SCF frequencies

Note (SCF frequencies scaled by 0.91 correlated frequencies scaled by 0.95). 

SCF frequencies typically overestimate the various vibrational frequencies in H-bonded complexes as well as in their constituent subunits. Once correlation is added, with MP2 usually a satisfactory approach, the computations can match fairly well the experimental spectra, particularly if the basis set is large and flexible enough. Calculation of accurate vibra-... 

Just as one can consider the effects of dimerization upon the frequencies or intensities of the monomer modes, it is useful to ponder how juxtaposing two dimers within a trimer affects the vibrational spectra of the dimer. Kofranek et al. provided such information, reported in Table 5.4, which suggests that the SCF data graphed in Fig. 5.4 are quite representative of the correlated level as well. All of the trends in the SCF frequencies are mirrored in the CPF data. The similarity of the last two columns in the table indicates no major perturbations of the intermolecular band intensifications caused by electron correlation. 

Concerning the scaling of the SCF frequencies, another point should be made. An implicit assumption underlying the use of empirical scaling factors is... 

Figure 3. (a) Conventional SCF frequencies using integrals stored on disk, (b) Direct SCF frequencies, avoiding storage of the two electron integrals. 

The first column of Table 5 lists the frequencies calculated for the HF monomer with a variety of different theoretical schemes. This information is followed by the stretching frequencies of the two HF molecules in the dimer. A scan of the SCF data in the upper portion of the table reveals the familiar overestimation of all frequencies in comparison to the experimental values in the last row of the table. Incorporation of electron correlation lowers the SCF frequencies by several hundred wave numbers, taking them into the vicinity of the experimental values. A primary source of disagreement is the use of the harmonic approximation in calculating these frequencies. Nevertheless, the correlated frequencies calculated by Michael et al. using a triple-C polarized basis set [97] fall quite close to the experimental range. 

In contrast to the structures and energetics of these complexes which can be treated rather well at modest levels of theory, the vibrational spectra are much less tractable. It is well known that SCF frequencies are uniformly too large this is true in H-bonded complexes as well as in single molecules. Inclusion of electron correlation, coupled with use of a sufficiently flexible basis set, can bring the internal frequencies of the individual subunits quite close to experimental values. On the other hand, if one is interested primarily in shifts in these frequencies induced by formation of a H-bond, the SCF treatment seems to provide quite reasonable results in many cases, even with relatively modest-sized basis sets. 

Figure 1 Theoretically simulated, Lorentzian lineshape of 5 cm half width at half height, and experimental (CS2) VCD, and IR spectra of (2R,3R)-dimethyloxirane-2-d, 9 in the region 700-1500 cm (Reference 72). SCF frequencies are scaled by 0.9.

The CCSD model gives for static and frequency-dependent hyperpolarizabilities usually results close to the experimental values, provided that the effects of vibrational averaging and the pure vibrational contributions have been accounted for. Zero point vibrational corrections for the static and the electric field induced second harmonic generation (ESHG) hyperpolarizability of methane have recently been calculated by Bishop and Sauer using SCF and MCSCF wavefunctions [51]. 

The frequency dependence is taken into accoimt through a mixed time-dependent method which introduces a dipole-moment factor (i.e. a polynomial of first degree in the electronic coordinates ) in a SCF-CI (Self Consistent Field with Configuration Interaction) method (3). The dipolar factor, ensuring the gauge invariance, partly simulates the molecular basis set effects and the influence of the continuum states. A part of these effects is explicitly taken into account in an extrapolation procedure which permits to circumvent the sequels of the truncation of the infinite sum-over- states. 

The electronic structure of dichorodiphenylplumbane was calculated by the SCF-MS (self-consistent field multiple scattering) molecular orbital method and compared to that of dichlorodiphenylstannane. The results suggest that one has to look for 35C1 NQR (nuclear quadrupole resonance) frequencies of dichorodiphenylplumbane in the 5-6 MHz region1613. 

Most of the calculations have been done for Cu since it has the least number of electrons of the metals of interest. The clusters represent the Cu(100) surface and the positions of the metal atoms are fixed by bulk fee geometry. The adsorption site metal atom is usually treated with all its electrons while the rest are treated with one 4s electron and a pseudopotential for the core electrons. Higher z metals can be studied by using pseudopotentials for all the metals in the cluster. The adsorbed molecule is treated with all its electrons and the equilibrium positions are determined by minimizing the SCF energy. The positions of the adsorbate atoms are varied around the equilibrium position and SCF energies at several points are fitted to a potential surface to obtain the interatomic force constants and the vibrational frequency. 

The ab initio SCF cluster wavefunction has been used to investigate the bonding of CO and CN- on Cu,0 (5,4,1), (5 surface layer, 4 second layer and 1 bottom layer atoms), and to calculate their field dependent vibrational frequency shifts in fields up to 5.2 x 107 V/cm(46). A schematic view of the Cu10 (5,4,l)CO cluster is shown in Figure 8. In order to assess the significance of Lambert s proposal, that the linear Stark effect is the dominant factor in the field dependent frequency shift, the effect of the field was calculated by three methods. One is by a fully variational approach (i.e., the adsorbate is allowed to relax under the influence of the applied field) in which the Hamiltonian for the cluster in a uniform electric field, F, is given by... 

When the experimental results are considered together with the calculations the following model can be envisioned. In the region of negative potential Ny is adsorbed parallel to the surface and can not be observed by IRRAS. The symmetric vibration and the bending modes are observed in this region by SERS (52) and the vibrational frequency is not seen to shift very much with potential, consistent with the SCF calculations. As the potential is made more positive the concentration increases and adsorption tends to perpendicular orientation which is detected by IRRAS. 

Efficiency of HSC mobilization depends on longevity of G-SCF injections and the dosage used. In humans for supporting treatment after the chemotherapy as well as for the HSC mobilization 5-10 pg/kg for 7-14 days is used . In some cases patients receive multiple repeated G-SCF courses. The mobilizing dose for murine HSC is considerably higher than for human ones usually from 200 up to 300 pg/kg is injected for 5-17 days leading to more then 10-fold increase of the number of different hematopoietic precursors in the peripheral blood . When 10 times lower dose is used CFU-S number in the peripheral blood experienced a 4-fold increase (versus 32-fold increase in case the mobilizing concentration is used) while in the bone marrow HSC frequency almost was halved . 

Table 4. The Relative Energies in kcal mol of the CH5 (Hj) structures (as Shown in Figure 4) at the TZ2P CISD+Q + ZPVE(TZ2P SCF) Level of Theory. (The Number of Imaginary Frequencies is in Squared Brackets)...

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