Semiempirical Extended Huckel

Fig. 2.9 Semiempirical (extended Huckel theory) band structure E ip k)) for a onedimensional chain of hydrogen atoms with H-H distances of 3 A and 2 A (in grey) and 1 A (in black). The shape of the extended wave function has been iconized for three different k points, r (left), k = n/2a (middle), and X (right).

Fig. 2.19 Semiempirical (extended Huckel theory) band structure, density-of-states, and crystal orbital overlap population for a one-dimensional chain of hydrogen atoms spaced at 2.0 A. Due to a Gaussian smoothing, DOS and COOP plots appear slightly...

After a number of semiempirical (extended Huckel, CNDO/2,< > INDO,< and MINDO< >) calculations in 1970, Andre performed the first ab initio band-structure computation of an infinite polyethylene chain. Since this polymer is mass-produced in the plastics industry, the theoretical study of its properties (especially of its mechanical properties, see Chapter 10) is of great practical interest, which explains the large... 

Molecular mechanics and semiempirical calculations are all relativistic to the extent that they are parameterized from experimental data, which of course include relativistic effects. There have been some relativistic versions of PM3, CNDO, INDO, and extended Huckel theory. These relativistic semiempirical calculations are usually parameterized from relativistic ah initio results. 

Prior to considering semiempirical methods designed on the basis of HF theory, it is instructive to revisit one-electron effective Hamiltonian methods like the Huckel model described in Section 4.4. Such models tend to involve the most drastic approximations, but as a result their rationale is tied closely to experimental concepts and they tend to be inmitive. One such model that continues to see extensive use today is the so-called extended Huckel theory (EHT). Recall that the key step in finding the MOs for an effective Hamiltonian is the formation of the secular determinant for the secular equation... 

Photoelectron spectra have been reported for 2,4 and V-methylisoindole and the ionization potentials (IP) assigned in the light of nonempirical calculations using Koopmans theorem. Linear correlations of the type Pobs = I Peak + were obtained in all three cases. As was noted, extended Huckel, PPP, and other semiempirical calculations also led to satisfactory correlations of the first three IPs, but the scatter was generally larger. The first IP of 4 lies in the order of 7.9 eV (Fig. 1 of Palmer and Kennedy ) a value of 7.91 eV has been reported by other authors. In comparison, the first IP of l,3-diphenylbenzo[c]furan is 7.09 eV. ... 

The molecular structure entry is performed by sketching the compounds on a graphics terminal, and then storing them as connection tables. The geometries are optimized using adapt s molecular mechanics routine, MM2 [4], the semiempirical molecular orbital program (MOPAC) [5], or a newly developed extended Huckel method [6]. 

To facilitate subsequent discussion a brief review of certain properties of the heteropoly oxometalates is essential. Semiempirical quantun mechanical techniques, such as the extended Huckel method, when applied to structural fragments which simulate the heteropoly anions, have shown that the charge on the terminal or outer oxygen atoms of the anion containing P and W is approximately equal to that containing Si and W (Fig. 4) (ref. 23). In... 

A number of studies have compared the use of the multiple regression technique using semiempirical parameters such as tt and o-, and parameters calculated for the particular molecules from molecular orbital theory. Hermann, Culp, McMahon, and Marsh (23) studied the relationship between the maximum velocity of acetophenone substrates for a rabbit kidney reductase. These workers were interested in the reaction mechanism, and two types of quantum chemical calculations were made (1) extended Huckel treatment, and (2) complete neglect of differential overlap (CNDO/2). Hydride interaction energy and approaching transition-state energies were calculated from the CNDO/2 treatment. All these parameters plus ir and a values were then subjected to regression analysis. The best results are presented in Table II. 

Tel. 33-88-67-98-00, fax 33-88-67-98-01, e-mail e702bs%frccsc21.bitnet Sequence analysis and biomolecular modeling. PRO-SIMULATE for molecular simulations with GROMOS, AMBER, and BOSS via a graphical interface. PRO-QUANTUM for semiempirical (MOPAC, Extended Huckel) and ab initio (CADPAC) calculations via a graphical interface. FDCALC and ESCALC for electrostatics calculations. N-DEE for analysis of NMR data. UNIX workstations. Also PC-PROT+ (sequence analysis), PC-TAMMO-i- (protein-lipid modeling), and MASCA (statistics) for PC. 

X) is most likely, and the observation of two different vicinal fluorine-fluorine coupling constants from the analysis of the variable temperature F NMR spectrum (Section XI), indicated that one rotamer must predominate (143). However semiempirical and extended Huckel LCAO-MO calculations suggest that the stability of the various conformations for P2F4 decreases in the order gauche > cis > trans- (69a). 

Zalis and Vlcek studied the electronic structure of [M(mnt)2]" (M = Co, Ni or Cu n = 1, 2 or 3) by semiempirical methods. Iterative extended Huckel methods (lEHT) and CNDO results were compared. Except for [Co(mnt)2f , both methods yielded as the HOMO for all d complexes for the exception, CNDO found 10, as the HOMO. lEHT and CNDO revealed a greatly reduced... 

Semiempirical methods are widely available in many programs. Gaussian (Section 15.15) includes the MNDO, AMI, PM3, MINDO/3, INDO, and CNDO methods. SPARTAN includes the MNDO, MNDO/d, AMI, PM3, and PM3(tm) methods and MacSPARTAN and PC SPARTAN have the AMI method. HyperChem has the MNDO, MNDO/d, AMI, PM3, MINDO/3, CNDO, INDO, INDO/S and extended HUckel methods. ZINDO (www.msi.com/) has the extended Hiickel, PPP, CNDO,... 

The geometrical structure of gaseous PH2 in its X Ai ground state appears to be similar to that of ground-state PH2 (with an internuclear distance of r=1.42 A and an interbond angle of a = 92° see p. 72). This was inferred from a sharp increase of the photodetachment cross section at threshold, measured by ion cyclotron resonance [2, 3] and from the predominance of the (0, 0, 0)<-(0, 0, 0) transition in the PH2, X Bi PH, X A photoelectron spectrum [4]. r=1.34 0.05 A and a = 92 5 were taken from the isoelectronic H2S molecule (and used to calculate the thermodynamic functions of PH, see p. 109) [5]. r and a have also been theoretically calculated by several ab initio MO methods, i.e., at an MP2 [6, 7], a CEPA (coupled electron pair approximation) [8], and an HF level [9 to 15]. r was also obtained from a united-atom approximation [16] a was also calculated by a semiempirical (CNDO/2) method [17] and estimated by extended Huckel calculations [18]. 

Thirdly, it has been demonstrated that shapes (Figure 1), nodal structures, momentum distributions, and symmetry properties of KS orbitals are similar to those calculated by the ab initio, semiempirical, and extended Huckel methods. ... 

The quantum chemical calculations differ as to the relative magnitude of AV(cis) and AV(trans). AV(cis)< AV(trans) was obtained by semiempirical methods using the experimentally determined geometry. AV(cis)> AV(trans) follows from ab initio calculations and also from the CNDO/2 and the MINDO methods if the energy is minimized with respect to the residual geometric parameters (EH = extended Huckel calculation) ... 

Semiempirical calculations for j or AEf were carried out by the SCF-MO method with integral approximations [23], by various versions of the CNDO [24 to 27] and INDO [1 to 4, 28] methods, by the MNDO method [29], by the extended Huckel and Pariser-Parr-Pople methods [30], and by a simple [31] MO method [32]. 

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