M. C. Caputo

On the theoretical determination of the static dipole polarizability of intermediate size silicon clusters

The B3PW91 method of the density functional theory has been applied to the study of the dipole polarizability of medium size silicon clusters employing pseudopotential on all of them. All electron calculations have been performed for those clusters with less than nine atoms. In addition, we have optimized the structures of the clusters with less than ten atoms. On using the modified genetic algorithm, fourteen conformers of silicon isomers with nine atoms have been determined. The corresponding geometry of these clusters was optimized and their relative stability determined. The calculated polarizabilities are compared with experimental data and previous theoretical results.

NMR Chemical Shielding and Spin-Spin Coupling Constants of Liquid NH3: A Systematic Investigation using the Sequential QM/MM Method

The NMR spin coupling parameters, (1)J(N,H) and (2)J(H,H), and the chemical shielding, sigma((15)N), of liquid ammonia are studied from a combined and sequential QM/MM methodology. Monte Carlo simulations are performed to generate statistically uncorrelated configurations that are submitted to density functional theory calculations. Two different Lennard-Jones potentials are used in the liquid simulations. Electronic polarization is included in these two potentials via an iterative procedure with and without geometry relaxation, and the influence on the calculated properties are analyzed. B3LYP/aug-cc-pVTZ-J calculations were used to compute the (1)J(N,H) constants in the interval of -67.8 to -63.9 Hz, depending on the theoretical model used. These can be compared with the experimental results of -61.6 Hz. For the (2)J(H,H) coupling the theoretical results vary between -10.6 to -13.01 Hz. The indirect experimental result derived from partially deuterated liquid is -11.1 Hz. Inclusion of explicit hydrogen bonded molecules gives a small but important contribution. The vapor-to-liquid shifts are also considered. This shift is calculated to be negligible for (1)J(N,H) in agreement with experiment. This is rationalized as a cancellation of the geometry relaxation and pure solvent effects. For the chemical shielding, sigma((15)N) calculations at the B3LYP/aug-pcS-3 show that the vapor-to-liquid chemical shift requires the explicit use of solvent molecules. Considering only one ammonia molecule in an electrostatic embedding gives a wrong sign for the chemical shift that is corrected only with the use of explicit additional molecules. The best result calculated for the vapor to liquid chemical shift Delta sigma((15)N) is -25.2 ppm, in good agreement with the experimental value of -22.6 ppm.

Theoretical study of the adsorption of H on Sin clusters, (n=3–10)

A recently proposed local Fukui function is used to predict the binding site of atomic hydrogen on silicon clusters. To validate the predictions, an extensive search for the more stable SinH (n=3-10) clusters has been done using a modified genetic algorithm. In all cases, the isomer predicted by the Fukui function is found by the search, but it is not always the most stable one. It is discussed that in the cases where the geometrical structure of the bare silicon cluster suffers a considerable change due to the addition of one hydrogen atom, the situation is more complicated and the relaxation effects should be considered.

Calculation of the fourth-rank molecular hypermagnetizability of some small molecules

A computational scheme has been developed within the framework of Rayleigh-Schrödinger perturbation theory to evaluate nonlinear interaction energy contributions for a molecule in the presence of an external spatially uniform, time-independent magnetic field. Terms connected with the fourth power of the perturbing field, representing the fourth-rank hypermagnetizabilities of five small molecules, have been evaluated at the coupled Hartree-Fock level of accuracy within the conventional common-origin approach. Gaugeless basis sets of increasing size and flexibility have been employed in a numerical test, adopting two different coordinate systems to estimate the degree of convergence of theoretical tensor components.

RESOLUTION OF ALKANE MOLECULAR POLARIZABILITIES INTO ATOMIC TERMS

Two additive schemes for resolving average molecular electric dipole polarizabilities into atomic contributions, based on the acceleration gauge for the electric dipole, are outlined. Extended calculations have been carried out for a few terms of the alkane series to test the reliability of the partition method. Gross atomic isotropic contributions evaluated for carbon, αAvC≈5.7 a.u., and hydrogen, αAvH≈2.7 a.u., are actually transferable from molecule to molecule, and can be used to predict fairly accurate average polarizabilities of higher homologous molecules in the alkane series.

Resolution of molecular polarizabilities of CH3–X and CH3–CH2–X derivatives into atomic terms

An additive scheme for resolving average molecular electric dipole polarizabilities into atomic contributions, based on the acceleration gauge for the electric dipole, has been applied to a series of methyl and ethyl derivatives, CH3–X and CH3–CH2–X. Extended calculations have been carried out to test the reliability of the partition method. Gross atomic isotropic contributions have been evaluated for carbon, hydrogen, and heteroatoms, showing a good degree of transferability from molecule to molecule. The theoretical values of atomic polarizabilities can be used to predict fairly accurate average polarizabilities of higher homologous molecules in the series of X-substituted alkanes.

Shielding polarizabilities via continuous transformation of the origin of the current density in the set of small molecules: H2O2,F2,H2C2,H2CO,NH3, HCN, and HNC

A procedure, based on a continuous transformation of the origin of the (quantum mechanical) current density that sets the diamagnetic contribution to zero (CTOCD-DZ ) all over the molecular domain, is applied to determine shielding polarizabilities to first order in a perturbing electric field. In any calculations relying on the algebraic approximation, irrespective of size and quality of the (gaugeless) basis set employed, all the components of the CTOCD-DZ magnetic shielding polarizability are origin independent, and the constraints for charge and current conservation are exactly satisfied. The effects of a static uniform electric field on the nuclear magnetic resonance (NMR) shielding of H2O2, F2, H2C2, H2CO, NH3, HCN, and HNC molecules have been investigated within the CTOCD-DZ method, and compared with the conventional results evaluated via the same basis sets, and with theoretical results taken from the literature.

Theoretical study of the magnetic properties of water molecules in non-uniform magnetic fields

Abstract The interaction Hamiltonian within the Bloch gauge for the potentials of the electromagnetic field has been used to define electromagnetic multipole moment operators and operators for the magnetic field of electrons acting on the nuclei of a molecule. Perturbation theory has been applied to evaluate the induced electronic moments and magnetic field at the nuclei. Multipole magnetic susceptibility and nuclear magnetic shielding tensors have been defined to describe the contributions arising in non-uniform magnetic fields, and their origin dependence has been analyzed. Extended numerical tests on the water molecule in a static, non-uniform magnetic field have been carried out, using the random-phase approximation within the framework of accurate Hartree-Fock zero-order wavefunctions.

Sum rules related to third-order properties: a numerical check

Abstract Although electrodynamics is formally invariant in a gauge transformation, the values of some physical quantities, e.g., magnetic properties, depend on the approximation employed to calculate them. The conditions for gauge independence of third-rank tensor properties that describe the response of a molecule in the presence of three perturbations, that is, external electric and magnetic field, and intramolecular nuclear magnetic dipoles, are discussed. The relationships for invariance of the physical properties to a gauge translation are exactly the same as the constraints for charge conservation. They are expressed in terms of second-rank response properties, namely electric polarizabilities and electric shielding at the nuclei. An extended numerical test has been carried out to determine the Hartree–Fock limit for a series of quantities entering the gauge-invariance sum rules.

Conditions for invariance of molecular magnetic properties in Landau gauge transformations

General constraints for invariance of magnetic properties in a gauge transformation are analyzed. Sum rules relative to the transformation from Coulomb to Landau gauges are examined in particular. Numerical tests for hydrogen fluoride, water, ammonia, and methane molecule have been carried out in large basis set calculations, using random‐phase approximation. The conditions for invariance are severe conditions for accuracy of variational molecular wave functions.