Electronic excited states semiempirical

CIS calculations from the semiempirical wave function can be used for computing electronic excited states. Some software packages allow Cl calculations other than CIS to be performed from the semiempirical reference space. This is a good technique for modeling compounds that are not described properly by a single-determinant wave function (see Chapter 26). Semiempirical Cl... 

Most of the semiempirical methods are not designed to correctly predict the electronic excited state. Although excited-state calculations are possible, particularly using a CIS formulation, the energetics are not very accurate. However, the HOMO-LUMO gap is reasonably reproduced by some of the methods. 

M. R. Silva-Junior and W. Thiel. Benchmark of electronically excited states for semiempirical methods MNDO, AMI, PM3, OMl, OM2, OM3, INDO/S, and INDO/S2, J. Chem. Theory Comput., 6 1546-1564 (2010). 

One of the methods most frequently used in calculations of electronic excited states is the configuration interaction technique (CI). When combined with semiempirical Hamiltonians the CI method becomes an attractive method for investigations of electronic structure of large organic systems. Undoubtedly, it is the most popular method for calculations of electronic contributions to NLO properties based on the SOS formalism. The discussion of the CI/SOS techniques is presented in Section 4. 

This review of semiempirical quantum-chemical methods outlines their development over the past 40 years. After a survey of the established methods such as MNDO, AMI, and PM3, recent methodological advances are described including the development of improved semiempirical models, new general-purpose and special-purpose parametriza-tions, and linear scaling approaches. Selected recent applications are presented covering examples from biochemistry, medicinal chemistry, and nanochemistry as well as direct reaction dynamics and electronically excited states. The concluding remarks address the current and future role of semiempirical methods in computational chemistry. 

In general, a qualitatively correct description of the ground state of a closed-shell molecule is provided by a single Slater determinant. This is why semiempirical (one-determinant) self-consistent field (SCF) methods can be applied quite successfidly to the determination of ground-state properties such as geometries, vibrational frequencies, and relative energies. Many electronically excited states, however, contain more then one dominant configuration state function. The simplest description of an excited state is the orbital picture where one electron has been moved from an occupied to an... 

The underlying theoretical approach is characterized by the type of the wavefunction and the choice of the basis set. Most current general-purpose semiempirical methods are based on molecular orbital theory and employ a minimal basis set for the valence electrons. Electron correlation is treated explicitly only if this is necessary for an appropriate zero-order description (e.g., in the case of electronically excited states or transition states in chemical reactions). Correlation effects are often included in an average sense by a suitable representation of the two-electron integrals and by the overall parametrization. 

DCPH has a pair of quasi-degenerate jt-electronic excited states, L) = 5 Bu and H) = 6 Bu, with energy gap IfiAco = 0.11 eV. In this semiempirical model, the angular momentum operator is defined as... 

The heat capacity C , thermodynamic functions S , -(G -Hj.)/T, H"- Hj., and the equilibrium constant K for the formation of PH as an ideal gas from the elements have been calculated for a standard-state pressure of 1 atm and tabulated for 298.15 K and between 0 and 6000 K at 100 K intervals [2, 4]. The JANAF data with T = 298 K are based on early spectroscopic data [7, 8] and semiempirical estimates for Dq and the electronically excited states [3]. In the third edition of the JANAF Tables [1], the old values were only converted to Joule units and to a standard pressure of 0.1 MPa. In the Russian compilation [4], values for a reference temperature T = 0 K are given that are based on a partition function established by using spectroscopic data for the X a A, A rij states [9,10] and theoretical data for the b and c 11 states [3, 11]. Selected values from [4] are ... 

A few experimental investigations, but predominantly ab initio calculations, supplied the data on the geometry and electron configurations of NHj in the electronic ground state X Bi and seven electronically excited states presented in Table 17. Additional electronic states 1 Ai, 2 Bi, 3 Ai, 2 Bi, 4 Ai [1], and 1 A2 [1, 2] were treated by ab initio methods. Semiempirical calculations were reported for NH2 in low-lying electronic states [3 to 13]. 

The interpretation of MCD spectra requires a close interaction with theory. So far, this has been nearly exclusively semiempirical theory, but the time appears ripe for ab initio calculations, at least for the smaller among r-electron systems, including not only purely electronic but also vibronic effects. Concurrently, high-resolution spectra will need to be measured for many of the molecules for which only low-resolution spectra are available today. A qualitatively higher level of understanding of electronically excited states of n systems can be expected to emerge from this combination. 

Although semiempirical methods are usually parameterized using ground-state systems, these methods have often been successfully applied to the study of transition states and electronic excited states. Three examples of rotational barriers are of interest the rotation of a methyl group in ethane, around the double bond in ethylene, and about the partial double bond in the peptide linkage. In one of these, the barrier to rotation in the peptide linkage, the PM3 method does extremely poorly. 

Indazoles have been subjected to certain theoretical calculations. Kamiya (70BCJ3344) has used the semiempirical Pariser-Parr-Pople method with configuration interaction for calculation of the electronic spectrum, ionization energy, tt-electron distribution and total 7T-energy of indazole (36) and isoindazole (37). The tt-densities and bond orders are collected in Figure 5 the molecular diagrams for the lowest (77,77 ) singlet and (77,77 ) triplet states have also been calculated they show that the isomerization (36) -> (37) is easier in the excited state. 

This formalism was originally devised for single ionization of ground-state atoms, but has now been successfully applied to the calculation of electron impact ionization cross sections for a range of molecules, radicals, clusters, and excited state atoms. Like many of the semiempirical and semiclassical methods used to describe the electron impact process, the theory has its roots in work carried out by J.J. Thomson, who used classical mechanics to derive an expression for the atomic electron impact ionization cross section,2... 

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