SCF Functions Research Articles

PP2ACdc55 regulates G1 cyclin stability

Maintaining accurate progression through the cell cycle requires the proper temporal expression and regulation of cyclins. The mammalian D-type cyclins promote G1-S transition. D1 cyclin protein stability is regulated through its ubiquitylation and resulting proteolysis catalyzed by the SCF E3 ubiquitin ligase complex containing the F-box protein, Fbx4. SCF E3-ligase-dependent ubiquitylation of D1 is trigged by an increase in the phosphorylation status of the cyclin. As inhibition of ubiquitin-dependent D1 degradation is seen in many human cancers, we set out to uncover how D-type cyclin phosphorylation is regulated. Here we show that in S. cerevisiae, a heterotrimeric protein phosphatase 2A (PP2ACdc55) containing the mammalian PPP2R2/PR55 B subunit ortholog Cdc55 regulates the stability of the G1 cyclin Cln2 by directly regulating its phosphorylation state. Cells lacking Cdc55 contain drastically reduced Cln2 levels caused by degradation due to cdk-dependent hyperphosphorylation, as a Cln2 mutant unable to be phosphorylated by the yeast cdk Cdc28 is highly stable in cdc55-null cells. Moreover, cdc55-null cells become inviable when the SCFGrr1 activity known to regulate Cln2 levels is eliminated or when Cln2 is overexpressed, indicating a critical relationship between SCF and PP2A functions in regulating cell cycle progression through modulation of G1-S cyclin degradation/stability. In sum, our results indicate that PP2A is absolutely required to maintain G1-S cyclin levels through modulating their phosphorylation status, an event necessary to properly transit through the cell cycle.

Core correlating basis functions for elements 31–118

Gaussian functions for correlation of all core shells of elements from Z = 31 to Z = 118 have been optimized in relativistic singles and doubles CI calculations, performed on the shell of highest angular momentum for each principal quantum number. The SCF functions were derived from the double-zeta, triple-zeta, and quadruple-zeta basis sets previously optimized by the author. Only those Gaussian functions that are not represented in the SCF basis sets were optimized. The functions are available from the Dirac program web site, http://dirac.chem.sdu.dk .

Infrared intensities of polyatomic molecules calculated from SCEP dipole-moment functions and anharmonic vibrational wavefunctions. I. Stretching vibrations of the linear molecules HCN, HCP and C 2N 2

Infrared intensities of transitions between a variety of stretching vibrational states of various isotopomers of HCN, HCP and C 2N 2 have been calculated from SCF and SCEP dipole-moment functions and anharmonic vibrational wavefunctions. Best agreement with experiment, usually with deviations of the order of 10% for the fundamentals, is obtained by CEPA when the dipole moment is calculated as an energy derivative. The performance of the familiar “double-harmonic approximation” is investigated and found to work well in the absence of vibrational resonances and strongly curved dipole-moment functions.

Stabilization calculations of resonance energies for chemical reactions

Resonance energies for chemically reactive systems are computed from square-integrable wave functions, using both SCF and CI trial functions. We consider three mass combinations (H+FH, H+H2, and H+MuH) and compare to accurate scattering calculations for model potential energy surfaces.

Perturbation calculation of molecular correlation energy using Gaussian-type geminals. Second-order pair energies of LiH and BH

The second-order pair energies of LiH and BH are calculated using Rayleigh–Schroedinger perturbation theory. The first-order perturbed pair functions are expanded in terms of explicitly correlated Gaussian functions. The nonlinear parameters entering the Gaussian geminals are optimized with reference to crude SCF functions according to the method proposed previously. The final values of the second-order pair energies are then calculated using accurate SCF orbitals. At this final stage only the linear parameters are reoptimized. The calculated second-order correlation energies of LiH and BH are compared with recent diagrammatic many-body perturbation theory results. The basis sets composed of two optimized Gaussian geminals for each spin-adapted pair function are shown to give quite reliable second-order correlation energies. The results obtained with four geminals for each pair function are superior to the most accurate many-body perturbation theory data. It is stressed that the nonlinear parameters of Gaussian geminals can be given a simple physical interpretation which facilitates their reasonable guess. The first-order pair functions represented in terms of Gaussian geminals have a very attractive compact and simple form. If properly optimized they can also provide highly accurate values of the second-order molecular correlation energies.

