Effect of time-dependent basis functions and their superposition error on atom-centered density matrix propagation (ADMP): Connections to wavelet theory of multiresolution analysis

Abstract

We present a rigorous analysis of the primitive Gaussian basis sets used in the electronic structure theory. This leads to fundamental connections between Gaussian basis functions and the wavelet theory of multiresolution analysis. We also obtain a general description of basis set superposition error which holds for all localized, orthogonal or nonorthogonal, basis functions. The standard counterpoise correction of quantum chemistry is seen to arise as a special case of this treatment. Computational study of the weakly bound water dimer illustrates that basis set superposition error is much less for basis functions beyond the 6-31+G(*) level of Gaussians when structure, energetics, frequencies, and radial distribution functions are to be calculated. This result will be invaluable in the use of atom-centered Gaussian functions for ab initio molecular dynamics studies using Born-Oppenheimer and atom-centered density matrix propagation.

Quantum Wavepacket Ab Initio Molecular Dynamics: An Approach for Computing Dynamically Averaged Vibrational Spectra Including Critical Nuclear Quantum Effects

“…83,[108][109][110][111]129,130 To arrive at this step, we first note that under conditions of "adiabatic control'' 84,109,110,131 extended Lagrangian formalisms 132,133 such as ADMP provide good approximations to single-particle (Hartree-Fock, DFT, and semiempirical treatments) BornOppenheimer molecular dynamics (BOMD). 11,13,109 When ADMP is used to describe the dynamics of the electrons, subsystem C is described through propagation of the single-particle electronic density matrix, P C , as Here, µ is a fictitious inertia tensor 83,[108][109][110] describing the motion of P C , and Λ is a Lagrangian multiplier matrix used to impose N-representability of P C .…”

“…167 On the basis of eqs 5 and 6, a variety of hierarchical wavelet bases have been developed. 111,115,117,[142][143][144][145] Here, we expand the multidimensional, positive semidefinite TDDS function as a multiconfigurational (sum-of-products) expansion of Haar scaling functions where the Haar scaling function, H(x), is a square function equal to 1, for 0 e x e 1, and zero otherwise. The quantity N GEN is the number of wavelet generations, and the underline below the summations is meant to indicate that there are N Dim summations, [j 1 ,j 2 , ..., j NDim ], and c i,{j} implies that the coefficients depend on i and the entire set of j-indices.…”

“…We include the bulk of the nuclear and electronic degrees of freedom within subsystems B and C. Ab initio molecular dynamics (AIMD) 63,[79][80][81][82][83]85 is used to treat the evolution of these subsystems, where the nuclei in subsystem B are treated using classical mechanics. Both extended Lagrangian 81, 83,84,[107][108][109][110][111] and Born-Oppenheimer treatment 82,85,86 options are available. We have derived and tested a scheme [97][98][99] that allows simultaneous dynamics of all three subsystems coupled through a time-dependent procedure.…”

Experimental and Ab Initio Dynamical Investigations of the Kinetics and Intramolecular Energy Transfer Mechanisms for the OH + 1,3-Butadiene Reaction between 263 and 423 K at Low Pressure

“…67 AIMD techniques, such as ADMP and BOMD, have recently been utilized in many state-of-the-art studies to obtain dynamically averaged, temperature-dependent, vibrational properties of weakly bound hydrogen-bonding clusters. 54,55,[60][61][62][63]68,69 V(a). Simulation Details.…”

“…This approximation has been found to provide reasonable approximations to cluster temperature for a variety of ADMP studies. 52,54,55,[60][61][62][63][64][65] The vibrational-energy-transfer mechanism was probed by considering (a) the evolution of the Fourier transform of the velocity-velocity autocorrelation function (FT-VAC) as a function of time for the full molecule as well as the individual fragments, (b) a detailed analysis of the evolution of contributions from the individual Harmonic modes (to be discussed in section VI(c)) as a function of time, and (c) the evolution of the individual fragment kinetic energies as a function of time. It must be noted that the FT-VAC provides a representation of the vibrational density of states sampled during finite temperature simulations.…”