Derivative Hartree Fock Research Articles

New integral transforms for molecular properties and application to a massively parallel GIAO-SCF implementation

We present several new Gaussian integral transforms to be used with the Rys quadrature numerical integration method. These transforms lead to an elegant unified methodology for the calculation of the atomic Gaussian integrals that enter the calculation of many molecular wavefunctions and properties. The unified methodology is highlighted for several types of integrals that are at the heart of other modern electronic structure theoretical developments, including electric and magnetic properties. We make use of these transforms in a massively parallel implementation of the Gauge-Invariant-Atomic-Orbital (GIAO) method for the calculation of chemical shifts at the ab initio HF SCF level of theory. The implementation follows the original GIAO theory that bypasses computational tasks that are not massively scalable. Indeed the response of the wavefunction to the magnetic field is calculated by means of the Derivative Hartree–Fock method (DHF). The DHF method is amenable to high parallel efficiency as it involves only the calculation of Fock-like matrices from density-like matrices. The computationally intensive steps are shown to be highly scalable.

Derivative Hartree–Fock approach to molecular Sternheimer shielding. Calculation of intermolecular influence on nuclear quadrupole coupling

Molecular Sternheimer shielding constants, γ, the proportionality constants relating the electric field gradient at a quadrupolar nucleus to an external electric field gradient are usually introduced phenomenologically. In this report, we take a comprehensive view of the sensitivity of the electric field gradient at a nucleus to arbitrary external electrical potentials and we show how the response can be obtained from analytically determined properties via derivative Hartree–Fock theory. From application of this ab initio technique, values have been obtained for the first and second order changes in nuclear quadrupole coupling with respect to external fields and field gradients, as well as nearby ideal multipole moments, for HCN and HCl. These values have been used to evaluate the change in the nuclear quadrupole coupling for several weakly bound complexes and to provide a nonempirical approach to relative effects on Sternheimer shielding. In weak molecular complexes, the effect of uniform fields can be as sizable as the effect of external field gradients in the overall change in nuclear quadrupole coupling, and so the underlying issue of convergence of multipolar expansions is considered over a range of geometries. This is important for structural interpretations of both nuclear magnetic resonance (NMR) and microwave data, and a simple formula, representing a practical point of truncation, is presented for quadrupole coupling analysis.

Chemical-shift ranges in proteins

The results of ab initio derivative Hartree-Fock calculations of the dipole and quadrupole shielding polarizabilities and hyperpolarizabilities of a number of small molecules are reported, together with estimates of the electric fields and field gradients present in proteins. It is argued that weak electrical interactions, mediated via these shielding polarizabilities, make major contributions to the chemical-shift nonequivalencies observed in proteins due to folding into their native conformations. The electric-field-induced shifts may be very large (≈5 ppm for 13C, ≈10 ppm for 17O and 17F), due to the low dielectric constants found in proteins, and in some cases they may dominate the experimentally observed spectral shifts.

Multipole polarizabilities and hyperpolarizabilities of AHn and A2Hn molecules from derivative Hartree-Fock theory

Multipole polarizabilities and hyperpolarizabilities of AHn and A2Hn molecules from derivative Hartree-Fock theory

Electrical effects on the vibrational transitions of hydrogen fluoride due to hydrogen bonding and applied fields

Derivative Hartree-Fock (DHF) theory has been used to study the transition dipole moment of hydrogen fluoride in several hydrogen-bonded complexes and in the presence of applied fields. DHF is an open-ended, analytical means for finding energy derivatives with respect to any number of parameters, and large basis set calculations going through the seventh dipole hyperpolarizability (ninth derivative) are reported. Using multipole moments, multipole polarizabilities and hyperpolarizabilities, the intermolecular electrical influence on vibrational transitions is analyzed.

Electrical properties of ammonia and the structure of the ammonia dimer

Electrical multipole moments, polarizabilities, and hyperpolarizabilities of ammonia have been calculated with large basis sets through application of derivative Hartree–Fock (DHF) theory. With these properties, the orientational dependence of the electrical interaction between two ammonia molecules has been examined. The electrical interaction model indicates that the orientational angles of the two ammonias with respect to the a-inertial axis are strongly coupled. Internal rotation about the ammonia C3 axes is coupled as well. There are 18 equivalent minimum energy structures for the ammonia dimer and the lowest barrier for inversion is found to be about 250 cm−1. The predicted equilibrium structure differs noticeably from the recently determined experimental structure. Certain of the assumptions used in obtaining the experimental structure, we feel are not justified, in light of the coupling of internal motions apparent in the potential surface.