Gaussian geminal basis set optimization with crude SCF reference state

Gaussian geminal basis functions for second-order correlation energy calculations according to the Sinanogˇlu method are optimized with reference to rather crude SCF functions. The optimized geminal basis set is then used in a one-step calculation of the correlation energy with respect to the near-Hartree-Fock reference State. The numerical results for the beryllium atom indicate the usefulness of the proposed technique.

Corrections to the Born-Oppenheimer approximation and electronic effects on isotopic exchange equilibria. II

If nonadiabatic effects are neglected (the adiabatic approximation), the potential energy for the motions of the nuclei of a molecule is the sum of the Born-Oppenheimer electronic energy and the adiabatic correction (diagonal nuclear motion correction). This adiabatic correction has been evaluated at the experimental equilibrium internuclear separation for a number of first- and second-row diatomic hydrides and deuterides. The electronic wavefunctions which have been used in these calculations are LCAO MO SCF functions which range in quality from so-called minimum basis set functions to so-called near-Hartree-Fock functions. The explicit R dependence of the LCAO coefficients has been taken into account. The adiabatic corrections to the electronic energy are functions of the nuclear masses. With the assumption of the distance independence of the adiabatic correction, the calculations here can be used to evaluate the effect of the adiabatic correction on the equilibrium constants for the isotopic exchange reactions HX+HD=DX+H2. For the HX systems on which calculations were done here, these correction factors range, with good single configuration wavefunctions, from 0.963 to 1.113 at 300°K.

The effect of covalency on the spin—orbit coupling constant

It is shown that the spin—orbit coupling constant, ζ, for a series of 3d transition metal ions may be satisfactorily evaluated using approximate double-zeta SCF functions. The radial distance dependence of ζ has been calculated, and the results indicate that the reduction of ζ below the free-ion value on complex formation should be dominantly to symmetry restricted covalency, rather than to central field effects.

On radial weighting effects in gaussian expansions of self-consistent field atomic orbitals

Gaussian expansions of the SCF functions for the first row atoms, boron through fluorine, in ground and low-lying electronic states have been generated under a wide range of radial weighting conditions by a full least-squares procedure. Typical results are presented and the quality of the wavefunctions obtained are analyzed in terms of regional electron densities and a variety of expectation values including energies. A novel method for recursive evaluation of repeated integrals of the error function, F l (α,ζ), is adopted and analyzed. These integrals are central quantities in the least-squares procedure employed.

Rydberg Terms of the CH3 Radical

Spectroscopic terms are calculated for two of the three observed Rydberg series in CH3. One-center SCF functions of CH3+, determined by Joshi are used for the core orbitals. The molecular geometry of CH3+ is assumed to be unchanged for the Rydberg states. The calculated terms are in good agreement with experimentally observed terms but suggest a possible reinterpretation of the latter.

Alternative Technique for the Calculation of Single-Determinant Open-Shell SCF Functions Which Are Eigenfunctions of S2

The most general possible restriction is developed such that a single-determinant open-shell SCF wavefunction shall be an eigenfunction of S2. A method of satisfying this restriction by partitioning of the variational basis set is given. The method is computationally distinct from the equivalence restriction procedure of Roothaan, but yields results equivalent to it. A pilot calculation on the Σ+2 state of BO is carried out as an explicit example of the new method.

