Hartree-Fock data

Figgen, D., Rauhut, G., Dolg, M. and StoD, H. (2005) Energy-consistent pseudopotentials for group 11 and 12 atoms adjustment to multi-configuration Dirac-Hartree-Fock data. Chemical Physics, 311, 227-244. 

Table 8.1. Hartree-Fock data for neon [FF/72] relevant for a demonstration of...

It is not simple to demonstrate that 7/3 is the correct power of Z for real atoms when Z < 100. In fact Foldy showed that up to this value of Z, Hartree and Hartree-Fock data are slightly better fitted with Z12/6. Nevertheless, for a non-relativistic theory there can be no doubt that for really large values of Z the total binding energy must vary as Z7/3. We shall see below, when we deal with... 

The correlation energies given by this approach are, however, only semiquantitativs and their combination with near Hartree-Fock data cannot be expected to provide highly accurate predictions. 

Errors in calculated energies of reaction with respect to Hartree-Fock data... 

DZ, DZ+P, extended Koopmans theorem generally within 0.2-0.4 eV with respect to Hartree-Fock data occasionaly over 1 eV for the DZ basis set 468, 482, 512, 513... 

Peptide models. XXXIII. Extrapolation of low-level Hartree-Fock data of peptide conformation to large basis set SCF, MP2, DFT, and CCSD(T) results. The Ramachandran surface of alanine dipeptide computed at various levels of theory80... 

Direct dynamics attempts to break this bottleneck in the study of MD, retaining the accuracy of the full electronic PES without the need for an analytic fit of data. The first studies in this field used semiclassical methods with semiempirical [66,67] or simple Hartree-Fock [68] wave functions to heat the electrons. These first studies used what is called BO dynamics, evaluating the PES at each step from the elech onic wave function obtained by solution of the electronic structure problem. An alternative, the Ehrenfest dynamics method, is to propagate the electronic wave function at the same time as the nuclei. Although early direct dynamics studies using this method [69-71] restricted themselves to adiabatic problems, the method can incorporate non-adiabatic effects directly in the electionic wave function. 

Hartree-Fock MO approach, the minimization of energy should provide the most accurate description of the electronic field. The mathematical problem is to define each of the terms, with being the most challenging. The formulation carmot be done exactly, but various approaches have been developed and calibrated by comparison with experimental data. The methods used most frequently by chemists were developed by A. D. Becke. " This approach is often called the B3LYP method. The computations can be done with... 

The systems discussed in this chapter give some examples using different theoretical models for the interpretation of, primarily, UPS valence band data, both for pristine and doped systems as well as for the initial stages of interface formation between metals and conjugated systems. Among the various methods used in the examples are the following semiempirical Hartree-Fock methods such as the Modified Neglect of Diatomic Overlap (MNDO) [31, 32) and Austin Model 1 (AMI) [33] the non-empirical Valence Effective Hamiltonian (VEH) pseudopotential method [3, 34J and ab initio Hartree-Fock techniques. 

Regarding current ab initio calculations it is probably fair to say that they are not really ab initio in every respect since they incorporate many empirical parameters. For example, a standard HF/6-31G calculation would generally be called "ab initio", but all the exponents and contraction coefficients in the basis set are selected by fitting to experimental data. Some say that this feature is one of the main reasons for the success of the Pople basis sets. Because they have been fit to real data these basis sets, not surprisingly, are good at reproducing real data. This is said to occur because the basis set incorporates systematical errors that to a large extent cancel the systematical errors in the Hartree-Fock approach. These features are of course not limited to the Pople sets. Any basis set with fixed exponent and/or contraction coefficients have at some point been adjusted to fit some data. Clearly it becomes rather difficult to demarcate sharply between so-called ab initio and semi-empirical methods.4... 

As was the case with lanthanide crystal spectra (25), we found that a systematic analysis could be developed by examining differences, AP, between experimentally-established actinide parameter values and those computed using Hartree-Fock methods with the inclusion of relativistic corrections (24), as illustrated in Table IV for An3+. Crystal-field effects were approximated based on selected published results. By forming tabulations similar to Table IV for 2+, 4+, 5+ and 6+ spectra, to the extent that any experimental data were available to test the predictions, we found that the AP-values for Pu3+ provided a good starting point for approximating the structure of plutonium spectra in other valence states. However,... 

Table IV. Comparison of Energy Level Parameters Computed Using Hartree-Fock Methods and Those Evaluated from Fitting Experimental Data for An + (all in cm l).

Experimental data vs. calculated solubilities for hydrolysis reactions. 325-30 Experimental data vs. Hartree-Fock methods, energy level... 

Figure 4.13 Excitation energies for the s-d and s-p gaps of the Group 11 elements. Experimental (Cu, Ag and Au) and coupled cluster data (Rg) are from Refs. [4, 91]. For the s-p gap of Rg we used Dirac-Hartree-Fock calculations including Breit and QED corrections.

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