Ermanno Gianinetti

Valence‐Bond Theory for Simple Hydrocarbon Molecules, Radicals, and Ions

Valence‐bond (VB) theory is formulated in a general form, to be applied to states of any multiplicity, with inclusion of both spin and orbital degeneracy. Structures are related to products of spin functions, the leading terms, and a one‐to‐one correspondence is established between these products and extended Rumer diagrams. A relationship is also found with genealogical spin functions. The leading terms can be directly used in the calculation of energy eigenvalues and eigenvectors. Applications to simple hydrocarbon systems are shown, and the results are compared with experimental data.

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.

Hartree–Fock limit properties of the water dimer in absence of BSSE

Abstract A series of calculations has been accomplished employing uncontracted even tempered basis set expansions of increasing dimension. The SCF–MI (self-consistent field for molecular interactions) binding energy and force constant for the O–H stretching involved in the hydrogen bond of the water dimer system in the limit of very extended basis set have been computed. The most extended even tempered basis set (548 functions) included diffuse f gaussian functions on oxygen and d functions on hydrogen. The effect of functions with higher angular momentum has been investigated by a different scheme. The basis set superposition error (BSSE) was avoided in an a priori fashion by applying the SCF–MI method. Bader analysis showed that the amount of charge transferred between the interacting units agrees with that computed by standard SCF supermolecule wave functions. The geometry of the system was optimised using the algorithm implemented into GAMESS-US program based on analytic first derivatives of the SCF–MI energy. The resulting SCF–MI interaction energy was estimated to be −3.45 kcal/mol, in close accordance with recently reported values. The calculated Hartree–Fock limit for the water monomer was −76.0676 au to be compared with the previous value of −76.0675 au.

New ab initio VB interaction potential for molecular dynamics simulation of liquid water

Abstract SCF-MI (Self Consistent Field for Molecular Interactions) and non orthogonal CI were used to determine a water-water interaction potential, from which BSSE is excluded in an a priori fashion. The new potential has been employed in molecular dynamics simulation of liquid water at 25°C. The simulations were performed using MOTECC suite of programs. The results were compared with experimental data for water in the liquid phase, and good accordance was found, both in radial distribution functions and thermodynamic properties, as well as in geometric parameters.

Effects of hydrated Mg++ interacting with the guanine site in cytosine–guanine nucleic acid–base pair: an ab initio Hartree–Fock study in the absence of basis set superposition error

Abstract The structures and energetics of complexes between guanine⋯cytosine Watson–Crick (GCWC) DNA base pair and the hydrated Mg++ cation were investigated by an ab initio Hartree–Fock study in the absence of basis set superposition error. The explicit hydration of the cation with four and five water molecules was considered. The various charged fragments were allowed to interact with the N7 and O6 sites of guanine. The BSSE-free gradient geometry optimisation were performed in the framework of the SCF-MI (self-consistent field for molecular interactions) theory. The structures of the complexes were analysed showing that the coordination of the GC pair can generate highly distorted non-Watson–Crick hydrogen bonding patterns.

A new methodology in quantum chemistry: use of partially orthogonalized orbitals

Abstract Partially orthogonalized orbitals are proposed as a basis for variational calculations of molecular wavefunctions. The relevant computational problems encountered during the implementation of a pilot program based on such a methodology are presented and the solutions outlined.

Ab initio non-orthogonal approaches to the computation of weak interactions and of localised molecular orbitals for QM/MM procedures

Abstract The research carried out by our group in the framework of the VB theory is reviewed. The modification of the Roothaan equations to avoid the basis set superposition error (BSSE) at the Hartree–Fock level of theory is presented. Significant applications of the resulting scheme, called Self Consistent Field for Molecular Interactions (SCF-MI), are summarised. The successive development of the SCF-MI method to properly take account of electron correlation effects by a compact multistructure size consistent Valence Bond (VB) wavefunction is described. The central idea of the method is that of expanding the orbitals in the partitioned basis sets located on each fragment so as to exclude BSSE in an a priori fashion, while taking properly into account orbital and geometry relaxation effects and the natural non orthogonality of the MOs of the interacting fragments. The very recent extension of the SCF-MI formulae to the determination of extremely localised molecular orbitals (ELMO) is also reviewed.

A detailed analysis of error bounds for approximated coulombic integrals

Abstract Upper and lower bounds for approximated coulombic integrals are derived. The resulting bounds are the best possible under the given conditions. The problem and its development has been given a transparent geometrical interpretation.

Hartree-fock Study of Hydrogen-bonded Systems in the Absence of Basis-set Superposition Error the Nucleic-acid Base Pairs

The Roothaan equations have been recently modified for computing molecular interactions between weakly bonded systems at the SCF level in order to avoid the introduction of the basis-set superposition error (BSSE). Due to the importance that nucleic-acid base interactions play in DNA and RNA, which are 3-D structures, we present applications of this approach of Self Consistent Field for Molecular Interactions (SCF-MI) to the study of several hydrogen-bonded DNA bases. Nucleic-acid pairs are extensively investigated: structures and energies for both isolated and paired molecules are thoroughly studied. Cs-symmetry equilibrium geometries and binding energies are calculated in the framework of the SCF-MI formalism by using standard basis sets. SCF-MI/3-2 1G stabilisation energies for the studied base pairs lie in the range −22.5/−8.0 kcal/mol, in good agreement with previous, high-level theoretical values. The hydrogen bonding potential energy surface (PES) and propeller twist potentials are also calculated for some of the molecular complexes. The SCF-MI interaction density is used to interpret the nature of the interactions involved in the hydrogen bond formation: structure and stabilisation of the base pairs turn out to be determined mostly by electrostatic interactions. Preliminary calculations on stacked cytosine dimer are also reported. The SCF-MI/3-21G results show agreement with the counterpoise corrected SCF/6-31G** calculations.

The conjugate gradient method applied to the direct second-order minimization of energy

Abstract The conjugate gradient method is proposed for minimizing the second-order Δe. Formulae for derivatives are expressed in a constructive way: they specify to which derivatives and with which weight each integral (belonging to a non-redundant list) contributes. The case of geminal functions is fully treated. A test calculation on the BeH molecule is shown.