Accurate nonrelativistic energies for 2Po states of the Li isoelectronic series

With large Hylleraas-configuration interaction (CI) basis sets highly accurate upper bounds for the lowest ²P^o states of the Li isoelectronic series up to Ne are given. The corresponding Hamiltonian H and the operator Σ_{i < j}, ▿_i ▿_j are transformed into nonorthogonal coordinates expressed in interparticle and angular terms. The evaluation of the occurring integrals is reduced to the calculation of well-known auxiliary integrals. Furthermore some expectation values and isotope energies are calculated. The isotope energies are obtained using perturbation theory in first-order approximation. © 1997 John Wiley & Sons, Inc.     

Doubly excited 2Pe states in the lithium isoelectronic sequence

Accurate variational energies for even-parity core-excited ²P^e states in the lithium series (Li l-C IV) have been obtained by means of the superposition of correlated configurations (SCC) method. These energies can serve as a firm basis for the theoretical interpretation and proper assignments of several ²P^e → ²P^o transitions in lithium-like ions.     

g-Hartree ab-initio calculations of the total energies of the four-electron isoelectronic series

The atomic total energies of the four-electron isoelectronic series are calculated by theg-Hartree 2nd order perturbation theory and the Dirac-Hartree-Fock-Rayleigh-Schrödinger 2nd order perturbation theory. The Coulomb correlation energy is calculated by these theories. The Breit interaction, vacuum polarization, self-energy and Q.E.D. corrections are calculated by the lowest order approximation. The results show that theg-Hartree approach overestimates the Coulomb correlation energy. However, with an increase of the nuclear charge, it overestimates much less. In the case of the Hartree-Fock 2nd order calculation, it underestimates the Coulomb correlation energy. With an increase of the nuclear charge, it underestimates much more.     

Accurate values for the nonrelativistic energies of the lowest singlet and triplet S-states of the4He-Isotop

Accurate lower and upper bounds for the nonrelativistic lowest energies¹ E ₀ and³ E ₀ of the singlet and triplet-system of the⁴He-Isotop are calculated with the linearized method of variance minimization. The same was done for¹ E ₁ the energy of the first excitedS-state 2¹ S. The results especially for¹ E ₀ and³ E ₀ in a.u. are −2.9033076997₅ ≤¹ E ₀ ≤ −2.9033076921₈ −2.1749324263₇ ≤³ E ₀ ≤ −2.1749324245₉ i.e. the values are determined with an absolute error smaller than 0.00167 cm⁻¹ for¹ E ₀ and 0.00039 cm⁻¹ for³ E ₀.     

Excited states of boron isoelectronic series from explicitly correlated wave functions

The ground state and some low-lying excited states arising from the 1s2 2s2p2 configuration of the boron isoelectronic series are studied starting from explicitly correlated multideterminant wave functions. One- and two-body densities in position space have been calculated and different expectation values such as , , , , , and , where r, r12, and R stand for the electron-nucleus, interelectronic, and two electron center of mass coordinates, respectively, have been obtained. The energetic ordering of the excited states and the fulfillment of the Hund's rules is analyzed systematically along the isoelectronic series in terms of the electron-electron and electron-nucleus potential energies. The effects of electronic correlations have been systematically studied by comparing the correlated results with the corresponding noncorrelated ones. All the calculations have been done by using the variational Monte Carlo method.     

Calculation of ns2 configurations for the Helium isoelectronic series without matching

In the Hartree–Fock equations for the He isoelectronic series, the two-point boundary conditions on one of the differential equations is replaced by initial conditions specified at large distances. [The condition Y′(∞) = 0 replaces the condition Y (0) = 0.] This permits eigenvalues of ns² configurations to be determined as the zeros of a certain function arising from inward integrations, without having to match the solution with a corresponding outward integration. Calculations are performed for n = 1,2,3 for H^? through Be²⁺. Resulting energy values and radial densities are presented. Agreement is found, to the eight significant figures calculated here, with the n = 1 results given by Roothaan and Soukup.     

An accurate lower-bound calculation of the lowest triplet states of he and its isoelectronic series

Accurate lower bounds for the nonrelativistic lowest triplet states of ⁴He and ^∞He and the He isoelectronic series up to Z = 10 were calculated by the method of variance minimization using wave functions with logarithmic terms. Furthermore, the method of Lehmann/Goerisch was extended to self-adjoint operators with an essential spectrum. Both methods were compared for ⁴He. © 1992 John Wiley & Sons, Inc.     

Some potential-energy relationships for isoelectronic atomic series

Relationships between the total energy E, the nuclear-electronic attraction energy V_ne, and the interelectronic repulsion energy V^ee are derived for isoelectronic series of atoms and ions. Using these, it is possible to determine V_ne and V_ee for the members of such series from a knowledge of just their total energies. The method is applied to the ground and first excited states of the two-electron series, and the ground states of the three- and four-electron series, and the results are discussed.     

