Valence-electron method

More elaborated treatments have also been applied ab initio methods by Bouscasse (130) and Bernardi et al. (131) then the all-valence-electrons methods, derived from PPP. by Gelus et ai. (132) and by Phan-Tan-Luu et al. (133) and CNDO methods by Bojesen et al. (113) and by Salmona et al. (134). 

The description of configuration interaction given for rr-electron methods is also valid for all-valence-electron methods. Recently, two papers were published in which the half-electron method was combined with a modified CNDO method (69) and the MINDO/2 method was combined with the Roothaan method (70). Appropriate semiempirical parameters and applications of all-valence-electron methods are most probably the same as those reviewed for closed-shell systems (71). 

Until now, applications of semiempirical all-valence-electron methods have been rare, although the experimental data for a series of alkyl radicals are available (108,109). In Figure 9, we present the theoretical values of ionization potentials calculated (68) for formyl radical by the CNDO version of Del Bene and Jaffe (110), which is superior to the standard CNDO/2 method in estimation of ionization potentials of closed-shell systems (111). The first ionization potential is seen, in Figure 9, to agree fairly well with the experimental value. Similarly, good results were also obtained (113) with some other radicals (Table VII). 

For biological systems such as ferredoxins, problems arise when counting electrons by the valence electron method. This system assumes six Fe-Fe bonds within the tetrahedral iron-sulfur clusters, but Fe-Fe bond distances within biological iron-sulfur clusters, as found by X-ray crystallography, often... 

The semiempirical valence electron methods have been widely employed for calculating total energies as a function of the conformational degrees of freedom the relative stability of conformers and energy barriers are obtained in the different acyl heterocyclic derivatives. The degree of reliability of the different approaches varies, depending only on the molecular structure ... 

Among all electron methods, that of CNDO in its variants CNDO/2 and CNDO/S has been most used. Particularly worthy of note is the work of Galasso434 where -electron methods are compared with all valence electron methods for the 3a-azapentalene anion 246 and 3a,6a-diazapentalene 262a. The conclusion drawn from this study was that core polarization plays a fundamental role in determining overall charge distribution in the ground state but is relatively less important in interpreting electronic spectra. 

Both terms, however, are dependent on the total charge density of the atom. It is not surprising, therefore, that 13C shifts of atoms in conjugated molecules vary approximately linearly with the jr-electron density at the atoms (<513C= 160 Aq71). Of the available all-valence electron methods, chemical shifts have been calculated only by the CNDO approximation. 

In the preceding pages, we have reviewed some of the most important all-valence electron methods proposed for the S.C.F. calculation of properties of large organic molecules. 

The scientific interests of Huzinaga are numerous. He initially worked in the area of solid-state theory. Soon, however, he became interested in the electronic structure of molecules. He studied the one-center expansion of the molecular wavefunction, developed a formalism for the evaluation of atomic and molecular electron repulsion integrals, expanded Roothaan s self-consistent field theory for open-shell systems, and, building on his own work on the separability of many-electron systems, designed a valence electron method for computational studies on large molecules. 

What is the main advantage of an all-valence-electron method like, say, CNDO over a purely n electron method like PPP ... 

A nonempirical approach to the chemical reactivity may of course be made along the same lines as has been practised for years in treatments by semiempirical all-valence electron methods. Typically, the results of such treatments provide qualitative explanation of the observed facts and give guidance for further experiments. Here we shall deal only with what may be taken as the ultimate goal of ab initio calculations in the field of chemical reactivity - the predictions of absolute values of equilibrium and rate constants. 

All-valence electron methods recently suggested for organic molecules are derived from semi-empirical approaches developed earlier in another context, namely the Wolfsberg-Helmholz treatment of coordination compounds 40>, the Sandorfy treatment of paraffins 411 and the Parr-Pariser-Pople treatment of n electrons 42>43>. 

Table IV. Highest occupied it molecular orbital (ev), in all-valence electron methods...

A capital problem in the domain of purines, upon the study of which the introduction of the all-valence electrons methods had a particularly striking impact, is their tautomerism indeed, the calculation of the total molecular energies en-... 

The second fundamental aspect of the recent developments that we shall examine is the conformational one. As is well known, the activity of biological molecules and, in particular, of biopolymers is frequently strongly dependent upon their conformation. The understanding of the factors governing conformational stability of biomolecules and the evalution of the preferred conformers is therefore of utmost interest for the further development and broadening of quantum biochemistry. It is one of the major contributions of the all-valence electrons methods to have made this development feasible. 

The need for a rational approach to pharmacology has become very strong during these last years. Because of the chemical nature of the majority of drugs, which most frequently involve conjugated and saturated fragments and thus imply probably in their mechanism of action the intervention of their a and ir electrons, these compounds have for a long time evaded successful quantum-mechanical treatment. The advent of the all-valence electrons method opens up new vistas in this field. 

Clearly, the most satisfactory way to decide between conflicting concepts of the structure and nature of the hydrogen bond is to treat quantum-mechani-cally a hydrogen-bonded complex as a single large molecule entity with no truncation and to compare the results obtained for this supermolecule to those obtained for the separated molecules treated in the same approximation. This mode of approach is now possible, and a number of such computations using both all-valence electrons methods and the SCF MO non-empirical procedure have recently appeared. The references pertinent to biochemistry have been listed in Tables I and II. These concern only various hydrogen-bonded amides and the base pairs of the nucleic acids. 

The possibility of performing non-empirical calculations provides a means of verifying the conclusions reached by the valence-electrons method and offers an opportunity to go further. It must, however, be kept in mind that the results of SCF calculations depend on the atomic basis set adopted, particularly in the... 

The examples have been classified by method n methods (Table 1), allelectron or valence-electron methods (Table 2) semiempirical and non-empirical... 

In order to improve the model further we are currently taking quantum effects in the lattice into account, i.e. treating the CH units not classically but on quantum mechanical basis. To this end we use an ansatz state similar to Davydov s so-called ID,> state [96] developed for the description of solitons in proteins. However, there vibrations are coupled to lattice phonons, while in tPA fermions (electrons) are coupled to the lattice phonons. The results of this study will be the subject of a forthcoming paper. Further we want to improve the description of the electrons by going to semiempirical all valence electron methods or even to density functional theories. Further we introduce temperature effects into the theory which can be done with the help of a Langevin equation (random force and dissipation terms) or by a thermal population of the lattice phonons. Starting then the simulations with an optimized soliton geometry in the center of the chain (equilibrium position) one can study the soliton mobility as function of temperature. Further in the same way the mobility of polarons can be... 

Ab initio A quantum mechanical nonparametrized molecular orbital treatment (Latin from first principles ) for the description of chemical behavior taking into account nuclei and all electrons. In principle, it is the most accurate of the three computational methodologies ab initio, semi-empirical all-valence electron methods, and molecular mechanics. 

All valence electron methods In contrast to ab initio methods, the semi-empirical molecular orbital methods only consider the valence electrons for the construction of the atomic orbitals. Well-known semi-empirical methods are EHT, CNDO, MNDO, PCILO, AMI, and PM3. These methods are orders of magnitude faster than ab initio calculations. 

CNDO Complete Neglect of Differential Overlap. One of the first semi-em-pirical all-valence electron methods formulated by J. A. Pople et al. in the 1960s. Because of the drastic simplifications dictated by the speed of the computers in those days, CNDO methods are superseded by more elaborate semi-empirical quantum chemical calculations such as AMI and PM3. 

EHT Extended Hiickel Theory. One of the first semi-empirical all-valence electron methods formulated by R. Hoffmann in the mid-1960s. 

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