CHF calculation

Besides the elementary properties of index permutational symmetry considered in eq. (7), and intrinsic point group symmetry of a given tensor accounted for in eqs. (8)-(14), much more powerful group-theoretical tools [6] can be developed to speed up coupled Hartree-Fock (CHF) calculations [7-11] of hyperpolarizabilities, which are nowadays almost routinely periformed in a number of studies dealing with non linear response of molecular systems [12-35], in particular at the self-consistent-field (SCF) level of accuracy. 

The theoretical results provided by the large basis sets II-V are much smaller than those from previous references [15-18] the present findings confirm that the second-hyperpolarizability is largely affected by the basis set characteristics. It is very difficult to assess the accuracy of a given CHF calculation of 2(ap iS, and it may well happen that smaller basis sets provide theoretical values of apparently better quality. Whereas the diagonal eomponents of the eleetrie dipole polarizability are quadratic properties for which the Hartree-Fock limit can be estimated with relative accuracy a posteriori, e.g., via extended calculations [38], it does not seem possible to establish a variational principle for, and/or upper and lower bounds to, either and atris-... 

Comparisons of rod bundle data with the Columbia correlation and other existing correlations were made using COBRA-IIIC code for predictions of all correlations. The DNBR (or CHFR) reported is not the critical power ratio as used by other authors. The DNBR errors reported by Reddy and Fighetti (1983) are based on the following analysis The measured local heat flux at the experimental location of the first or higher-rank CHF indications is compared with the predicted CHF calculated using local conditions from the subchannel analysis for the... 

CHF calculations of substituent effects on y(C,H) couplings in methane derivatives were reported by Musio and SciacovelU using MNDO wavefunc-tions. The CHF approach was implemented following refs 282 and 115 and results were compared with those obtained with the same perturbational approach but using both INDO and MINDO/3 wavefunctions. MNDO results describe substituent effects in these methane derivatives much better than those obtained with either of the latter two wavefunctions. However, at this point it should be recalled that MNDO wavefunctions for unsaturated hydrocarbons in general present quasi-instabiUties of the non-singlet type. ... 

Carry out a coupled Hartree-Fock (CHF) calculation of the frequency-independent polarizability tensor for the closed-shell HeH system. To achieve this goal, follow the eps given below. 

The T =0 time-dependent mean-field theory currently provides the best description of nuclear dynamics at low energies [5,6]. We consider two single-particle operators, Q, P interpreted as a collective coordinate and a collective momentum. Their nature depends on the kind of motion that we want to focus upon. We require that Q Q and P-r — P under time reversal and that IP, Q] 0. We then form a constrained Hartree-Fock (CHF) calculation on the many-body Hamiltonian H by minimizing the functional... 

The study of large amplitude collective motion at finite temperature is now reduced to the study of an energy surface obtained from a CHF calculation with four Lagrange parameters. Two of them (Ai, A2) are of dynamical nature and represent the force and velocity fields needed to describe collective motion in a given mode. The other two T, p) embody the thermal constraints on the motion. The numerical determination of these surfaces is quite feasible with realistic Hamiltonians. One result is the function H(P, Q, S, N) which, for constant S, N, yields the trajectory of isentropic motion as the line of constant H in the phase space of P and Q. For small amplitudes near an equilibrium point with values P = 0,Q = qq the surface can be expanded up to quadratic terms as... 

The experimental data (in the first row) are based on an earlier measurement of x PH, [7] (see also Phosphor C, 1965, p. 30) and on later observations of the Zeeman effect In rotational transitions of PHgD and PHDg [8]. The theoretical data (all for the experimental geometry) were often based on coupled Hartree-Fock (CHF) calculations (see the remarks) ... 

The theoretical results provided by the large basis sets II-V are much smaller than those from previous references [15-18] the present findings confirm that the second-hyperpolarizability is largely affected by the basis set characteristics. It is very difficult to assess the accuracy of a given CHF calculation of and it may well... 

Coriani, S. Lazzeretti, P Malagoli, M. Zanasi, R. On CHF calculations of 2nd-oider magnetic-properties using the method of continuous transformation of origin of the current-density. Theor. Chim. Acta, 1994, 89, 181. 

Recent CHF calculations with larger basis sets and distributed gauge origins suggest that Hartree-Fock results may still be reasonable for metal shifts of early transition metals in high formal oxidation states like Ti(IV) or Zr(IV) and, not too surprisingly, for d -systems (cf. examples in Ref. 1). Results on Mo shifts were much less satisfactory. For quantitative calculations of metal shifts in most transition metal compounds, the inclusion of electron correlation appears mandatory. 

