Method nonempirical quantum

The theory of resonance in chemistry is an essentially qualitative theory, w hich, like the classical structure theory, depends for its successful application largely upon a chemical feeling that is developed through practice. We may believe the theoretical physicist who tells us that all the properties of substances should be calculable by known method. —the solution of the Schrfldinger equation. In fact, however, we have seen that during the 30 years since the Schrodinger equation was discovered only a few accurate nonempirical quantum-mechanical calculations of the properties of substances in which the chemist is interested have been made. The chemist must still rely upon experiment for most of his information about the properties of substances Experience has shown that he can be immensely helped by the use of the simple chemical structure theory. The theory of resonance is a part of the chemical structure theory, which has an essentially empirical (inductive) basis it is not just a branch of quantum mechanics. 

Computational studies could shed light on molecular structures and properties of such systems. A series of tetrads of DNA bases has been recently investigated in our laboratory. Ab initio, nonempirical quantum chemical method has been used in these studies. The considered structures reveal different conformational preferences of DNA bases. They have also one common feature all tetrads are linked together by H-bonding patterns. 

Quantum-mechanical studies on the tautomerism of heterocyclic compounds involve, in general, two aspects. The first deals with the prediction of physicochemical properties of defined tautomeric forms (e.g., ultraviolet spectra, dipole moments, ionization potentials, etc.). This seems to be easy to handle. Using any semiempirical or nonempirical quantum-mechanical computational method, depending on approximations involved in the method, we are able to calculate properties that, more or less, agree with experimental values. Calculations of this type do not contribute to a direct estimation of the relative stability of the tautomers, however they are particularly important for cases in which a tautomeric form of a compound is so rare that it is not possible to measure it directly. 

The use of frozen orbitals, such as the bond orbitals connecting the quantum to the classical part of the system, can be extended to nonempirical quantum methods such as ab initio Hartree -Fock, post Hartree Fock, or DFT. In these cases, the overlap between atomic orbitals is taken into account and the orthogonality conditions are more difficult to fulfill. The mathematical formulation of the method has been developed in the original papers [26 28] and the process can be summarized as follows. 

Th6 theory and the analysis of calculational schemes of quantum chemistry have been dealt with in detail in a number of books [1-6] and review articles [7-12]. Here we give only a brief account of the main principles of the general theory of molecular orbitals (MO) that provides the basis for constructing the most important nonempirical methods of quantum chemistry. 

Rapid development of nonempirical quantum-chemical methods (both in the band and cluster approaches) made it possible to perform detailed investigations of both the electronic structure of the vacancies and the effects of nonstoichiometry on the crystal energy spectra and properties. This chapter reviews the relevant results obtained for transition metal carbides and nitrides. 

Figure 1.12 Determining the properties of drug molecules. Drug molecules may have their properties ascertained by either experimental or theoretical methods. Although experimental methods, especially X-ray crystallography, are the gold standard methods, calculational approaches tend to be faster and do provide high qnality information. Nonempirical techniques, such as ab initio quantum mechanics calcnlations, provide accnrate geometries and electron distribution properties for drng molecnles.

The ground-state wave function of cytosine has been calculated by practically all the semiempirical as well as nonempirical methods. Here, we shall discuss the application of these methods to interpret the experimental quantities that can. be calculated from the molecular orbitals of cytosines and are related to the distribution of electron densities in the molecules. The simplest v-HMO method yielded a great mass of useful information concerning the structure and the properties of biological molecules including cytosines. The reader is referred to the book1 Quantum Biochemistry for the application of this method to interpret the physicochemical properties of biomolecules. Here we will restrict our attention to the results of the v-SCF MO and the all-valence or all-electron treatments of cytosines. 

Hobza P, Kabelac M, Sponer J, Mejzlik P, Vondrasek J (1997) Performance of empirical potentials (AMBER, CFF95, CVFF, CHARMM, OPS, POLTEV), semiemprical quantum chemical methods (AMI, MNDO/M, PM3) and ab initio Hartree-Fock method for interaction of DNA bases comparison of nonempirical beyond Hartree-Fock results, J Comp Chem, 18 1136-1150... 

