Core-valence

The magnitude of the core correlation can be evaluated by including the oxygen Is-electrons and using the cc-pCVXZ basis sets the results are shown in Table 11.9. The extrapolated CCSD(T) correlation energy is —0.370 a.u. Assuming that the CCSD(T) method provides 99.7% of the full Cl value, as indicated by Table 11.7, the extrapolated correlation energy becomes —0.371 a.u., well within the error limits on the estimated experimental value. The core (and core-valence) electron correlation is thus 0.063 a.u.. 

The core electrons are replaced by a gaussian expansion which reproduces electrostatic and exchange core-valence interactions. 

Electron-electron repulsion integrals, 28 Electrons bonding, 14, 18-19 electron-electron repulsion, 8 inner-shell core, 4 ionization energy of, 10 localization of, 16 polarization of, 75 Schroedinger equation for, 2 triplet spin states, 15-16 valence, core-valence separation, 4 wave functions of, 4,15-16 Electrostatic fields, of proteins, 122 Electrostatic interactions, 13, 87 in enzymatic reactions, 209-211,225-228 in lysozyme, 158-161,167-169 in metalloenzymes, 200-207 in proteins ... 

Core-Valence Separation in the Study of Atomic Clusters... 

CORE-VALENCE SEPARATION IN THE STUDY OF ATOMIC CLUSTERS... 

The localized basis function for the set 0 (Is) are usual frozen-core valence-shell Cl states all the bound states involved in the present calculations are also described at this level. 

The active space used for both systems in these calculations is sufficiently large to incorporate important core-core, core-valence, and valence-valence electron correlation, and hence should be capable of providing a reliable estimate of Wj- In addition to the P,T-odd interaction constant Wd, we also compute ground to excited state transition energies, the ionization potential, dipole moment (pe), ground state equilibrium bond length and vibrational frequency (ov) for the YbF and pe for the BaF molecule. 

The MaxEnt valence density for L-alanine has been calculated targeting the model structure factor phases as well as the amplitudes (the space group of the structure is acentric, Phlih). The core density has been kept fixed to a superposition of atomic core densities for those runs which used a NUP distribution m(x), the latter was computed from a superposition of atomic valence-shell monopoles. Both core and valence monopole functions are those of Clementi [47], localised by Stewart [48] a discussion of the core/valence partitioning of the density, and details about this kind of calculation, may be found elsewhere [49], The dynamic range of the L-alanine model... 

Within the computational scheme described in the course of this work, the available information about the atomic substructure (core+valence) can be taken into account explicitly. In the simplest possible calculation, a fragment of atomic cores is used, and a MaxEnt distribution for valence electrons is computed by modulation of a uniform prior prejudice. As we have shown in the noise-free calculations on l-alanine described in Section 3.1.1, the method will yield a better representation of bonding and non-bonding valence charge concentration regions, but bias will still be present because of Fourier truncation ripples and aliasing errors ... 

The quality of quantum-chemical calculations depends not only on the chosen n-electron model but also critically on the flexibility of the one-electron basis set in terms of which the MOs are expanded. Obviously, it is possible to choose basis sets in many different ways. For highly accurate, systematic studies of molecular systems, it becomes important to have a well-defined procedure for generating a sequence of basis sets of increasing flexibility. A popular hierarchy of basis functions are the correlation-consistent basis sets of Dunning and coworkers [15-17], We shall use two varieties of these sets the cc-pVXZ (correlation-consistent polarized-valence X-tuple-zeta) and cc-pCVXZ (correlation-consistent polarized core-valence X-tuple-zeta) basis sets see Table 1.1. 

As can be seen from the table, the number of AOs increases rapidly with the cardinal number X. Thus, with each increment in the cardinal number, a new shell of valence AOs is added to the cc-pVXZ set since the number of AOs added in each step is proportional to X2, the total number (Nbas) of AOs in a correlation-consistent basis set is proportional to X3. The core-valence sets cc-pCVXZ contain additional AOs for the correlation of the core electrons. As we shall see later, the hierarchy of correlation-consistent basis sets provides a very systematic description of molecular electronic systems, enabling us to develop a useful extrapolation technique for molecular energies. 

In addition, for thermochemical purposes we are primarily interested in the core-valence correlation, since we can reasonably expect the core-core contributions to largely cancel between the molecule and its constituent atoms. (The partitioning between core-core correlation -involving excitations only from inner-shell orbitals - and core-valence correlation - involving simultaneous excitations from valence and inner-shell orbitals - was first proposed by Bauschlicher, Langhoff, and Taylor [42]). 

Optimization of augmenting functions for the description of electron affinities, weak interactions, or core-valence correlation effects. 

In the case of core-valence correlation effects, correlating functions were optimized at the CISD level of theory using the weighted core-valence scheme (5). In this case a cc-pwCVTZ-PP set consisted of the cc-pVTZ-PP basis set with the addition of 2.y2p2(5fl/core-valence correlating functions. 

Obtained via a 2-point /n extrapolation of the VQZ-PP and V5Z-PP total energies cc-pwCVTZ-PP (Y) and cc-pCVTZ (C) core-valence basis sets with valence-only (7) and all-electrons (17) correlated. 

Obtained by addition of the CBS results of (a) with the core-valence effects of (b). 

CBS plus core-valence effects of (c) with the addition of spin-orbit effects from Ref (46) (2-electron SO-PP values) Ref (42-44),... 

Includes 5s5p core-valence and spin-orbit corrections These values were cited in Ref (13). 

Relativistic Quantum Defect Orbital (RQDO) calculations, with and without explicit account for core-valence correlation, have been performed on several electronic transitions in halogen atoms, for which transition probability data are particularly scarce. For the atomic species iodine, we supply the only available oscillator strengths at the moment. In our calculations of /-values we have followed either the LS or I coupling schemes. 

In Tables -A, we report oscillator strengths for some fine structure transitions in neutral fluorine, chlorine, bromine and iodine, respectively. Two sets of RQDO/-values are shown, those computed with the standard dipole length operator g(r) = r, and those where core-valence correlation has been explicitly introduced, Eq. (10). As comparative data, we have included in the tables /-values taken from critical compilations [15,18], results of length and velocity /-values by Ojha and Hibbert [17], who used large configuration expansions in the atomic structure code CIVS, and absolute transition probabilities measured through a gas-driven shock tube by Bengtson et al. converted... 

The oscillator strengths obtained for the different transitions studied in the present work with the RQDO methodology, and the use of the two forms of the transition operator, the standard one, and that corrected for core-valence polarization, are collected in Tables 1 to 8, where other data, from several theoretical and experimental sources, have been included for comparative purposes. The former comprise the large-scale configuration interaction performed with the use of the CIVS computer package [19] by Hibbert and Hansen [20] The configuration interaction (Cl) procedure of... 

---