Nonempirical methods

The calculation of AH° and AS° values from the pK-temperature data in each solvent mixture was performed by the nonempirical method of Clarke and Glew (26) as simplified by Bolton (27). In this method the thermodynamic parameters are considered to be continuous, well-behaved functions of temperature, and their values are expressed as perturbations of their values at some reference temperature 0 by a Taylor s series expansion. The basic equation is ... 

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. 

Data from a CD detector can be used to successfully confirm the absolute stereochemistries of the eluted enantiomers and the elution order. This important application has been introduced by Salvadori and co-workers [23], More recently it was demonstrated that an on-line detection system can be made which measures the CD spectrum of the eluate by trapping and holding it in the HPLC cell. By comparing the spectrum with data in a CD spectral library, absolute configurations can be confirmed. Where spectra are unavailable, absolute configurations might be obtained by means of either empirical and semiempirical approach or by using nonempirical methods such as the exciton model or the DeVoe approach [22, 23]. 

The question whether d-orbitals play an important role in the ground state bonding of thiopyrylium ion has aroused much controversy. Palmer and Findlay, using a nonempirical method involving linear combination of gaussian orbitals, concluded that sulfur 3d orbitals appear to behave as polarization functions rather than bonding orbitals in the normal chemical sense, and therefore, they are used only to a trivial extent (72TL4165). In contrast with this view, Yoshida and co-workers pointed out that the H NMR spectra of thiopyrylium, pyrylium, and N-ethylpyridinium provide clear evidence of 3rf-orbital participation in the former cation, as illustrated by resonance hybrids 7a and 7b. To support their view, they... 

The resolution of Co(phen) has been achieved. This has enabled a comparison of empirical (sign of the Cotton effect of the longest wavelength d <-> d band, nd nonempirical methods of assignment... 

The activation energy of the insertion of coordinated ethylene estimated by the ab initio method was found to be 15 kcal/mol Despite the application of a more advanced calculation technique these results are less compatible with the experimental data on solid titanium chloride-based catalysts, when the activation energy of the propagation step is 3-6 kcal/mol (Table 10). Probably, this incompatability is due to the model used in ref. which describes the AC as a bimetallic complex CljTiCHj with A1(CH3)3. However, it is important to note that the calculations performed by means of the nonempirical method confirm the concept implying that in the active center the alkyl group occupies an intermediate position between the octahedral sites and that in olefin coordination the AC structure is reconstructed. 

To determine the absolute configuration of optically active organic compounds, there are two nonempirical methods. One is the Bijvoet method in the X-ray crystallographic structure analysis, which is based on the anomalous dispersion effect of heavy atoms. - The X-ray Bijvoet method has been extensively applied to various chiral organic compounds since Bijvoet first succeeded in determination of the absolute stereochemistry of tartaric acid in 1951. The second method is a newer one based on the circular dichroism (CD) spectroscopy. Harada and Nakanishi have developed the CD dibenzoate chirality rule, a powerful method for determination of the absolute configuration of glycols, which was later generalized as the CD exciton chirality method. 8 The absolute stereochemistry of various natural products has been determined by application of this nonempirical method. 

The CD exciton chirality method has been successfully applied to a variety of natural products to determine their ACs. This method enables one to deduce the AC of a chiral compound without any reference compound, and therefore, it is established as a nonempirical method. The principles of the CD exciton chirality method are explained using the steroidal bis(p-dimethylaminobenzoate) shown below as a model compound, where the nonempirical nature of this method is easily proved.8 11 1... 

Nonempirical Methods for Determining Absolute Configurations of Chiral Compounds... 

The methods for determining the absolute configurations of chiral compounds are summarized in Table 9.1 with the nonempirical methods in the top half of the table. 

Recenfly fhe ah initio calculation mefhod of vibrational circular dichroism (VCD), optical rotatory dispersion (ORD), and electronic circular dichroism (ECD) has been developed as fhe third nonempirical method [3, 4]. The method is applicable to compounds having no chromophore, and so should be widely used in future. 

Knowledge on the Sq —Ti energy gap of methylene was also improved significantly after 1975, particularly since nonempirical methods were used more extensively. A very informative compilation of values calculated using various computational schemes with minimal-to-very-large basis sets was published by Minkin et al. (1989, Table 2 see also Shavitt, 1985, and Schaefer, 1986). The same authors found that, among semiempirical methods (CNDO, INDO, MINDO/2, MINDO/3 and MNDO), preference should be given to the MINDO/3 method. 

The approach adopted is to emphasize exact, or at least nonempirical methods in the description of ufp kinetics. Experimental data and empirical formulas are employed only to substantiate or to illustrate particular theoretical approaches. 

The calculations of CD spectra have been carried out by using semiempirical " as well as nonempirical " theories, but the trend has been shifting to nonempirical methods for its accuracy and software availability. Especially, time-dependent density functional theory (TDDFT) calculation, a recently developed nonempirical method, has become one of the most popular methods for small-to medium-sized molecules as it provides highly accurate CD predictions, though it is rather computationally demanding. ... 

Table 3.7 shows that the symmetry of locahzed orbitals does not depend in practice on the method of calculation of electronic structure. In particular, the method described here is equally applicable to results of SWX calculations where the atomic basis is not used at all. The change in energy ordering of the 6oi and 6 2 levels from that of the nonempirical method does not change the s3Tnmetry found for the localized orbitals. 

In the next section we discuss MSINDO semiempirical and HF nonempirical methods implementation of COM for the calculation of bulk properties of rutile crystal. The efficiency of the MSINDO method will be demonstrated that gives reasonable agreement with the results of HF calculations and at the same time is essentially simpler in practical reaUzation. 

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. 

In nonempirical methods of calculation, usually about 70% of the computer time is spent on computing the integrals of the interelectron interaction (/iv A(t) in Eq. (2.5). As the size of a molecular system is increased, the number of such integrals grows roughly proportionally to (N is the size of the AO basis set of... 

For example, unlike the nonempirical methods of calculation, which predict, in complete agreement with experiment, stability of protonated benzene in the form of a (x-complex XI [48], the CNDO/2 calculation [49] gives considerable... 

The nonempirical methods provide, in the main, consistent results. The size of the basis set and inclusion of correlation effects affect the quantitative estimates without altering the qualitative conclusion as to the energetic preferability of the Cg structure. 

There have already been several theoretical investigations, using mainly nonempirical methods, into intermolecular concerted dihydrogen transfer concerned, for example, with hydrogenation of ethylene by ethane [92] or with reactions between hydroxymethylene and ethylene [93], acetic acid and methanol [94, 95], methanol and formaldehyde [96]. 

Mitchell JBO, Price SL (2000) A systematic nonempirical method of deriving model intermolecular potentials for organic molecules application to amides. J Phys Chem A 104 10958-10971... 

Both exciton-coupled CD and X-ray techniques are nonempirical methods for determining the absolute configuration of chiral compounds. Although these two methods differ in that CD is for solutions whereas X-ray is for crystals, both methods naturally give the same absolute configuration. 

Nonempirical methods for the calculation of PES are purely theoretical. The starting information is only data on the composition of the considered system (the number and charges of particles), which allows us to name nonempirical calculations ab initio because only first principles are operated in them. 

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