Coupled Hartree Fock Research Articles

Ab initio calculations of linear and nonlinear polarizabilities in the side-chain direction on the conjugated polymers

Linear polarizabilities and third-order hyperpolarizabilities in the side-chain direction are calculated using the ab initio coupled Hartree—Fock method on polyacetylene and its derivatives. From these calculations, it is found that hyperpolarizabilities become larger by interactions between the main chain and the side chains; and, especially, the third-order hyperpolarizabilities are sensitively affected by the substituent group.

Correlated calculations for the nuclear magnetic shieldings of CO and HCN

Nuclear magnetic shielding tensors and spin rotation constants are calculated for CO and HCN using both the coupled Hartree-Fock (CHF) and the second-order polarization propagator approximation (SOPPA). For CO we find that SOPPA recovers about half of the difference between CHF and experiments for both nuclei. For HCN there is no effect of SOPPA for H, little for C, but a large effect for N, where the resulting isotropic shielding, σ n = -17 ppm, is in good agreement with the most recent experiment. We have also analysed some earlier correlated calculations of shieldings of CO. Isotope effects on the shieldings are reported for CO.

Time-dependent Hartree–Fock second-order molecular properties with a moderately sized basis set. II. Dispersion coefficients

Time-dependent coupled Hartree–Fock frequency-dependent polarizabilities are used to obtain ab initio dipole–dipole C6, dipole–quadrupole C8, and triple–dipole ν, dispersion coefficients. The moderately sized 6-31G (+sd+sp) basis set optimized for calculation of molecular static dipole polarizabilities has enabled the computation of dispersion coefficients for a wide variety of molecules containing atoms up to chlorine. Results are presented for 48 molecules including benzene, cyclohexane, SF6, and CCl4. Appropriate scaling of 6-31G(+sd+sp) results for C6 and ν enables the prediction of these coefficients to within 3% of experimental estimates that are based on dipole oscillator strength distributions. Results for the mean static quadrupole polarizability C̄(0) and C8 dispersion coefficient are presented for nondipolar molecules and the origin dependence of C8 is investigated.

Time-dependent Hartree–Fock second-order molecular properties with a moderately sized basis set. I. The frequency dependence of the dipole polarizability

Time-dependent coupled Hartree–Fock calculations of the frequency-dependent mean polarizability α(ω) and its anisotropy Δα(ω) are presented for a wide range of molecules containing first and second row atoms. The Cauchy moments S(−2) and S(−4), which describe the dispersion in α(ω), are systematically underestimated by 20% and 40%, respectively, with the 6-31G(+sd+sp) basis set. The dispersion in Δα(ω) is also underestimated, typically by 50%. Many exceptions to this behavior are observed, most of which appear to be an underestimate of the experimental dispersion in Δα(ω) by a greater amount. This seems to be the result of systematic experimental overestimates of dispersion in Δα(ω) for molecules with very small Rayleigh depolarization ratios (ρ0<10−2), suggesting that the vibrational Raman contribution in these experiments is not only important, but significantly frequency dependent.

Polarisability of the oxide ion in crystalline BeO

The polarisability of an oxide ion in the BeO lattice is obtained from all-electron coupled Hartree—Fock calculations on an embedded ion cluster. The ion is nearly isotropic, with calculated mean polarisability ▪ au and a small positive anisotropy. The result agrees to within 3% with the value of 8.77 au derived from an extended Lorentz-Lorenz treatment of the refractive index of solid BeO, thus supporting an ionic picture of the electronic structure of this material. The unstability of the Gladstone—Dale equation for determination of ionic and molecular polarisability is discussed.

Cotton—Mouton constants and electric hyperpolarizabilities for the helium isoelectronic sequence

The Cotton—Mouton constants and hyperpolarizabilities are evaluated in the coupled Hartree—Fock approximation for members of the helium isoelectronic sequence with nuclear charges in the range 2 to 10 and compared with their values from correlated calculations. A relationship between magnetic and electric-field-gradient induced birefringences is derived for spherical molecules.

NMR shielding calculations beyond coupled Hartree—Fock: second-order correlation effects in localized-orbital/local-origin calculations of molecules containing phosphorus

The localized-orbital/local-origin (LORG) method and the second-order polarization propagator approximation (SOPPA) are combined to form a local gauge theory of nuclear magnetic shielding that includes electron-correlation effects through second order in the fluctuation potential. Calculations are presented for the NMR shielding tensors of a set of molecules spanning the range of 31P shieldings. The results show that correlation effects on the shielding can be significant, and that the use of local gauge origins yields marked improvement over common-origin calculations.

