Electronic structure representation energy value

Morante S, Rossi GC, Testa M (2006) The stress tensor of a molecular system an exercise in statistical mechanics. J Chem Phys 125 034101 66. Nelson DF, Lax M (1976) Asymmetric total stress tensor. Phys Rev B 13 1770-1776 Das A (1978) Stress tensor in a class of gauge theraies. Phys Rev D 18 2065-2067 Cohen L (1979) Local kinetic energy in quantum mechanics. J Chem Phys 70 788-789 Cohen L (1984) Representable local kinetic tmergy. J Chem Phys 80 4277-4279 Cohen L (1996) Local values in quantum mechanics. Phys Lett A 212 315-319 Ayers PW, Parr RG, Nagy A (2002) Local kinetic tmergy and local temperature in the density-functional theory of electronic structure. Int J Quantum Chem 90 309-326 Cohen L (1966) Generalized phase-space distribution functions. J Math Phys 7 781-786 Cohen L (1966) Can quantum mechanics be formulated as classical probability theory. Philos Sci 33 317-322... 

The raw output of a molecular structure calculation is a list of the coefficients of the atomic orbitals in each LCAO (linear combination of atomic orbitals) molecular orbital and the energies of the orbitals. The software commonly calculates dipole moments too. Various graphical representations are used to simplify the interpretation of the coefficients. Thus, a typical graphical representation of a molecular orbital uses stylized shapes (spheres for s-orbitals, for instance) to represent the basis set and then scales their size to indicate the value of the coefficient in the LCAO. Different signs of the wavefunctions are typically represented by different colors. The total electron density at any point (the sum of the squares of the occupied wavefunctions evaluated at that point) is commonly represented by an isodensity surface, a surface of constant total electron density. 

Unfortunately, measured vibrational frequencies have some anharmonic component, and the vibrational frequencies computed in the manner above are harmonic. Thus, even the most accurate representation of the molecular structure and force constant will result in the calculated value having a positive deviation from experiment (Pople et al. 1981). Other systematic errors may be included in calculations of vibrational frequencies as well. For instance, Hartree-Fock calculations overestimate the dissociation energy of two atoms due to the fact that no electron correlation is included within the Hartree-Fock method (Hehre et al. 1986 Foresman and Frisch 1996). Basis sets used for frequency calculations are also typically limited (Curtiss et al. 1991) due to the requirements of performing a full energy minimization. Thus, errors due to the harmonic approximation, neglect of electron correlation and the size of the basis set selected can all contribute to discrepancies between experimental and calculated vibrational frequencies. 

Fig. 20. Schematic representation of the reaction coordinate for tryptophan fluorescence quenching induced by hydrogen transfer and aborted decarboxylation. The electronic nature of the Si surface changes character along the Si path due to two avoided crossings between jSi and S2 The first one occurs between the covalent state and the ionic La state along the reaction coordinate that interconverts the i9i-Min and. Si-Exc minima. The second one occurs between the ionic La state and the biradical Bi, state along the tautomerization coordinate that leads to the excited-state tautomerized form S -Taut. This point does not corresponds to a minimum on the potential-energy surface and it is found that evolution along a decarboxylation coordinate leads to a -Si /-So conical intersection, where efficient radiationless decay to the ground state takes place. The values of the relevant structural parameters are given in A. Data from Ref. 102.

An electrostatic interaction model has been presented for the calculation of the static electronic polarizability of hydrocarbons, which, contrary to previous models, can describe aliphatic, olefinic, and aromatic systems. It is based on the representation of the C and H atoms by induced electric charges and dipoles, where the actual values of the charges and dipoles are those that minimize the electrochemical energy of the molecule. The electrostatic interactions are described in terms of normalized propagators, which improves both the consistency and the numerical stability of the technique. The calibration of the model is sought by reproducing the molecular polarizabilities obtained by current density functional theory for a set of 48 reference structures. An excellent agreement with the reference data has been obtained as evidenced by the relative errors on the mean molecular polarizabilities of 0.5, 1.4, and 1.9% for alkanes, alkenes, and aromatic molecules, respectively. 

---