Semiempirical methods Huckel method

The logical order in which to present molecular orbital calculations is ab initio, with no approximations, through semiempirical calculations with a restricted number of approximations, to Huckel molecular orbital calculations in which the approximations are numerous and severe. Mathematically, however, the best order of presentation is just the reverse, with the progression from simple to difficult methods being from Huckel methods to ab initio calculations. We shall take this order in the following pages so that the mathematical steps can be presented in a graded way. 

The Huckel method and is one of the earliest and simplest semiempirical methods. A Huckel calculation models only the 7t valence electrons in a planar conjugated hydrocarbon. A parameter is used to describe the interaction between bonded atoms. There are no second atom affects. Huckel calculations do reflect orbital symmetry and qualitatively predict orbital coefficients. Huckel calculations can give crude quantitative information or qualitative insight into conjugated compounds, but are seldom used today. The primary use of Huckel calculations now is as a class exercise because it is a calculation that can be done by hand. 

As indicated above, early attempts to use semiempirical methods had proved unsatisfactory, due to the wrong choice of parameters. A similar situation had existed in the Pople 14> treatment of conjugated molecules using the Huckel o, ir approximation the parameters in this were chosen to fit spectroscopic data and with these the method gave poor estimates of ground state properties. Subsequent work in our laboratories has shown JS) that this approach can lead to estimates of heats of atomization and molecular geometries that are in almost perfect agreement with experiment if the parameters are chosen to reproduce these quantities. 

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... 

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... 

Huckel (properly, Huckel) molecular orbital theory is the simplest of the semiempirical methods and it entails the most severe approximations. In Huckel theory, we take the core to be frozen so that in the Huckel treatment of ethene, only the two unbound electrons in the pz orbitals of the carbon atoms are considered. These are the electrons that will collaborate to form a n bond. The three remaining valence electrons on each carbon are already engaged in bonding to the other carbon and to two hydrogens. Most of the molecule, which consists of nuclei, nonvalence electrons on the carbons and electrons participating in the cr... 

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) ... 

The charge distribution, calculated semiempirically (presumably by the extended Huckel method), is given in [7]. 

---