Quantum mechanical analysis

Arai, T., J. Chem, Phys. 26, 435, New approach to the quantum-mechanical analysis of the electronic structure of molecules. The method of deformed atoms in molecules. A modification of Moffitt s method. 

Since the elementary quantum-mechanical treatment does not seem to give a high enough barrier, various treatments of the problem have been proposed which use empirical data such as bond dipole moments and steric repulsive forces. These treatments do not introduce any new forces which would not be included in a proper quantum-mechanical analysis, but they attempt to short-circuit these difficult and uncertain calculations. 

The study of atoms and molecules in external fields is a fascinating area of research that has attracted much attention from different areas of science and engineering. Following the influential work of Loudon in 1959, in which he performed the quantum mechanical analysis of the behavior of a one-dimensional hydrogen atom in various Coulomb potentials [1], many studies have been carried out to understand the physics of excitons (hydrogen-like electron-hole pair) and some related systems [2-5]. The discovery of neutron stars and white dwarf stars further motivated rapid development of this field since it stimulated the interest of studying the variation of electronic structure and behavior of atomic and... 

The simple probabihstic model was also confirmed by quantum-mechanical analysis [72]. Quantum-mechanical analysis gave expressions for ae and a2y that are very similar to each other. This similarity indicates that TPA of entangled and accidentally coincident photons is essentially identical. Differences between both expressions arise mainly due to the fact the expression for entangled photon TPA cross-section accounts for correlations between the photons it has a constant factor l/(TeAe). Moreover, it includes complex entanglement time-dependent siunmation coefficients, which may lead to periodic modiflation in the ae(Te) dependence, or entanglement-induced two-photon transparency. 

R. B. Bernstein. Quantum mechanical analysis of differential elastic scattering of molecular beams. J. Chem. Phys., 33 795, 1960. 

This remark is associated with the amount of calculation performed and is not intended as a criticism. This work provides a valuable quantum mechanical analysis of a three-dimensional system. The artificial channel method (19,60) was employed to solve the coupled equations that arise in the fully quantum approach. A progression of resonances in the absorption cross-section was obtained. The appearance of these resonances provides an explanation of the origin of the diffuse bands found... 

Lam, Y.-h. Honk, K. N. Scheffler, U. Mahrwald, R. Stereoselectivities of histidine-catalyzed asymmetric aldol additions and contrasts with proline catalysis A quantum mechanical analysis, J. Am. Chem. Soc. 2012,134, 6286-6295. 

Although we will not consider the details of Allen s quantum mechanical analysis, it is useful to compare Allen s and Pauling s values for some of the more important representative elements (Table 13.2). While many values are similar, some significant differences appear. 

There arc fundamental dil fcrcnees between the quantum and molecular mechanics approaches. They illustrate the dilemma that cun confront the medicinal chemist. Quantum mechanics is derived from basic theoretical principles at the atomic level. The model itself is exact, but the equations used in the technique are only approximate. The molecular properties are derived from the electronic structure of the molecule. The assumption is made that the distribution of electrons within a molecule can be described by a linear. sum of functions that represent an atomic orbital. (For carbon, this would be s./>,./>,. etc.) Quantum mechanics i.s computation intensive, with the calculation time for obtaining an approximate solution increasing by approximately N time.s. where N i.s the number of such functions. Until the advent of the high-.speed supercomputers, quantum mechanics in its pure form was re.stricted to small molecules. In other words, it was not practical to conduct a quantum mechanical analysis of a drug molecule. 

O. Guvench and A. D. MacKerell, Jr., Quantum mechanical analysis of 1,2-ethanediol conformational energetics and hydrogen bonding, /. Phys. Chem. A, 110 (2006) 9934-9939. 

Quantum mechanical analysis based on a simple two-level model [22] and bond-order alternation (BOA) principle exploiting aromaticity [23] have worked surprisingly well in providing useful structure/property relationships for the design of chromophores with ever improving molecular hyperpolarizability. Table 1 provides some representative examples with improved molecular optical nonlinearity developed over the past decade. It has been shown that very large nonlinearities... 

The weak genotoxicity and the very weak carcinogenicity of benzojejpyrene appear to contradict the bay region diol epoxide hypothesis. Quantum mechanical analysis of the ringed structure strongly... 

The effects of functional groups on chemical activity and structure are also important considerations. In oxidative phosphorylation, for example, the addition of a phosphate (PO4) group can fundamentally change the three-dimensional structure of an enzyme or other protein. Since the function of these molecules is critically dependent upon their stereochemistry, this process can activate or deactivate a particular protein or enzyme to perform (or to not perform) some particular function. The particular arrangement of a molecule is determined, fundamentally, through a quantum mechanical analysis of the interactions among the electron clouds and the nuclei in the molecule. Such an analysis can be extremely complicated for even relatively small molecules, but there are less exacting techniques that can be applied to yield approximate results. 

Ornstein, R.L. and Zheng, Y. (1997) Ab initio quantum mechanics analysis of imidazole C-H- - -O water hydrogen bonding and a molecular mechanics forcefield correction,... 

Sequential Monte Carlo - Quantum Mechanical Analysis... 

---