Alexander O. Mitrushenkov

Quantum chemistry using the density matrix renormalization group

A new implementation of the density matrix renormalization group is presented for ab initio quantum chemistry. Test computations have been performed of the dissociation energies of the diatomics Be2, N2, HF. A preliminary calculation on the Cr2 molecule provides a new variational upper bound to the ground state energy.

Quantum chemistry using the density matrix renormalization group II

We have compared different strategies for ab initio quantum chemistry density matrix renormalization group treatments. The two starting orbital blocks include all valence and active orbitals of the reference complete active space self consistent field wave function. To generate the remaining blocks, we propose following the order of the contributions to the correlation energy: a posteriori using approximate occupation numbers or a priori, using a Moller–Plesset type of arguments, by explicit evaluation of second-order interactions. We have compared two different schemes for orbital localization to identify the important and less important orbital interactions and simplify the generation of the orbital blocks. To truncate the expansion we have compared two approaches, keeping constant the number m of components or the threshold λ to fix the residue of the expansion at each step. The extrapolation of the energies is found to provide accurate estimates of the full configuration interaction energy, making the...

Passing the several billions limit in FCI calculations on a mini-computer

Abstract An efficient realization of a determinant-based algorithm for the large full configuration interaction (FCI) problem is presented; it effectively exploits the sparsity of the CI vector. Within this technique we reproduced the one billion calculation for the 1 S ground state of the Mg atom on a Sparc IPC minicomputer to an uncertainty of 10 −4 hartree within a threshold of 10 −5 for the CI vector. Calculations are also performed for the 1 P excited state of Mg. As an example, which is at the limit of the hardware available on our computer, the ground state of the H 2 O molecule in the [5s3p1d/3s1p] ANO basis set is calculated. The FCI expansion of the ground state vector yields over 7.2 billion C 2v determinants. A ground state energy of −76.305 hartree with an estimated accuracy of 2 × 10 −3 hartree in this basis set is obtained within the total time of 170 h. One iteration of the CI vector in this basis set with a threshold of 10 −5 is performed in 100 Mbyte disk space and took 4200 min of the total computation time.

Dissociation energies and heats of formation of NH and NH

Starting from the results of a recent ion–molecule reactive scattering experiment [Tosi et al., J. Chem. Phys. 100, 4300 (1994)], a precise estimate of the upper bound for the heat of formation of NH+ has been derived [ΔHf,0(NH+)⩽17.175±0.006 eV], and from this, upper and lower bounds for the heat of formation of NH and for the dissociation energies of NH+ (X 2Π and a 4Σ− states) and NH (X 3Σ−), respectively. In order to verify the degree of accuracy attainable on the theoretical counterpart for these systems, high level ab initio computations, using extended multireference configuration interaction expansion and recently developed core-valence correlation consistent basis sets [Woon et al., J. Chem. Phys. 103, 4572 (1995)], have been also performed, comparing the results with the corresponding values estimated from the experimental data and previous theoretical literature values.

Energy levels of HCN+ and DCN+ in the vibronically coupled X 2Π and A 2Σ+ states

The X 2Π and A 2Σ+ electronic states of HCN+ have been studied using a previously developed method [Carter et al., Mol. Phys. 98, 1967 (2000)] suitable for triatomic molecules showing three-state (Renner-Teller+vibronic) interactions. Ab initio three-dimensional diabatic potential energy surfaces for the 2Π(1 2A′,1 2 A″) and 2Σ+(2 2A′) states have been computed at the multireference configuration interaction level of theory, using extended Gaussian basis sets. Additional computations were done to determine the barrier to isomerization over the three surfaces and the spin–orbit constant for the 2Π state. Energies, spin–orbit splittings, and rotational constants have then been calculated for all rovibronic levels of Σ and Π symmetry up to 5800 cm−1 for HCN+ and 4800 cm−1 for DCN+. Assignments based on plots of vibrational wave functions are also provided. These computations have been finally used to revise previous interpretations of photoelectron spectra.