A solubihty parameter of 24.5-24.7 MPa / [12.0-12.1 (cal/cm ) ] has been calculated for PVF using room temperature swelling data (69). The polymer lost solvent to evaporation more rapidly than free solvent alone when exposed to air. This was ascribed to reestabUshment of favorable dipole—dipole interactions within the polymer. Infrared spectral shifts for poly(methyl methacrylate) in PVF have been interpreted as evidence of favorable acid—base interactions involving the H from CHF units (70). This is consistent with the greater absorption of pyridine than methyl acetate despite a closer solubihty parameter match with methyl acetate. 

Available data sets for flow boiling critical heat flux (CHF) of water in small-diameter tubes are shown in Table 6.9. There are 13 collected data sets in all. Only taking data for tube diameters less than 6.22 mm, and then eliminating duplicate data and those not meeting the heat balance calculation, the collected database included a total of 3,837 data points (2,539 points for saturated CHF, and 1,298 points for subcooled CHF), covering a wide range of parameters, such as outlet pressures from 0.101 to 19.0 MPa, mass fluxes from 5.33 to 1.34 x lO kg/m s, critical heat fluxes from 0.094 to 276 MW/m, hydraulic diameters of channels from 0.330 to 6.22 mm, length-to-diameter ratios from 1.00 to 975, inlet qualities from —2.35 to 0, and outlet thermal equilibrium qualities from -1.75 to 1.00. 

The present paper is aimed at developing an efficient CHF procedure [6-11] for the entire set of electric polarizabilities and hyperpolarizabilities defined in eqs. (l)-(6) up to the 5-th rank. Owing to the 2n+ theorem of perturbation theoiy [36], only 2-nd order perturbed wavefunctions and density matrices need to be calculated. Explicit expressions for the perturbed energy up to the 4-th order are given in Sec. IV. 

Using Eqs. (5-42)-(5-46) in Section 5.3.2.2 with iterative calculations, the predicted CHF were compared with Columbia University data (Fighetti and Reddy, 1983). The comparison was made by examining the statistical results of critical power ratios (DNBRs), where... 

The uncertainty in the predicted CHF of rod bundles depends on the combined performance of the subchannel code and the CHF correlation. Their sensitivities to various physical parameters or models, such as void fraction, turbulent mixing, etc., are complementary to each other. Therefore, in a comparison of the accuracy of the predictions from various rod bundle CHF correlations, they should be calculated by using their respective, accompanied computer codes.The word accompanied here means the particular code used in developing the particular CHF correlation of the rod bundle. To determine the individual uncertainties of the code or the correlation, both the subchannel code and the CHF correlation should be validated separately by experiments. For example, the subchannel code THINC II was validated in rod bundles (Weismanet al., 1968), while the W-3 CHF correlation was validated in round tubes (Tong, 1967a). 

Ab initio calculations using the CHF-GIAO approach on the optimized geometrical configurations of the compounds have also allowed to predict the 111, 13C, and 1SN nuclear magnetic resonance (NMR) spectra of the quinolizidine series. The calculated spectra fit fairly well the experimental data, with the exception of some signals... 

NMR shifts ( H, 13C, and 1SN) of 1-alkyl-, 2-alkyl-, and 3-aryltetrazolo[l,5- ]pyridinium salts have also been measured <1999JST119>. The data are compiled in Table 3. The 1SN shifts of these salts seemed of particular importance as they revealed quite big shielding changes for the nitrogen nuclei. These chemical shifts were also calculated by the ab initio GIAO-CHF method, and the result was found to be in fairly good agreement with the experimental values. 

Figure 8. Snapshot of BOMD calculations (a) for CHf in its close CJform, (b) near the transition state for bond-to-bond migration from one 3c2e bond to a C-Hfrom the tripod (Civ), and (c) sum of the superimposed structures, illustrating the fluxional character of the CHf.

The data used in these calculations and the results are listed in Table I. This shows that even allowing for the considerable uncertainty in the 0(R+ - CHf) values, these are... 

Any desired dilution of HF cx (in weight%) can be prepared from a concentrated HF solution whose concentration cHf (in %) and specific weight f (in kg T1) are known, by mixing a certain volume of pure water VH,0 (in 1) with the calculated volume of concentrated HF (in 1) ... 

---