FH Molecules Research Articles

The quadratic response function in the THFD approximation and its application to frequency-dependent hyperpolarizabilities of the FH molecule

Frequency-dependent hyperpolarizabilities of the FH molecule are calculated in the TDHF quadratic response function formalism. Various first hyperpolarizabilities β(−ω.σ, ω1, ω2) which depend on two different frequencies are calculated, as well as the case of a monochromatic optical oscillating field. The validity of Shelton's approximation is discussed. Second hyperpolarizabilities γ(−ω.σ, ω1, ω2, ω3) for the dc-induced second-harmonic generation and the dc-induced optical rectification, as well as for the static case, are calculated using a finite-difference technique to differentiate the analytical β(−ω.σ, ω1, ω2). A new type of basis set (the “smooth-tempered” basis set) is implemented, as a modification of the even-tempered basis set. The method is applied to the largest basis set P2 ([14s10p6d4f/9s8p3d]) in this work. Basis P2 almost solves the unsaturation problem of basis sets in practice, and results for dipole moment, polarizability, and first and second hyperpolarizability with P2 are near the Hartree—Fock limit.

Finite-field fourth-order MBPT calculations of dipole moments, field, and field-gradient polarizabilities of diatomic molecules

The dipole moments and the independent components of the field polarizability α for H 2, CO, F 2,CH + and OH − and of the field-gradient polarizability A for CH +, CO and FH molecules were calculated at the self consistent field Hartree-Fock (SCF-HF) and at the complete fourth order many body perturbation theory (MBPT (4) ) level of approximation using the POL1 basis sets described recently by Sadlej. Excellent overall agreement with respect to the best values available is obtained for all electric properties and for all the species examined in this work. The only exceptions are the relatively low values obtained for the α xx component of the dipole polarizability of the OH − ion and for the A x,xz component of the FH molecule, owing to the absence of f-type GTOs in the POL1 basis.

Very accurate correlated calculations on diatomic molecules with numerical orbitals: The hydrogen fluoride molecule.

Numerical orbital coupled-cluster calculations on the FH molecule are reported, which obtain 99% of the possible correlation energy. Instead of requiring explicit ${r}_{12}$ functions, it is demonstrated that a one-particle but very well-chosen numerical orbital basis set is adequate to recover essentially all effects of electron correlation. Further reduction of the dimension of the numerical orbital basis set is accomplished via our recently proposed optimized virtual-orbital-space technique. Augmented by the exact second-order energy, the latter allows a reduction to as small as 25% of the original space with no appreciable errors in the correlation energy.

Erratum: Numerical coupled Hartree–Fock study of the total (electronic and nuclear) parallel polarizability and hyperpolarizability for the FH, H+2, HD+, and D2 molecules [J. Chem. Phys. 8 4, 4988 (1986)

Erratum: Numerical coupled Hartree–Fock study of the total (electronic and nuclear) parallel polarizability and hyperpolarizability for the FH, H+2, HD+, and D2 molecules [J. Chem. Phys. <b>8</b> <b>4</b>, 4988 (1986)

Finite-field many-body perturbation theory

The results of complete fourth order many-body perturbation theory (MBPT) calculations of the quadrupole moment tensor for the FH and H2O molecules are presented. The finite-field method employed in this study is based on the coupled Hartree-Fock (CHF) solutions for the externally perturbed system. The results are very close to the available experimental data. Of interesting features of the correlation perturbation series for the quadrupole moment components one should mention that the fourth order correlation correction is dominated by contributions involving triple and single substitutions in the reference Hartree-Fock function. Moreover, the correlation perturbation series for quadrupole moments appears to be less regular than the corresponding series for molecular dipole moments. Additionally complete fourth order MBPT calculations are performed for the quadrupole polarizability tensor of FH and H2O. The correlation corrections to the corresponding CHF values are large and exhibit similar regularities...

Perturbation theory of the electron correlation effects for atomic and molecular properties VI. Complete active space (CAS) SCF and MBPT calculations of electric properties of the FH molecule

A comparative study of the applicability of the CAS SCF and different fourth-order MBPT methods for the calculation of molecular electric properties is performed. The accuracy of the CAS SCF results for the dipole moment and dipole polarizability tensor of the FH molecule is governed and limited by the size of the active orbital subspace, while the complete fourth-order MBPT results seem to suffer from the truncation of the correlation perturbation series. Relatively large fourth-order correlation corrections to the calculated properties, arising from single and triple substitutions, have been found and indicate the importance of a careful treatment of all substitutions contributing in the given order of the MBPT expansion.

Complete fourth-order many-body perturbation theory calculations of the dipole moment and dipole polarizability of FH

A complete fourth-order many-body perturbation theory calculation of the dipole moment and dipole polarizability tensor is carried out for the FH molecule. Different approximations for the reduced resolvent operator are studied. Both the SD MBPT and SDQ MBPT schemes are found to give similar results. However, the fourth-order correlation corrections are dominated by the contribution of triple substitutions which is by no means negligible. The importance of a systematic treatment of all intermediate states in truncated MBPT schemes is discussed.

Diagrammatic perturbation theory: An application to the LiH and FH molecules using a universal even-tempered basis set

Diagrammatic many-body perturbation theory is applied to the ground states of the LiH and FH molecules at their respective equilibrium nuclear geometries. The same universal even-tempered basis set of Slater exponential functions is employed in each calculation. 94.0% and 82.3% of the correlation energy is recovered in LiH and FH, respectively.

A fourth-order invariant in many-body perturbation theory. Application to FH, OH2, NH3, CH4, N2, CO, HCN

Full fourth-order diagrammatic many-body perturbation theory calculations of electron correlation energies, including all singly excited, doubly excited, triply excited and quadruply excited states, are reported for the FH, OH2, NH3, CH4, N2, CO and HCN molecules. Fourth-order quantities which are invariant to arbitrary changes in scale and shifts of origin in the zero-order reference spectrum are constructed from these results.

Complete fourth-order calculations of the correlation energy of closed-shell molecules by diagrammatic RSPT

Complete fourth-order diagrammatic RSPT calculations of the correlation energy tor the LiH, BH, and FH molecules with Pople's 6-31G ++ basis are presented. The equilibrium geometry and spectroscopic constants are calculated for different levels of diagrammatic perturbation theory. The results are compared with the Coester-Kümmel theory in its linear and CPMET approximations.

Electronic Structure of Some Diatomic Hydrides

The self-consistent field molecular orbital (SCF-MO) method is applied to the calculation of the ground states of the CH, CH+, NH, OH, and FH molecules. Results are reported for the ionization potentials, excitation energies, binding energies, and dipole moments. The relative behavior of the bonding in these molecules is exhibited by an electron distribution analysis and the importance of s-p promotion in a single configuration description of these molecules is emphasized.