Finite-field many-body perturbation theory IV. Basis set optimization in MBPT calculations of molecular properties. Molecular quadrupole moments

The choice of truncated basis sets and their optimization for MBPT calculations of molecular properties are discussed. It is pointed out that computing the correlation corrections to some kth order property by using the MBPT approach requires the knowledge of accurate perturbed orbitals through the kth order. Hence, it is argued that the basis set functions can be optimized with respect to the perturbed energies calculated within the coupled Hartree-Fock method. The proposed procedure is illustrated by MBPT calculations of quadrupole moments of H₂ and FH. Additionally, also some estimates of the quadrupole polarizability tensor components for these molecules are obtained.     

The electronic structure of molecules by a many-body approach: VI. The assignment of the HeII photoelectron spectrum of SF6

The ionization potentials of SF₆ are studied by an ab initio many-body approach which includes the effects of electron correlation and reorganization beyond the one-particle approximation. The ordering of the ionization potentials in the energy range of the HeII line obtained in the SCF approximation is 1t_1g 5t_1u, 3e_g + 1t_2u, 1t_2g, 4t_1u, 5a_1g (the “+” sign denotes nearly equal ionization potentials), whereas in the many-body calculation it is 1t_1g, 5t_1u + 1t_2u, 3e_g, 1t_2g, 4t_1u, 5a_1g. The second band in the photoelectron spectrum thus corresponds to two ionization potentials and the third one to only one.     

Wellenmechanische Untersuchungen an der Wasserstoffbrücke zwischen zwei Berylliumatomen

The systems Be₂H⁺ and Be₂H^? have been investigated for different nuclear positions, the H atom being situated between the Be atoms, taking all electrons into account, using the Allgemeines Programmsystem/SCF –MO –LC (LCGO ) Verfahren. For Be₂H⁺ there results a minimum total energy of ?29.3824 a.u. in the linear symmetric configuration with a bond distance of 1.609 Å. The ionization energy was estimated to be 12.37 eV. The formation of Be₂H⁺ can be interpreted as an addition of Be to BeH⁺ with an exotherm heat of reaction of 7.0 kcal/mole. The electron affinity of BeH⁺ (ionization energy of BeH) was estimated to be approximately 7.24 eV. All force constants of Be₂H⁺ and BeH⁺ have been computed. Using SCF results, the Be₂H^? was found to be unstable.     

SCF LCAO MO studies on the hydration of ions: The system F− · 2H2O

The energy surface of the dihydrated fluoride anion (F·2H₂O)^–1 is studied for a number of different geometry points near the equilibrium structure within the SCF LCAO MO framework, using an extended gaussian basis set to approximate the molecular wavefunctions. For the first and second hydration step of the fluoride anion the corresponding hydration energies are calculated to beB ₁ ^scf =24.1 kcal/mole andB ₂ ^SCF =20.8 kcal/mole (experimental measurements: 23.3 kcal/mole and 16.6 kcal/mole, respectively). The hydration energies and equilibrium bond distances obtained for the dihydrated fluoride anion (F·2H₂O)^– are compared with those found for the monohydrate (FHOH)^– and with corresponding results of the dihydrated lithium cation (Li · 2H₂O)⁺. The system (F·2H₂O)^– is taken as a very simple model to discuss some basic features of the hydration process of small ions and to study the influence of a negative ion on an adjacent hydrogen bond.We would like to thank our technical staff for valuable help in carrying out these calculations.     

Wellenmechanische Absolutrechnungen an Molekülen und Atomsystemen mit der SCF?MO?LC(LCGO) Methode. III. Das Cyclopropan (C3H6)

The C₃H₆ has been investigated ab initio, taking all 24 electrons into account, using the Allgemeines Programmsystem/SCF ? MO ? LC (LCGO ) Methode. Variation of the C? C distance gives a total energy of ?116.02 a.u. at a C? C distance of 2.91 a.u. The ionization energy was found to be 10.33 eV.     

Wellenmechanische Absolutrechnungen an Molekülen und Atomsystemen mit der SCF?MO?LC(LCGO) Methode. IX. Das System (Li2H)−

The system (Li₂H)^? has been investigated ab initio for several nuclear positions, taking all eight electrons into account, using the Allgemeines Programmsystem/SCF ? MO ? LC (LCGO ) Verfahren. A stable molecule was found for the linear symmetric configuration with a bond distance of R_LiH = 3.41 a.u., and a total energy of ?15.3874 a.u., which is about 0.0114 a.u. (0.311 eV, 7.61 kcal/mole) lower than the sum of the comparable SCF energies of the systems LiH and Li^?. The force constant of the symmetric vibration was estimated to be k = 1.64722 × 10⁶ dyn/cm and the frequency to be ω = 1998.9 cm^?1. The results are discussed.     

Second-order polarization propagator calculations of dynamic dipole polarizabilities and C6 coefficients

The frequency-dependent dipole polarizability, α(E), is calculated using the second-order polarization propagator approximation (SOPPA ). We have shown how to express α(E) as a function of E² and thus obtained a form of α(E) that can be used to compute C₆-coefficients without invoking complex arithmetic. For He we find that SOPPA recovers a large fraction of the correlation contribution for all frequencies, whereas for H₂ where the correlation contributions are much smaller and also basis set-dependent, we find a less definite trend of SOPPA relative to RPA .     

Wellenmechanische Absolutrechnungen an Molekülen und Atomsystemen mit der SCF?MO?LC(LCGO) Methode. II. Das Benzol (C6H6)

The C₆H₆ has been investigated ab initio for the equilibrium distance of the centers, taking into account all 42 electrons, using the Allgemeines Programmsystem/SCF ? MO ? LC (LCGO ) Methode. A total energy of ?227.27 a.u. and an ionization energy of 8.5 eV were found. Further one of the π orbitals was more strongly binding than some of the σ orbitals.     

Direct evaluation of one-electron properties in coupled cluster methods

Summary An analysis of a method for approximate calculations of expectation values for one-electron operators from available coupled cluster amplitudes is presented and illustrated numerically for the polarizability of the Be atom. The one-particle density matrix resulting from the present approach is accurate through the fourth order in the electron correlation perturbation. It has been found that, in order to obtain quantitative agreement between the energy derivative results and the approximate expectation value formalism, the third orderT ₁ T ₂⁽⁰⁾ wave function term must be included into the calculation of the one-particle density matrix. The present method is also considered as a promising tool for calculations of higher-order atomic and molecular properties from high level correlated wave functions.