Many-body calculation of the electric field gradient in the hydrogen molecule

The electric field gradient in the hydrogen molecule has been calculated by diagrammatic many-body perturbation theory (MBPT ) in Gaussian basis sets. The procedure through third order in electron correlation gives a value for the field gradient of 0.34041 a.u., which is 0.8% greater than the accurate value. The result is discussed in terms of the completeness of the basis sets and the convergence of the perturbation expansion.     

Unitary group approach to crystal field theory: Projection operator approach

A treatment for a strong crystal field of cubic symmetry is given using the unitary group approach. Projection operator techniques are utilized to achieve results equivalent to those given recently by Wen Zhenyi.     

Bipolar electrode focusing: tuning the electric field gradient

Bipolar electrode (BPE) focusing is a developing technique for enrichment and separation of charged analytes in a microfluidic channel. The technique employs a bipolar electrode that initiates faradaic processes that subsequently lead to formation of an ion depletion zone. The electric field gradient resulting from this depletion zone focuses ions on the basis of their individual electrophoretic mobilities. The nature of the gradient is of primary importance to the performance of the technique. Here, we report dynamic measurements of the electric field gradient showing that it is stable over time and that its axial position in the microchannel is directly correlated to the location of an enriched tracer band. The position of the gradient can be tuned with pressure-driven flow. We also show that a steeper electric field gradient decreases the breadth of the enriched tracer band and therefore enhances the enrichment process. The slope of the gradient can be tuned by altering the buffer concentration: higher concentrations result in a steeper gradient. Coating the channel with the neutral block co-polymer Pluronic also results in enhanced enrichment.     

Near-Hartree—Fock calculation of the electric field gradient tensor at the hydrogen nucleus in water

The electric field gradient tensor at the hydrogen nucleus in water has been calculated in an SCF calculation with local near-Hartree—Fock quality using asymmetric basis sets. The results are in excellent agreement with results obtained by Davidson and Feller with a basis set of uniform near-Hartree—Fock quality and deviate only a few percent from experimental results. Calculated and experimental data are combined to improve the transformed experimental values.     

Application of the projection operator formalism to non-hamiltonian dynamics

Reconstruction of equations of motion from incomplete or noisy data and dimension reduction are two fundamental problems in the study of dynamical systems with many degrees of freedom. For the latter, extensive efforts have been made, but with limited success, to generalize the Zwanzig-Mori projection formalism, originally developed for hamiltonian systems close to thermodynamic equilibrium, to general non-hamiltonian systems lacking detailed balance. One difficulty introduced by such systems is the lack of an invariant measure, needed to define a statistical distribution. Based on a recent discovery that a non-hamiltonian system defined by a set of stochastic differential equations can be mapped to a hamiltonian system, we develop such general projection formalism. In the resulting generalized Langevin equations, a set of generalized fluctuation-dissipation relations connect the memory kernel and the random noise terms, analogous to hamiltonian systems obeying detailed balance. Lacking of these relations restricts previous application of the generalized Langevin formalism. Result of this work may serve as the theoretical basis for further technical developments on model reconstruction with reduced degrees of freedom. We first use an analytically solvable example to illustrate the formalism and the fluctuation-dissipation relation. Our numerical test on a chemical network with end-product inhibition further demonstrates the validity of the formalism. We suggest that the formalism can find wide applications in scientific modeling. Specifically, we discuss potential applications to biological networks. In particular, the method provides a suitable framework for gaining insights into network properties such as robustness and parameter transferability.     

Relativistically corrected electric field gradients calculated with the normalized elimination of the small component formalism

Based on the analytic derivatives formalism for the spin-free normalized elimination of the small component method, a new computational scheme for the calculation of the electric field gradient at the atomic nuclei was developed and presented. The new computational scheme was tested by the calculation of the electric field gradient at the mercury nucleus in a series of Hg-containing inorganic and organometallic compounds. The benchmark calculations demonstrate that the new formalism is capable of reproducing experimental and theoretical reference data with high accuracy. The method developed can be routinely applied to the calculation of large and very large molecules and holds considerable promise for the interpretation of the experimental data of biologically relevant compounds containing heavy elements.     

Numerical integration of overlap and ligand contributions to the electric field gradient

The total electric field gradient (EFG) tensor V _pq is calculated by numerical integration of threedimensional integrals. Each of them is solved a) by integrating over one dimension analytically and b) by integrating over the remaining two dimensions on the basis of a Gauss-type integration rule. The use of 100 abscissas in the twodimensional numerical integration scheme yields satisfactory accuracy which was checked by evaluating overlap integrals; an increase to 400 abscissas does not increase the result drastically. Calculating quadrupole splittings E _Q from numerically integrated electric field gradient tensors V _pq we observe that depending a) on the amount of covalency and b) on the amount of deviation from octahedral or tetrahedral symmetry, involved in a molecular system, overlap and ligand contributions to V _pq play an important role. Especially for the sandwich compound ferrocene, Fe(C₅H₅)₂, we find a significant difference between E _Q ^{num. int.} which follows from the numerical integration method, and E _Q ^conventional which is derived from effective charges.Supported by Deutsche Forschungsgemeinschaft     

Molecular orbital calculation of hyperfine interactions,electric field gradient and quadrupole splitting in reduced rubredoxins

The active site of rubredoxins, the simplest class of iron-sulfur, electron-transfer proteins consists of a single Fe atom surrounded by a distorted tetrahedral array of four cysteine sulfur atoms. In a previous paper on the oxidized rubredoxins, we calculated the electric field gradient at the Fe⁵⁷ nucleus, the resultant quadrupole splitting and the hyperfine field due to interaction between the Fe nucleus spins and the net electron spin of the molecular complex. In this paper, we are going to present our calculated results of the same set of properties for the reduced state, using the molecular orbitals similarly obtained from an Iterated Extended Hückel calculation. Significant contribution of the anisotropy to the hyperfine field as well as the sign of the electric field gradient, and hence the quadrupole splitting allow us to pin down conformations which give the best agreement with the experimental results. In fact, the conformation (conformer A) which represents a small movement of one of the S atoms from its crystal structure position in such a way that pairs of S atoms lie in ⊥ planes yield remarkably good results for all the physical properties calculated in both oxidation states. This consistency also suggests that there is no appreciable conformational change through the oxidation process.     