Mikheikin et al. (11) have formulated an alternative approach where terminal valencies are saturated by monovalent atoms whose quantum-chemical parameters (the shape of AO, electronegativity, etc.) are specially adjusted for the better reproduction of given characteristics of the electron structure of the solid (the stoichiometry of the charge distribution, the band gap, the valence band structure, some experimental properties of the surface groups, etc.). Such atoms were termed pseudo-atoms and the procedure itself was called the method of a cluster with terminal pseudo-atoms (CTP). The corresponding scheme of quantum-chemical calculations was realized within the frames of CNDO/BW (77), MINDO/3 (13), and CNDO/2 (30) as well as within the scope of the nonempirical approach (16). 

Stacked NA base pairs AMBER 4.1 with the force field of Cornell et al [16] best reproduces the ab initio stabilization energies and geometries. The success of the Cornell et al force field is probably due to the derivation of atomic charges. It must be also mentioned that this force field provides a better description of interaction energies of NA base pairs than any semiempirical quantum chemical method or even nonempirical ab initio technique of a lower quality than that of the MP2 procedure (DFT or ab initio HF methods). 

An alternative to the MO method for the quantum mechanical treatment of molecular systems is the so-called Valence-Bond (VB) theory where molecular wavef unctions Eire obtained as linear combinations of covalent and ionic structures. It was shown long ago 181> that for distances larger than equilibrium distances, VB approximate wave functions should be better than MO functions of the same level, and hence VB theory should find its most profitable application in the evaluation of potential surfaces and reaction paths. Although true in principle, this statement has little influence in practice this is mostly because VB theory has only recently been formulated in a nonempirical form 182-184) so that applications are only just beginning to appear. 

Electronic structure calculations may be carried out at many levels, differing in cost, accuracy, and reliability. At the simplest level, molecular mechanics (this volume, Chapter 1) may be used to model a wide range of systems at low cost, relying on large sets of adjustable parameters. Next, at the semiempirical level (this volume, Chapter 2), the techniques of quantum mechanics are used, but the computational cost is reduced by extensive use of empirical parameters. Finally, at the most complex level, a rigorous quantum mechanical treatment of electronic structure is provided by nonempirical, wave function-based quantum chemical methods [1] and by density functional theory (DFT) (this volume, Chapter 4). Although not treated here, other less standard techniques such as quantum Monte Carlo (QMC) have also been developed for the electronic structure problem (for these, we refer to the specialist literature, Refs. 5-7). 

Quantum chemical investigations have also been carried out on the 1,2-proton shift in protonated five-membered heterocycles <84CHE966>. As the proton travels round the ring, the intermediates are either at the local minima or in a transition state and consequently, the ehange in energy can be calculated. Calculations for thiophene by the SCF-MO-LCAO method in the MINDO/3 approximation and nonempirically in the OST-3GF basis both indicated protonation at the a-position to be more favorable, in line with results observed above. 

Recent publications calculate the basicity of aromatic compounds and the electronic structure of the respective arenium ions by quantum chemical methods in different approximations — by semi-empirical methods MO LCAO (methylbenzenes " ), CNDO, CNDO/2 and CNDO/2FK (benzene " , toluene and other monoalkylbenzenes " , anisole , a series of monosubstituted benzoles , poly-methylbenzenes , monomethylnaphthalenes and polycyclic aromatic hydrocarbons ) INDO (benzene , cresols ) MINDO-2 and MINDO-3 (benzene , toluene ) by nonempirical (ab initio) methods using the basis... 

The geometric, electronic and optical properties of oligothiophenes of two, four, six and eight units of head-to-head-tail-to-tail (HH-TT) regioselectivity and substituted by methyl, thiol and thiomethyl groups (Chart 8.15) were characterized in their neutral and p-doped states with quantum chemical calculations derived from semiempirical HF approaches and with the nonempirical valence effective Hamiltonian (VEH) method. Such calculations provide a good insight into the electronic properties measured for electropoly-merized chains [91]. 

---