EPSTEIN-NESBET SECOND-ORDER PERTURBATION TREATMENT OF DYNAMICAL ELECTRON CORRELATION AND GROUND STATE POTENTIAL ENERGY CURVE OF CR2

Abstract The Cr 2 potential energy curve is obtained by treating the dynamical correlation energy terms using a CI procedure based on determinants, equivalent to multi-reference second-order perturbation theory with the Epstein-Nesbet partition of the Hamiltonian. One of the advantages of this treatment is that the level shifts required for the equivalent Moller-Plesset type of treatment to eliminate intruder states and avoid divergences in the ground state second-order energy expression, are not required. Moreover, by truncating the reference space, the dynamical and the non-dynamical correlation energy is included also for the 3s, 3p electrons. The potentials are compared to experiment and to the most accurate theoretical potential curves in the literature.

Passing the several billion limit in FCI calculations on a mini-computer. A norm-consistent zero CI threshold estimate within the dynamic CI approach

Abstract An efficient procedure for the energy estimate in the zero CI threshold limit is suggested within the dynamic CI approach. The procedure gives accurate estimates of full-CI energies. It is illustrated by numerical examples for some large scale full-CI problems including 7.2 billion determinants calculations for the H 2 O molecule.

Adsorption and nonadiabatic processes in the photodesorption of molecular oxygen from the reduced TiO2(110) surface

We review the adsorption and desorption of molecular oxygen on a reduced TiO 2 (110) surface. This system is known to play a fundamental role in heterogeneous photocatalysis. Periodic calculations are performed with the objec- tive of characterizing the variety of stable species of O 2 that are known to exist on the TiO 2 surface. The implications of our results for recent experiments are discussed. We also consider a direct optical excitation mechanism for the ultraviolet (UV) light-desorption process and model the most stable O 2 /TiO 2-x system as a cluster. High-level ab initio calculations of the excited states and interaction matrix elements are performed using different orbitals, separately optimized for the target states. The nonadiabatic and dipole-moment couplings are calculated directly from the corre- lated wave functions by a special transformation to bi-orthonormal (dual) orbital sets to preserve their structure. The method used for the electronic structure calculations is described in detail. Finally, the effect of the electronic coupling in the UV- photodesorption dynamics is analyzed in detail.

EFFICIENT TRUNCATION STRATEGIES FOR MULTI-REFERENCE CONFIGURATION INTERACTION MOLECULAR ENERGIES AND PROPERTIES

Modified virtual orbitals are proposed for multi-reference configuration interaction (MRCI) treatments and a modified Fock operator is defined for the orbital transformation. The main property of the modified orbitals is to improve the convergence properties of the configuration interaction (CI) expansion, which can be exploited to truncate, partially, the expansion in the external space. Simple tests are presented to show that the orbital transformation may be useful to perform FullCI type of treatments for subsets of orbitals and electrons, and to improve the MRCI second-order corrections and energies. Compared to other well-established techniques for accurate MRCI treatments, it is believed that this method offers advantages for electronic structures with many active orbitals and electrons using large orbital basis sets.

Numerical techniques for the evaluation of non-adiabatic interactions and the generation of quasi-diabatic potential energy surfaces using configuration interaction methods

CI techniques, based on nearly complete expansions over determinants for subsets of molecular orbitals and electrons, have been extended to evaluate, by finite differences, non-adiabatic interactions arising from the nuclear kinetic energy operator. A functional of the non-adiabatic interactions is defined and, from the minimum condition of the functional, a simple expression is obtained for the transformation matrix to the quasi-diabatic basis. Two different schemes for the minimization of the functional, with and without constraints to the form of the transformation matrix, have been compared. Simple tests are presented to verify the numerical accuracy of the non-adiabatic interactions and to compare the two schemes for the minimization of the functional.