The hydrogen bonding influence on polarizability and hyperpolarizability. A derivative hartree-fock study of the electrical properties of hydrogen fluoride and the hydrogen fluoride dimer

Derivative Hartree—Fock calculations have been carried out to explore the dependence of the molecular dipole polarizability and hyperpolarizability tensors of the HF dimer as a function of the intermolecular separation. The results show a diminishing axial hyperpolarizability (β) in the course of hydrogen bond formation. The polarizability (α) changes little. The changes in the hyperpolarizability can be well explained as arising from the hyperpolarizability induced by the field of one monomer via the second and third hyperpolarizability of the other. This is consistent with the important role of simple electrical interactions in hydrogen bonding and indicates that the electrical properties of the dimer can be well predicted from the electrical properties of the isolated monomers.

Vibrational motion effects on molecular polarizabilities. Shifts in vibrational transition frequencies and transition moments of lithium hydride from applied electrical fields

Lithium hydride has been used to provide representative information on the effects of vibrational motion on molecular polarizabilities. Dipole and quadrupole polarizability and hyperpolarizability tensors were calculated using derivative Hartree–Fock (DHF) theory. Many of the calculated tensor elements were found to be changing with internuclear separation even in the vicinity of the equilibrium. Vibrational wave functions obtained from a numerical vibrational analysis were used to vibrationally average the electrical properties (tensor elements) of the lowest four vibrational states, and this showed that the averaged polarizabilities of the states have important differences. A manifestation of these differences is that there are shifts in the vibrational transition frequencies along with changes in the transition moments of LiH from applying electrical fields and field gradients. Field gradients can augment the shifts arising from uniform axial fields. This was determined by variationally finding vibrational state energies and transition frequencies as a function of the applied electrical potential.

Polarizabilities and hyperpolarizabilities of methane. The importance of valence charge polarization in polyatomic molecules

Derivative Hartree-Fock (DHF) theory has been used with several different basis sets to evaluate the dipole, quadrupole and octupole polarizabilities of methane through the second dipole hyperpolarizability. While for atoms and certain diatomic molecules, it is well established that dipole polarizabilities and possibly other moments and polarizabilities can be accurately evaluated only with large, extended basis sets, these calculations on methane counter the notion that this requirement carries over fully to polyatomics. It was found that what was essentially a singly polarized valence basis yields very many of the electrical properties in good agreement with extended basis set results. The reason for this is that the polarization of a polyatomic molecule is much more a transfer of charge along the molecular skeleton, an interatomic valence polarization, than a polarization of the charge cloud around each constituent atom.

Dipole (electric field) and quadrupole (field gradient) polarizabilities of hydrogen, nitrogen, and acetylene from the application of derivative Hartree–Fock theory

The electrical polarizabilities of a molecule are of potential importance in the molecule’s response to an applied field or in the interaction with other proximate molecules. Derivative Hartree–Fock (DHF) theory, which is an open-ended, uniform procedure for calculating properties corresponding to derivatives of the electronic energy, has been applied in obtaining electrical polarizabilities of hydrogen, nitrogen, and acetylene. In order to provide a more complete description than previously available, this has been carried through the third level of differentiation with respect to electric field and field gradient components, thereby yielding dipole and quadrupole hyperpolarizabilities. Extensive basis set tests performed on hydrogen reinforce the established need for extended sets with diffuse functions, and for balance in the flexibility of the s, p, d,...type functions on each center. DHF is well suited to the use of such large basis sets and in the case of acetylene, a basis of 100 functions was used to calculate its electrical properties.

Derivative Hartree—Fock theory to all orders

The means for determining all orders of derivatives of molecular orbitals is demonstrated. The corresponding energy derivatives are also generated as well as the next-higher energy derivatives. Any wavefunction obtainable witli a Fock operator method can be differentiated this way, and in the case of the first energy derivative of a closed-shell wavefunction, it reduces to the original approach of Pulay. The generality of the approach has made possible an implementation which, apart from the separate step of calculating derivatives of atomic basis function integrals, has no restriction on the degree of differentiation. Results of calculations carried out with this method are presented through the third hyperpolarizability function of carbon monoxide.