Ab initia MO calculation in terms of localized orbitals of the 14N electric field gradient in nitriles

The contributions of each localized orbital of the CN group and of the molecular remainder to the N electric field gradient (EFG) were calculated for nitriles with R=H, F, CH₃, OH, NH₂, CCH, COH, NO, CN and the E and Z forms of iminoacetonitrile. The changes in the EFG introduced by substituents resulted mainly from the polarization and conjugation of the C-N bonds, with a small contribution from the N lone pair. The total EFG has a large and rather constant contribution from the N lone pair, which is modified by the contributions from the three C-N bonds and the molecular remainder. The resulting EFG is determined by the signs and magnitudes of the C-N bonds' contributions for each substituent and to a lesser degree by the molecular remainders. The asymmetry parameter of the EFG is mainly determined by the inequivalence of the C-N bonds with a very small contribution from the molecular remainder. The molecular remainder and the crystal field in solids contribute more to the largest component of the EFG than to the asymmetry parameter. All these results have allowed us to discuss the validity of the assumptions made in the Townes and Dailey theory when it is applied to nitriles.     

Mean value of the electric field gradient in a molecule

The relationship between the mean value of the second derivative of the electrostatic potential of the electronic shell of a molecule on its axis and the first derivative of the energy of the molecule with respect to the internuclear distance has been established.Scientific-Research Institute of Physics, Leningrad State University. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 2, pp. 47–50, March–April, 1991.     

Self-consistent field calculation of the proton affinity of the NH 2 − ion

The result for NH ₂ ^– is used in a refinement of an earlier calculation in the same approximation for the NH₃ molecule. The calculated proton affinity of NH ₂ ^– is compared with experimental values.Read at the Third All-Union Conference on Quantum Chemistry, Kishinev, 1963.     

Zero electric field gradient mixtures for the elucidation of orientational mechanisms

A novel zero electric field gradient nematic liquid crystal made up from two nematic liquid crystal components is employed as a solvent for a series of molecules ranging from small molecules to mesogens themselves. Nuclear magnetic resonance is used to determine the degree of order of the solute and solvent molecules. Results are compared to those obtained for two completely different zero electric field gradient nematic mixtures. The comparison strongly indicates that for a variety of molecules largely differing in size, shape and flexibility their degree of order can be described by a single orientation mechanism. This mechanism can be adequately modelled by a simple phenomenological mean field model based on the size and shape anisotropy of the dissolved species. The use of zero electric field gradient mixtures in combination with this mean field model allows the prediction of solute order parameters at approximately the 10 per cent level.     

Energy gradient in a multi-configurational SCF formalism and its application to geometry optimization of trimethylene diradicals

Previous methods of analytic evaluation of the potential energy gradient with respect to nuclear coordinates have been limited to single determinant Hartree-Fock wavefunctions. An expression and a practical method are presented for analytic gradient evaluation for MCSCF wavefunctions of certain widely applicable types. A geometry optimized of trimethylene diradical reaction intermediates has been actually accomplished by the use of the energy gradient for an ab initio MCSCF wavefunction.     

The generalized separated electron pair model. 1. An application to NH3

The utility of the separated electron pair (SEP ) model (strongly orthogonal geminals) is examined quantitatively, for pyramidal and planar nuclear configurations of the NH₃ molecule. The best SEP wave function computed for each species is capable of recovering about half of the correlation energy obtained by a fairly accurate configuration interaction (CI ) calculation, (corresponding to roughly 25% of the total molecular correlation energy). It is illustrated that the model can be systematically extended with only a modest effort to yield more accurate results (about 40% of the total correlation energy). The fact that the corrections to the SEP model have a simple physical interpretation suggests that this model may be a useful starting point for “brute force” CI calculations on larger chemical systems.     

Numerical evaluation of matrix elements of the electric field and electric field gradient operators in a slater basis set

A method is proposed for evaluating all matrix elements of the electric field and electric field gradient operators in a Slater basis set fo systems with an arbitrary number of nuclei and geometry. These integrals are evaluated using a numerical quadrature after having modified the integrand to remove all infinities. The integration ranges are broken to avoid integrating through cusps in the integrand. With reasonable grids these procedures are adequate for numerical evaluation with an accuracy of five to six decimal places (in a.u.). Particular cases are briefly discussed.     

The generalized separated electron pair model. II. An application to NH,NH3, NH,NH2− and N3−

The Separated Electron Pair (SEP) model (Strongly Orthogonal Geminals) and methods for its systematic extension has been applied to the series: NH, NH₃, NH, NH^2? and N^3?. On going from NH to N^3?, the SEP model, in its most general form, recovers 85–75% of the intrapair correlation energy and 60–55% of the interpair correlation energy obtainable with the given basis set. The best wave functions for each species recovered about 45–50% of the total empirical correlation energy which is expected to be very close to the basis set limit. It was apparent that the SEP model yields a set of one-electron functions that are very useful for further improvement of the wave function. This fact apparently remains true even when the SEP model itself gives very poor energies.