David Moncrieff

On the accuracy of the algebraic approximation in molecular electronic structure calculations. III. Comparison of matrix Hartree-Fock and numerical Hartree-Fock calculations for the ground state of the nitrogen molecule

A comparison of matrix Hartree-Fock calculations using basis sets of Gaussian-type functions with numerical Hartree-Fock studies is made for the ground state of the nitrogen molecule. The use of both atom- and bond-centred functions is investigated. It is shown that by employing systematic sequences of even-tempered basis sets the accuracy achieved in the numerical Hartree-Fock calculations can be approached when basis sets of atom-centred functions are employed and can be matched when bond-centred functions are included. An energy of -108.993 823 Hartree is obtained within the algebraic approximation which should be compared with -108.993 808 Hartree from previously reported fully numerical and semi-numerical calculations. The advantages of the matrix Hartree-Fock method are emphasized.

Finite basis set versus finite difference and finite element methods

Abstract The finite basis set Hartree—Fock method is compared with the finite difference and finite element counterparts. A comparison of the total and orbital energies for two diatomic systems demonstrates that the finite basis set approach can afford an accuracy approaching that achieved in finite difference and finite element methods provided that the large and flexible basis sets are systematically constructed. Some advantages of the finite basis set technique (the algebraic approximation) are emphasized.

A comparison of finite basis set and finite difference methods for the ground state of the CS molecule

A comparison is made of the accuracy with which the total electronic energy can be calculated by using either the finite basis set approach (the algebraic approximation) or finite difference methods in calculations using the Hartree-Fock model for the ground (X1 Sigma +) state of the carbon monosulphide molecule. The CS molecule is considered as a prototype for systems containing atoms from different rows of the periodic table. The convergence of the calculations carried out within the algebraic approximation is monitored by employing systematically constructed basis sets of increasing size. The dependence of the finite difference calculations on the numerical grid employed is studied.

A comparison of finite difference and finite basis set Hartree-Fock calculations for the ground state potential energy curve of CO

The Hartree-Fock ground state potential energy curve for the carbon monoxide molecule is calculated using both the finite difference and the finite basis set methods. The results of calculations performed at ten internuclear separations are reported and a comparision is made of the calculated potential energy curves over the range of internuclear separations, 1.970-2.330 a0, around the experimental equilibrium value. Potential energy curve constants and spectroscopic constants are determined.

A universal basis set for high precision electronic structure studies

The accuracy of the total energies obtained for the series of 14 electron molecules N2, CO, BF, NO+ and CN- by means of matrix Hartree-Fock calculations using a universal basis set of Gaussian-type functions is reaccessed in the light of improved finite difference calculations.

The observation of a Pb–Li bond; synthesis, structure and model molecular orbital (MO) calculations on the monomeric Ph3Pb–Li·(pmdeta) complex [pmdeta =(Me2NCH2CH2)2NMe]

The title compound has been synthesised by the cleavage reaction of Ph3Pb–PbPh3 with BunLi and has been shown to have a monomeric Pb–Li bonded structure in the solid state; ab initio calculations have been used to probe the nature of the early main group metal/heavy p block metal bonding involved.

A comparison of finite basis set and finite difference Hartree-Fock calculations for the BF, AlF and GaF molecules

A comparison is made of the accuracy with which the total electronic energy can be calculated by using either the finite basis set approach (the algebraic approximation) or finite difference methods in calculations using the Hartree-Fock model for the ground (X1Σ+) states of the Group IIIb fluorides: boron fluoride, aluminium fluoride and gallium fluoride molecules. The XF molecules, X = B, Al, Ga, are considered as a prototype for systems containing increasingly heavy atoms and numbers of electrons. The convergence of the calculations carried out within the algebraic approximation is monitored by employing systematically constructed basis sets of increasing size. The dependence of the finite difference calculations on the numerical grid employed is studied and it is found to be necessary to employ a multiple grid for the heaviest system, GaF, in order to achieve the target accuracy of 1 μE h for the total energy.

On the accuracy of the algebraic approximation in molecular electronic structure calculations: VI. Matrix Hartree - Fock and many-body perturbation theory calculations for the ground state of the water molecule

The use of distributed Gaussian basis sets in reducing the total basis set truncation error in matrix Hartree - Fock and second-order many-body perturbation theory calculations is investigated for the ground state of the water molecule at its equilibrium geometry. A distributed basis set of even-tempered Gaussian functions centred not only on the atomic nuclei but also on the O - H bond centres and at the midpoint of the line H - H is shown to give a matrix Hartree - Fock energy of . For diatomic molecules, distributed basis sets of this type have been shown to yield matrix Hartree - Fock energies which approach an accuracy of . The present distributed basis set, which includes functions of s, p, d and f symmetry, is employed in a second-order many-body perturbation theory study of correlation effects recovering 97.6% of an estimate of the exact second-order correlation energy given by Klopper. The effects of higher harmonics in the basis set are investigated and a basis set, which includes functions of s, p, d, f and g symmetry, is shown to be capable of recovering 98.6% of the exact second-order energy. The reliability of simple extrapolation techniques to estimate the effects of basis functions of h symmetry and higher is investigated and shown to support 99.8% of the estimate of the exact second-order correlation energy component.

Distributed basis sets of s-type Gaussian functions in molecular electronic structure calculations

The use of distributed basis sets of s-type Gaussian functions is investigated for the ground states of the one-electron, homonuclear, diatomic ions H2 +, He2 3+, Li2 5+ and Be2 7+ and for the ground states of the corresponding neutral species H2, He2, Li2 and Be2. Empirical schemes are employed both to generate the exponents defining the basis functions and to define their distribution in space. For the one-electron systems it is shown by comparing with the exact solutions of the Schrodinger equation that sub-μHartree accuracy can be achieved. For the many-electron systems the accuracy achieved decreases with increasing number of electrons but remains below ∼0·15 mHartree even for the largest of the molecular systems considered.

Comparison of the polarizabilities and hyperpolarizabilities obtained from finite basis set and finite difference Hartree-Fock calculations for diatomic molecules

A comparison is made of the accuracy by which the electric dipole polarizability αzz and hyperpolarizability βzzz can be calculated by using the finite basis set approach (the algebraic approximation) and finite difference method in calculations employing the Hartree-Fock model. The numerical and algebraic methods were tested on the ground states of H2, LiH, BH and FH molecules at their respective experimental equilibrium geometries. For the FH molecule at its experimental equilibrium geometry, a sequence of distributed universal even-tempered basis sets have been used to explore the convergence pattern of the total energy, dipole moment and polarizabilities. The comparison of finite difference and finite basis set methods is extended to geometries for which the nuclear separation, RFH, lies in the range 1.5-2.2 b. The methods give consistent results to within 1% or better. In the case of the FH molecule the dependence of truncation errors of the total energy, dipole moment and polarizabilities on the geometry have been studied and are shown to be negligible.