonian for high performance infrared spectrum computation

“…An other pertinent criteria for subspace selection is the residue. It is widely adopted in Davidson like methods [48,49,50,51] and has recently been implemented in A-VCI [20,21] sharing same structure than the A k decomposition [3]. In the A k theory, one considers primary and secondary spaces respectively called B and B S .…”

“…With definitions (19), (20), the program builds the set of occupation-numbers associated to the non void local force fields 6…”

Perspective: Computing (ro-)vibrational spectra of molecules with more than four atoms

“…2,39,40,60,69-74 (2) has been used in some recent papers. [75][76][77][78][79][80][81] If the harmonic frequencies of all the coordinates are similar, then a product harmonic oscillator basis (HOB) can be effectively pruned by retaining only basis functions for which…”