Multiconfiguration Pair-Density Functional Theory for Transition Metal Silicide Bond Dissociation Energies, Bond Lengths, and State Orderings

Abstract

Transition metal silicides are promising materials for improved electronic devices, and this motivates achieving a better understanding of transition metal bonds to silicon. Here we model the ground and excited state bond dissociations of VSi, NbSi, and TaSi using a complete active space (CAS) wave function and a separated-pair (SP) wave function combined with two post-self-consistent field techniques: complete active space with perturbation theory at second order and multiconfiguration pair-density functional theory. The SP approximation is a multiconfiguration self-consistent field method with a selection of configurations based on generalized valence bond theory without the perfect pairing approximation. For both CAS and SP, the active-space composition corresponds to the nominal correlated-participating-orbital scheme. The ground state and low-lying excited states are explored to predict the state ordering for each molecule, and potential energy curves are calculated for the ground state to compare to experiment. The experimental bond dissociation energies of the three diatomic molecules are predicted with eight on-top pair-density functionals with a typical error of 0.2 eV for a CAS wave function and a typical error of 0.3 eV for the SP approximation. We also provide a survey of the accuracy achieved by the SP and extended separated-pair approximations for a broader set of 25 transition metal–ligand bond dissociation energies.

Chemical Bonding in Isoelectronic NdO2and SmO22+

“…Overall, for XMS-PDFT, on-top functionals ftBLYP, ftOPBE, and ftOreLYP give good spin-splitting energies of Nd + (error ≤0.03 eV), but for CMS-PDFT, only the on-top functional ftOrelYP gives an error in the spin-splitting energy that is that small. The better performance of the fully translated functionals can in principle be attributed to their inclusion of an added ingredient in the functional, namely, the gradient of the on-top pair density, although our overall experience is that the difference between these kinds of functionals is usually smaller than the error in either of them, and in such cases, either kind may be more accurate in a particular case. ,,− …”

Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

“…For example, for the ground state of TaSi, the nom -CPO CASSCF reference wave function has 2320 CSFs, whereas the nom -CPO SP reference wave function has only 272 CSFs. 39 …”

“…In this method, each subspace contains only one or two orbitals and only one, two, or three electrons. This scheme is called the separated pair (SP) approximation 38 and it was included in our previous review; 9 therefore, we limit the discussion here to a statistical analysis, published 39 aer that review, of our applications of the SP approximation to 25 diatomic molecules that contain one or two transition metal atoms and for which accurate bond dissociation energies are available [39][40][41][42] (for two of the cases, we use extended SP theory rather than SP theory; in extended SP theory, one puts all singly occupied orbitals and their correlating orbitals into a single subspace 42 ). In each case we also carried out CAS-PDFT calculations for comparison.…”

“…For example, for the ground state of TaSi, the nom-CPO CASSCF reference wave function has 2320 CSFs, whereas the nom-CPO SP reference wave function has only 272 CSFs. 39 The success of the SP and extended SP approximations is particularly encouraging in light of a recommendation we made in a paper devoted to the study of active space dependence, where we wrote 45 "This leads to the recommendation that, at least with the presently available on-top density functionals, MC-PDFT should be employed with a small active space, large enough to account for near-degeneracy correlation but not so large as to include signicantly more dynamic correlation". The SP and extended SP methods can be considered an attempt to systematically dene an active space that is large enough to account for near-degeneracy correlation in reactions involving bond breaking but is not signicantly larger (although one expects a problem for very large active spaces, unless one derives new density functionals appropriate for them, in practice we have found that the error does not depend strongly on the precise constitution of the active space for alternative reasonable choices of the active space).…”

Dipole Moment Calculations Using Multiconfiguration Pair-Density Functional Theory and Hybrid Multiconfiguration Pair-Density Functional Theory

“…MC-PDFT is a multireference method that uses a multiconfigurational wave function as the reference function and computes the total energy from the kinetic energy, density, and on-top pair density of that wave function . While the computational cost of MC-PDFT is lower than that of multireference perturbation theories or multireference configuration interaction, it has been shown to provide good accuracy for calculating the excitation energies, bond energies, reaction barriers, and molecular geometries. − In this paper, we derive an analytical procedure for computing dipole moments by MC-PDFT, we present illustrative applications, and we compare MC-PDFT dipole moments to those computed by complete active space self-consistent field (CASSCF) calculations, complete active space second-order perturbation theory (CASPT2), and multireference configuration interaction with single and double excitations and a Davidson correction for quadrupole excitations (MRCISD+Q). − The applications consist of equilibrium dipole moments of 18 first-row transition-metal diatomics, six polyatomic molecules, and nonequilibrium dipole moments of HF, CO, NO, and AlO for bond-stretched geometries.…”