A relation between energies of the short-lived negative ion states and energies of unfilled molecular orbitals for a series of bromoalkanes

A series of bromoalkanes was investigated by means of electron transmission spectroscopy in the gas phase. Experimental values of vertical electron affinities associated with occupation of the LUMO by an incoming electron were assigned using ab initio quantum chemical calculations. The predicted vertical electron affinity values differ from measured ones by at most ±0.2 eV. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1222–1224, June, 2007.     

Estimation of the ground state correlation energy for isoelectronic series of 2 to 20 electrons

Correlation energies for all isoelectronic sequences of 2 to 20 electrons andZ=2 to 25 are obtained by taking differences between theoretical total energies of Dirac-Fock calculations and experimental total energies. These are pure relativistic correlation energies because relativistic and QED effects are already taken care of. The theoretical as well as the experimental values are analysed critically in order to get values as accurate as possible. The correlation energies obtained show an essentially consistent behaviour fromZ=2 to 17. ForZ>17 inconsistencies occur indicating errors in the experimental values which become very large forZ>25.     

Exchange-correlation potentials for high-electron-density ions in the Be isoelectronic series

Accurate reference wave functions and their densities have been used to obtain accurate exchange-correlation potentials for the beryllium isoelectronic sequence Be, Ne(+6), Ar(+14), and Kr(+32). The exchange-correlation potentials for the four-electron cations with high Z in this sequence exhibit structure prior to the intershell peak that is not present in neutral atoms. The kinetic energy contribution to the exchange-correlation potential contributes to the early structure as well as to the intershell peak. The near degeneracy in this four-electron sequence plays a significant role in the structure prior to the intershell peak. Several of the quantities on which the Perdew-Burke-Ernzerhoff and Tao-Perdew-Staroverov-Scuseria functionals are dependent are examined. The generalized gradient approximations appear not to account for the near degeneracy in this series.     

Structure and bonding in the PtCO isoelectronic series

The equilibrium geometries and harmonic frequencies of PtXY, XY = CO, N₂, CN⁻ and NO⁺, in the ¹∑⁺ state have been calculated by the ab initio self-consistent field method with gradients using appropriate effective core potentials. An analogous analysis was also carried out on the free ligands for comparison purposes. The ligands are compared with respect to changes in X-Y bond lengths and stretch frequencies upon complexation, and Pt-XY bond lengths, stretch frequencies and bond energies. The calculated results for PtCO and PtN₂ are compared with matrix-isolated infrared spectra.     

Non-expanded dispersion energies and damping functions for Ar2 and Li2

The non-expanded second-order dispersion energies and damping functions associated with the long-range dispersion energies varying as R⁻⁶, R⁻⁸and R⁻¹⁰ have been calculated for Ar₂ and Li₂ with the time-dependent Hartree-Fock method, using extended Gaussian basis sets. These results are used to discuss the difficulties associated with ab initio computations of these quantities.     

Perturbation calculation of oscillator strengths for the isoelectronic series of light atoms

Transition probabilities and oscillator strengths are calculated for the configurations 1s² 2sⁿ¹ and 1s² 2s^n1-1 2pⁿ²⁺¹, which are, respectively, of the form P=a/Z (1+/Z+) andf=/Z (1+/Z+). Numerical values are given fora, ,, and.     

Accurate second-order correlation energies for Mg and Ar

A p-version finite element method has been used to calculate second-order pair and total correlation energies for closed-shell Mg and Ar. Comparison with the best results found in the literature suggests that the present values are the most accurate and that the method should perform comparatively better for heavier elements. © 1993 John Wiley & Sons, Inc.     

One-Parameter double-zeta atomic functions for the hartree–fock energies of helium isoelectronic sequence

The double-zeta atomic functions are characterized by the nuclear charge z of the two-electron atomic system. The Hartree–Fock total energies and the corresponding orbital energies are calculated using various atomic wave functions for the helium isoelectronic sequence. The expectation values rⁿ of various wave functions are also examined. It is found that the accuracy of our one-parameter double-zeta functions corresponds to the accuracy of the usual five-parameter double-zeta functions.     

Accurate free energies of micelle formation

We determine the free energy of micelle formation for model surfactants in a Lennard-Jones solvent by employing a hybrid semi-grand Monte Carlo simulation scheme in combination with umbrella sampling and configurational bias techniques. Comparing the results to theoretical prediction, we obtain good agreement for large micellar sizes. We also study the effect of changing the surfactant headgroup size and tail length on the critical micelle concentration. The values of and the trends in the calculated critical micelle concentrations do agree with experimental observation for nonionic surfactants. The results open up the way for the calculation of critical micelle concentrations using realistic atomic force fields.