Coupled Hartree–Fock dipole polarizabilities of the smaller n-alkanes CnH2n+2(n≤7)

We have calculated the dipole polarizabilities of the ‘‘chain’’ alkanes CnH2n+2 (n ≤7) using the coupled Hartree–Fock method. Our average values are 97%–98% of gas phase experimental values. For the larger alkanes, each CH2 unit adds 12.3 a.u. to the average value (within 2%). The anisotropic polarizability also agrees well with gas phase experimental values, but it continues to increase with the length of the chain. We have also obtained dipole moments for the odd alkanes−propane, pentane, and heptane. For propane, there is a gas phase experimental value with which we agree quite well.

Ab initio 13C shielding parameters in acetylene clusters

The coupled Hartree—Fock method has been used to calculate ab initio carbon magnetic shielding tensors for small clusters of acetylene molecules. The chemical shift increases from the monomer to the dimer and the trimer. This is mainly due to increased diamagnetism, which is imperfectly cancelled by increased paramagnetism due to loss of axial symmetry. Anisotropic effects are shown to be small in both the dimer and the trimer.

Frequency-dependent polarizabilities and van der Waals coefficients of half-open-shell systems in the time-dependent coupled Hartree–Fock approximation

In this paper we present a derivation of time-dependent coupled Hartree–Fock (TDCHF) theory for the case of half-open shells. With this method frequency-dependent polarizabilities are calculated for the hydrogen and nitrogen atom, as well as for the diatomics CN, NH, and OH+. van der Waals coefficients of the half-open-shell systems with the H atom and the H2 molecule are computed. Other dispersion coefficients for dimers consisting of these monomers are available upon request.

D9 dipole dispersion coefficients

A formula is derived for D 9, the first correction to the usual single-term approximation for the dispersion dipole of a pair of dissimilar atoms. The expression is a Casimir—Polder integral involving dipole and quadrupole polarisabilities, dipole—dipole—quadrupole and dipole— quadrupole—octopole hyperpolarisabilities on each atom. A coupled Hartree—Fock scheme for its ab initio calculation is implemented and static approximation to D 9 show it to be of the same sign as D 7 but larger in magnitude (when both are expressed in atomic units). CHF calculations on H and He give D 9(H +He −)=−3390 au, i.e. over 25 a 2 0 times D 7, and the R −9 local dipole in H…H is over 30 R −2 times the better known R −7 moment.

Nuclear magnetic shieldings and spin rotation constants of HF and N2

The paramagnetic contribution to the nuclear magnetic shieldings and the spin rotation constants are calculated using polarization propagator theory. Results are reported both in the first order approximation [equivalent to the coupled Hartree–Fock (CHF) method] and in the second order polarization propagator approximation (SOPPA). It is demonstrated how the constant Cgauge which gives the gauge origin dependence of the total nuclear magnetic shielding in a finite basis set [σ(Rc+d)=σ(Rc)+d⋅Cgauge] can be calculated from the polarization propagator. The magnetic shieldings of H and F in HF are nearly the same in CHF and SOPPA and results from both levels of theory agree well with experiment. For N2, σ(SOPPA)=−72.2 ppm, also in good agreement with the most recent measurement. However, for N2 there is a large correlation effect since σ(CHF)=−106.5 ppm. The computed spin rotation constant for N2 is M(15N)=20 kHz, i.e., about 2 kHz lower than its measured value. This value of M(15N) corresponds to σ(N)=−72.2 ppm.

Calculation of NMR shieldings and other properties for three and five coordinate Si, three coordinate O and some siloxane and boroxol ring compounds

Valuable information on the geometric and electronic structure of both predominant and defect species in the bulk and on the surface of amorphous SiO 2 can be obtained from solid state 29Si and 17O NMR. Most previous NMR.studies have made assignments of structure types to NMR signals by relying on a comparison to crystalline reference materials. Using the quantum mechanical technique of Coupled Hartree-Fock Perturbation Theory (CHFPT) we can directly calculate NMR shielding tensors, σ, for Si and O and electric field gradients tensors, q for O in silicates. Previous CHFPT calculations on (SiH 3) 2O at 〈 Si O Si = 180° to 140° semiquantitatively reproduced observed trends in σ for SiO 2 polymorphs. These calculations have been improved and extended to 〈SiOSi = 120° in (SiH 3) 2O and to the small siloxane rings H 4Si 2O 2, H 6Si 3O 3, H 8,Si 4O 4 which are models for the ring structures which may occur in the bulk and surface of amorphous SiO 2. Thus, predictions can be made of the 17O and 29Si NMR characteristic of such species. We have also calculated NMR shieldings and other properties for three and five coordinate Si and for three coordinate O. The 29Si NMR shielding increases with coordination, as expected, and five coordinate Si shows an anisotropy which although large is still smaller than that inferred from spin-lattice relaxation times in silicate melts. O q values are also calculated for (BH 2) 2O and H 3B 3O 6. The results are consistent with O EFGs and Raman frequencies observed in B 2O 3 glass, supporting a boroxol ring model.