Atomic Multiconfiguration Self-Consistent-Field Wavefunctions

The ground-state 1S wavefunctions of the atomic isoelectronic series with two and four electrons (Z = 1 – 8, and 3–8, respectively), were calculated using the MC–SCF method restricted to pair replacements. These calculations were to test and demonstrate how rapidly the configuration expansions of the MC–SCF wavefunctions converge. In the two-electron series, nine configurations were required to yield 97% of the correlation energy, while ten configurations accounted for 86% of the correlation energy in the four-electron series. The quality of the reported wavefunctions has been tested by computing the expectation values of several one- and two-electron operators. The results obtained agree in general satisfactorily (deviations of ∼1%) with values computed from more complex wavefunctions, indicating that the compact MC–SCF functions reported are indeed of high quality.

Nonpairwise Additivity in the Exchange Energy for a Trio of Carbon Atoms in an Equilateral Triangle

In order to gauge the importance of deviation from pairwise additivity in the intermolecular potential, a calculation of the exchange energy of a model system consisting of three carbon atoms arranged in a triangle has been performed. The calculations were carried out using both Slater and SCF functions as a basis set. Each of these functions are expanded in terms of Gaussian orbitals, so that the appropriate three-center integrals can be evaluated. It has been shown that deviations are considerable at distances that are normally taken to be nonbonding, the deviation calculated using SCF functions being about twice as large as that calculated using Slater functions.

Use of Atomic SCF Functions with Minimal Basis Sets

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MOMENTUM DISTRIBUTIONS OF TWO PHOTON ANNIHILATING POSITRON–ELECTRON PAIRS IN HEXANE AND DECANE

Momentum distributions are calculated for electrons in the C–C and C–H bonds in hydrocarbons, using analytic SCF functions for atomic carbon orbitals and Heitler–London-type functions for the two paired electrons in the C–C and C–H bonds. The positron wave function is assumed to be a constant. The computed momentum distributions are then compared with high-precision experimental distributions obtained from positron-annihilation angular correlation experiments.

Some One-Electron Properties of H2O and NH3

Several one-electron properties have been evaluated for H2O and NH3 using ab initio SCF functions. The functions are obtained from the Hartree—Fock—Roothman equations using a minimal Gaussian-lobe basis. The diamagnetic-susceptibility tensor, quadrupole-moment tensor, diamagnetic nuclear shielding tensor at O, N, and H, and the nuclear quadrupole coupling constants for 17O, 14N, and D have been evaluated. These properties have been compared, when possible, with experiment. The total magnetic susceptibility tensor for NH3 and H2O and the diagonal elements (in the principal inertia system) of the absolute nuclear shielding tensor at H and N in NH3 have been estimated by combining the ab initio diamagnetic results with the experimental paramagnetic contributions available from measurements of the rotational magnetic moment and the spin—rotation interaction, respectively.

Atomic Screening Constants from SCF Functions. II. Atoms with 37 to 86 Electrons

Minimal basis-set atomic functions for the ground-state atoms from Rb(Z=37) to Rn(Z=86) are presented. These functions are analyzed in order to obtain systematic data for the screening constants and atomic radii following the work initiated by Slater.

Spin-Projected and Extended SCF Calculations

A comparison is presented of the energies associated with different SCF types: spin restricted, unrestricted, projected unrestricted, and extended. A method of obtaining spin-extended SCF functions is discussed. Sample calculations are done for simple hydrocarbon pi-electron radicals in the Pariser—Parr approximation, and both energies and spin densities are reported.

Overlap as a Criterion for Conduction in the Cubic Tungsten Bronzes

Overlap calculations using Slater orbitals with exponents adjusted to match SCF functions have been performed on eight pairs of orbitals which have been considered to have some pertinence to conduction in the cubic sodium tungsten bronzes. The results support the dπ—pπ model proposed by Sienko and by Good-enough and clearly indicate where the overlap criterion alone breaks down, namely for the case of sodium—sodium pσ—pσ overlap.

Second-Order Density Matrix for a Spin-Projected Single Determinant

We have obtained the irreducible tensorial components of the second-order density matrix corresponding to a spin-projected, single-determinantal function. The results are applicable to projected-unrestricted or spin-extended SCF functions. The natural basis set for the problem is provided by the eigenfunctions of the first-order charge density matrix.