Mario Raimondi

MODIFICATION OF THE ROOTHAAN EQUATIONS TO EXCLUDE BSSE FROM MOLECULAR INTERACTION CALCULATIONS

The Roothaan equations have been modified to compute molecular interactions between weakly bonded systems at the SCF level of theory without the basis set superposition error (BSSE). The increase in complication with respect to the usual SCF algorithm is negligible. Calculation of the SCF energy on large systems, such as nucleic acid pairs, does not pose any computational problem. At the same time, it is shown that a modest change in basis-set quality from 3-21G to 6-31G changes the binding energy by about 50% when computed according to standard SCF “supermolecule” techniques, while remaining practically constant when computed without introducing BSSE. Bader analysis shows that the amount of charge transferred between the interacting units is of the same order of magnitude when performed on standard SCF wave functions and those computed using the new method. The large difference between the corresponding computed energies is thus ascribed to the BSSE.

Modern valence bond representations of CASSCF wavefunctions

Exact transformations of “N electrons inN orbitals” CASSCF structure spaces are examined that lead to modern valence bond representations, in which the total wavefunction is dominated by covalent structures built from a common product ofnonorthogonal orbitals. The resulting descriptions of the electronic structure may be compared directly with those that arise in the spin-coupled (orfull-GVB) approach. Using singlet methylene, methane and ozone as representative examples, various overlap-based and energy-based criteria are investigated for generating modern VB representations of “N inN” CASSCF wavefunctions, which we denote CASVB.

Spin-coupled valence bond theory

Abstract In the spin-coupled description of molecular electronic structure, an N-electron system is described by N distinct—but non-orthogonal—orbitals, whose spins are coupled to the required resultant S in all possible ways. The coefficients of the basis functions comprising the orbitals and the coefficients of the different spin functions are fully optimized. The orbitals are frequently highly localized, and hence the model incorporates considerable electron correlation while retaining a high degree of visuality. The spin-coupled wave function is refined by non-orthogonal configuration interaction, and the final wave functions are of high quality but very compact. The various aspects of this theory are illustrated by a series of examples of increasing complexity: the H2 molecule, the BeH molecule, the 3B1 and lA1 states of CH2 and the cycloaddition of CH2 to ethenes, the 7t-electron system of benzene, and diazomethane (CH2N2). The results provide clear descriptions of the electronic structure and the a...

Core-valence separation in the spin-coupled wave function: a fully variational treatment based on a second-order constrained optimization procedure

The theory of the spin‐coupled (SC) wave function with core‐valence separation, in which the core electrons are confined to a closed shell of doubly‐occupied orbitals and the valence electrons are described with the complete set of features of the SC formalism, is developed to produce an efficient approach which makes possible its fully variational determination. The simultaneous optimization of the core orbitals, valence orbitals, and spin‐coupling coefficients is achieved through a second‐order nonlinear elimination constrained minimization algorithm which exhibits excellent convergence properties. It is no longer necessary to introduce an ad hoc preselection of core and valence orbitals−this is carried out by the minimization procedure itself which makes an optimum choice from a variational point of view. The only important item left to personal judgment is the selection of the number of core and valence electrons in the problem under investigation. Simplifications such as ‘‘freezing’’ of a part of the...

Extension of the SCF-MI Method to the Case of K Fragments one of which is an Open-Shell System.

Roothaan equations have been modified in a previous work with the aim of avoiding BSSE at the Hartree-Fock level of theory. The resulting scheme, called SCF-MI (Self Consistent Field for Molecular Interactions), underlines its special usefulness for the computation of intermolecular interactions. In the present work we present the generalisation of the theory to the case of K interacting fragments one of which may be described by an open shell configuration. This extension implies a drastic modification of the procedure which is here reported in full detail. The method provides a complete a priori elimination of the BSSE while taking into account the natural non orthogonality of the MOs of the interacting fragments.

New basis set superposition error free ab initio MO-VB interaction potential: Molecular-dynamics simulation of water at critical and supercritical conditions

Recently, a controversy has come to light in literature regarding the structure of water in nonambient conditions. Disagreement is evident between the site–site pair correlation functions of water derived from neutron diffraction and those obtained by computer simulations which employ effective pairwise potentials to express the intermolecular interactions. In this paper the SCFMI method (self-consistent field for molecular interaction) followed by nonorthogonal CI (configuration interaction) calculations was used to determine a new water–water interaction potential, which is BSSE (basis set superposition error) free in an a priori fashion. Extensive calculations were performed on water dimer and trimer and a new parametrization of a NCC-like (Niesar–Corongiu–Clementi) potential was accomplished. This was employed in the molecular-dynamics simulation of water. The effect of temperature and density variations was examined. Acceptable agreement between site–site correlation functions derived from neutron di...

Determination of extremely localized molecular orbitals and their application to quantum mechanics/molecular mechanics methods and to the study of intramolecular hydrogen bonding

The extremely localized molecular orbitals (ELMOs) are a set of molecular orbitals strictly localized only on a few atoms of a molecule. They are obtained in an a priori fashion through the direct application of the variation principle. Even if the theoretical aspects of their determination have been discussed already in the literature, stable and fast algorithms to obtain ELMOs are still not trivial and a comparison between different methods is reported. We furthermore investigate the applicability of ELMOs to quantum mechanics/molecular mechanics (QM/MM) methods which employ frozen localized orbitals to represent covalent bonds across the QM and the MM region. In addition it is shown that ELMOs can be used to describe species with intramolecular hydrogen bonds, where a correct elimination of the intramolecular basis set superposition error can be essential to perform accurate conformational studies.

Expansion of the spin-coupled wavefunction in Slater determinants

SummaryThe expansion of the spin-coupled wavefunction in Slater determinants constructed from nonorthogonal spin-orbitals is discussed. It proves possible to generate from cofactors of the appropriate overlap matrix all the density matrices, up to fourth order, required for the variational optimization of the wavefunction. The computational effort inherent in this ‘super-cofactor’ strategy scales in a very acceptable manner with the number of electrons.

STUDY OF THE ELECTRONIC STATES OF THE BENZENE MOLECULE USING SPIN-COUPLED VALENCE BOND THEORY

The spin‐coupled VB method is used to study all the singlet and triplet valence excited states, as well as the n=3,4 singlet and triplet Rydberg states of benzene below the first ionization potential at 9.25 eV. The valence excited states are classified in an obvious physical way into covalent or ionic states, from which it follows at once that covalent states are well described using the approximation of σ/π separation and a frozen σ core, whereas the error in the computed transition energies to the ionic states is much larger and these states require additional σ/π correlation for their proper description. The Rydberg states are very well‐described, provided that a suitable σ core, derived from a calculation on the C6H+6 ion, is used. The numerical accuracy of the final results for the transition energies is at least the same as that given by the largest MO‐CI‐ or CASSCF‐CI‐based methods reported to date. The spin‐coupled VB approach has the obvious advantage in providing a compact and clear picture of ...

Possible reaction paths in the LiH+2 chemistry: a computational analysis of the interaction forces

Abstract The present study addresses the problem of establishing from fully ab initio quantum methods some quantitative features of the chemical interactions which play an important role in the ionic lithium chemistry of astrophysical relevance. In particular, the LiH + 2 energetics is examined by looking at the various possible chemical channels producing LiH, LiH + , H 2 and H + 2 . An accurate evaluation of the relative energy landscapes as the complex breaks up into its asymptotic partners is presented for the first time. It allows us to clearly select those reactive pathways which can be excluded when setting up a kinetic modeling of the lithium chemistry network in early universe processes.