Coupled Hartree-Fock calculations of atomic polar tensors and the dipole polarisability of the benzene molecule

Coupled Hartree-Fock perturbation theory has been applied within the framework of high-quality basis sets to estimate the Hartree-Fock limit for the nuclear electric shielding tensors and the electric polarisability of the benzene molecule.

Polarisability of the bromide anion in NaBr. Parameters for simulation of molten NaBr

Ab initio coupled Hartree–Fock calculations on Br– in NaBr give a polarisability of 27.6 a.u., a reduction of more than 35% from the free-ion value. Electron correlation, approximated by Moller–Plesset theory, adds 1 a.u. and brings the calculated bromide polarisability to within 1% of the value derived from the experimental refractive index of the solid. Polarisability derivatives with respect to nearest-neighbour displacements are calculated and interpreted in terms of changes in the confining potential well of a distorted solid.

Analysis of some significant processes for molecular polarization

The polarisability, the first and second hyperpolarisabilities of NH2—C6H4—CnHn—CHC5H4, where n= 2, 4 and 6, as well as of some related compounds are reported. The effects of isomerism, conjugation and charge-transfer on the properties are discussed. In addition the influence of increasing the length of the conjugation path on the linear and non-linear electric properties has been commented upon. The properties have been computed using an extended-basis CNDO wavefunction and the coupled Hartree–Fock perturbation theory of McWeeney et al. The employed basis sets have been shown to give polarisability (α) and second hyperpolarisability (γ) values, for some fragments of the considered molecules, in reasonable agreement with the experimental results.

Coupled Hartree-Fock calculation of the cotton-mouton constant and hyperpolarizability of helium

Expressions for the diamagnetic part of the Cotton-Mouton constant and the hyperpolarizability of helium are obtained within the coupled Hartree-Fock approximation; they involve solutions of integro-differential equations which are solved numerically in a calculation of these properties. An earlier result is recalled to yield the complete Cotton-Mouton constant.

Dynamic polarizabilities and Rydberg states of open shell atomic systems

Time dependent coupled Hartree-Fock (TDCHF) theory is applied to calculate frequency dependent polarizabilities, transition energies, oscillator strengths and effective quantum numbers of several excited states of the open shell ions Al, Si+, P2+, S3+, Cl4+, Ar5+, Cl and Ar+ in the 2P state within and beyond the normal dispersion region. The Roothaan formalism has been adopted to deal with the open shell problem. The excitation energies are extracted from the positions of the poles of an appropriate functional. Analytic representations of the singly excited Rydberg states have been found. The results obtained compare well with spectroscopic and other elaborate theoretical data wherever available. Inner shell excitations have been found for the first time within TDCHF theory.

Erratum: The second hyperpolarizability of HCl and the effect of basis set variation on this property in hydrogen fluoride by fully coupled Hartree–Fock perturbation theory with a method for circumventing the transformation of two-electron integrals. An a b i n i t i o study [J. Chem. Phys. 8 5, 2831 (1986)

Erratum: The second hyperpolarizability of HCl and the effect of basis set variation on this property in hydrogen fluoride by fully coupled Hartree–Fock perturbation theory with a method for circumventing the transformation of two-electron integrals. An <i>a</i> <i>b</i> <i>i</i> <i>n</i> <i>i</i> <i>t</i> <i>i</i> <i>o</i> study [J. Chem. Phys. <b>8</b> <b>5</b>, 2831 (1986)

NMR chemical shifts of CX and XCY molecules (X, Y = O, S, Se, Te): A comparison of coupled Hartree-Fock, semi-empirical rex and experimental results

Carbon-13 and selenium-77 NMR results are reported for CSe 2 dissolved in nematic liquid crystals. The obtained chemical shift anisotropies, Δσ, are 506 ± 30 ppm and 2210 ± 120 ppm for 13C and 77Se, respectively. The error limits include the estimated uncertainty from the unknown Δ J(CSe). Coupled Hartree-Fock (CHF) calculations are reported for the shielding tensors for the entire series CX and CX 2, X=OSe, and for OCS. The degree of incompleteness of the basis is tested using sum rules. All shielding tensors are calculated using at least two gauge origins. Dipole and quadrupole moments and electric field gradients are also given. Relativistic extended Hückel (REX) calculations are also reported, both for the paramagnetic chemical shift terms and for the spin-spin coupling tensors.