Integrated Molecular Transform

The int rated molecular transform (FT ) is a molecular descriptor calculated from the square ofthe molecular transform, by integrating the squared molecular transform in a selected interval of the scattering parameter s to obtain the area under the curve and finally taking the square root of the area [King, Kassel et al., 1990, 1991]. The square root of the integrated molecular transform, called SQRT index, was also proposed as molecular descriptor [Famini, Kassel et al., 1991]. 

Applications of integrated molecular transforms found in literature are ]King and Kassel, 1992 King, 1993, 1994 Molnar and King, 1995, 1998 King and Molnar, 1996, 1997, 2000]. 

King, J.W. and Kassel, R.J. (1991) Dimensional response ofthe integrated molecular transform. Int. J. Quantum Chem. Quant. Biol Symp., 18, 289-297. 

F or the characterization of the charge distribution in a molecule, the numerically unitary integrated molecular transform (FTm), its analogous electronic (FTe) and charge (FTC) transforms, and the normalized molecular moment (Mn), its analogous electronic (AQ and charge (Mc) moment, have been developed as molecular structure descriptors [45,46]. Those descriptors have been applied successfully for the development of QSAR models for various physicochemical, pharmacological, and thermodynamic properties of compounds. 

Molnar SP, King JW. Theory and applications of the integrated molecular transform and the normalized molecular moment structure descriptors QSAR and QSPR paradigms. Int J Quantum Chem 2001 85 662-675. 

The MCSCF optimization process is only the last step in the computational procedure that leads to the MCSCF wave function. Normally the calculation starts with the selection of an atomic orbital (AO) basis set, in which the molecular orbitals are expanded. The first computational step is then to calculate and save the one- and two-electron integrals. These integrals are commonly processed in different ways. Most MCSCF programs use a supermatrix (as defined in the closed shell HF operator) in order to simplify the evaluation of the energy and different matrix elements. The second step is then the construction of this super-matrix from the list of two-electron integrals. The MCSCF optimization procedure includes a step, where these AO integrals are transformed to MO basis. This transformation is most effectively performed with a symmetry blocked and ordered list of AO integrals. Step... 

Wetzel, D.L. (1993) A molecular mapping of grain with a dedicated integrated Fourier transform infrared microspectrometer, in Food Flavor,... 

Enzymes are protein molecules which catalyse chemical transformations of specific molecules (substrates). An integral step in the catalytic mechanism is the binding of the substrate to the enzyme (see section 1.2.3). Thus enzymes combine molecular recognition with molecular transformation. Amongst the nearly 2000 known enzymes there is a wide range of binding specificity and some representative examples of enzyme-substrate pairs are shown in Table 1.3. An advantage of enzymes in the context of biosensors is that... 

The calculation of first-order properties in the atom-centered matrix approximations is almost absurdly simple, particularly for contracted basis sets. What we have done in the approximations is to expand the molecular wave function in a set of atomic positive-energy one-particle functions. So all we need do for the first-order properties is to evaluate the primitive property integrals and transform them. In an uncontracted basis, the electric and magnetic property matrices are given by... 

Each of these tools has advantages and limitations. Ab initio methods involve intensive computation and therefore tend to be limited, for practical reasons of computer time, to smaller atoms, molecules, radicals, and ions. Their CPU time needs usually vary with basis set size (M) as at least M correlated methods require time proportional to at least M because they involve transformation of the atomic-orbital-based two-electron integrals to the molecular orbital basis. As computers continue to advance in power and memory size, and as theoretical methods and algorithms continue to improve, ab initio techniques will be applied to larger and more complex species. When dealing with systems in which qualitatively new electronic environments and/or new bonding types arise, or excited electronic states that are unusual, ab initio methods are essential. Semi-empirical or empirical methods would be of little use on systems whose electronic properties have not been included in the data base used to construct the parameters of such models. 

The functions put into the determinant do not need to be individual GTO functions, called Gaussian primitives. They can be a weighted sum of basis functions on the same atom or different atoms. Sums of functions on the same atom are often used to make the calculation run faster, as discussed in Chapter 10. Sums of basis functions on different atoms are used to give the orbital a particular symmetry. For example, a water molecule with symmetry will have orbitals that transform as A, A2, B, B2, which are the irreducible representations of the C2t point group. The resulting orbitals that use functions from multiple atoms are called molecular orbitals. This is done to make the calculation run much faster. Any overlap integral over orbitals of different symmetry does not need to be computed because it is zero by symmetry. 

MP2 correlation energy calculations may increase the computational time because a two-electron integral transformation from atomic orbitals (AO s) to molecular orbitals (MO s) is required. HyperChem may also need additional main memory and/or extra disk space to store the two-electron integrals of the MO s. 

In standard quantum-mechanical molecular structure calculations, we normally work with a set of nuclear-centred atomic orbitals Xi< Xi CTOs are a good choice for the if only because of the ease of integral evaluation. Procedures such as HF-LCAO then express the molecular electronic wavefunction in terms of these basis functions and at first sight the resulting HF-LCAO orbitals are delocalized over regions of molecules. It is often thought desirable to have a simple ab initio method that can correlate with chemical concepts such as bonds, lone pairs and inner shells. A theorem due to Fock (1930) enables one to transform the HF-LCAOs into localized orbitals that often have the desired spatial properties. 

The gradient of the energy is an off-diagonal element of the molecular Fock matrix, which is easily calculated from the atomic Fock matrix. The second derivative, however, involves two-electron integrals which require an AO to MO transformation (see Section 4.2.1), and is therefore computationally expensive. 

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