Quantum chemistry Hiickel

Prior to 1965, all we had in our armoury were the a and it Hiickel theories, and a very small number of rigorous calculations designated ab initio (to be discussed later). The aims of quantum chemistry in those days were to give total energies and charge distributions for real molecules, and the seventh decimal place in the calculated properties of LiH. Practical chemists wanted things like reliable enthalpy changes for reactions, reaction paths, and so on. It should come as no surprise to learn that the practical chemists therefore treated theoreticians with scepticism. 

It is interesting to note that all the simple theories (such as Hiickel jr-electron theory) have now reappeared as options in these very same packages Thus, very many scientists now routinely use computational quantum chemistry as a futuristic tool for modelling the properties of pharmaceutical molecules, dyestuffs and hiopolymers. I wrote the original Computational Quantum Chemistry text as... 

In the early years of quantum theory, Hiickel developed a remarkably simple form of MO theory that retains great influence on the concepts of organic chemistry to this day. The Hiickel molecular orbital (HMO) picture for a planar conjugated pi network is based on the assumption of a minimal basis of orthonormal p-type AOs pr and an effective pi-Hamiltonian h(ctT) with matrix elements... 

The simple, or Hiickel based, molecular orbital theory (HMO and PPP methods) frequently provides useful qualitative insights but cannot be used reliably in a quantitative manner. For this purpose it is necessary to use a method which takes account of all the electrons as well as their mutual repulsions. A major bottleneck in such calculations is in the computation and storage of the enormous number of electron-repulsion integrals involved. Early efforts to reduce this problem led Hoffmann to the EH approximation (I.N. Levine, Quantum Chemistry, 4-th ed., 1991, Prentice-Hall, Inc., Ch. 16, 17), and Pople and co-workers to the CNDO, INDO and NDDO-approximations (B-70MI40100). 

These methods appear rather simple, yet they were the starting point of a long evolution. Gilles Klopman, whose research interests at Case-Western Reserve University later turned to modeling bioactive molecules, was the first to use Sandorfy s methods. Kenichi Fukui made extensive use of them in his well-known work on the structures and reactions of saturated hydrocarbons and their derivatives. Fukui added his frontier orbital considerations. Around 1959 the milieu of developments in quantum chemistry contributed to inspire William N. Lipscomb to conceive the extended Hiickel method, which was subsequently implemented by Lawrence L. Lohr and Roald Hoffmann.83 Soon thereafter, John Pople and his coworkers introduced self-consistent field methods based on the zero-differential overlap approximation.815... 

H. Kragh, Before quantum chemistry Erich Hiickel and the physics-chemistry interface , Centaurus, 2001, 43, 1-16. 

The extended Hiickel method, which is a semiempirical quantum chemistry method, is often used as a preliminary step in the DFT study of molecular orbital analysis. The acetylide-bridged organometallic dinuclear complexes 5.2 were studied by Halet et al. using the extended Hiickel method for qualitative analysis and DFT for additional electronic properties [97], The extended Hiickel analysis concluded that the main contribution of the Pt-C bond arises from ct type interactions while the n back-donation is very weak. The DFT/BP86 calculation gives a 2.371 eV HOMO-LUMO gap. The electronic communication parameter Hdb between the bis-ferrocene compound linked with platinum acetylide (5.3) was calculated to be 0.022 eV, compared with 0.025 eV obtained experimentally by Rapenne and coworkers using DFT and the extended Hiickel method [98],... 

The most widely used semiempirical quantum chemistry technique for theoretical chemisorption studies is the Extended Hiickel Theory (EHT). The method was first proposed by Hoffmann/95/ in its nonrelativistic form, and by Lohr and Pyykko/96/ and also Messmer/97/ in its relativistic form, based on the molecular orbital theory for calculating molecular electronic and geometric properties. For a cluster the molecular orbitals are expanded as linear combinations of atomic orbitals... 

Most experimental chemists in Germany in those times did not believe that quantum theory beyond the simple Hiickel model had any use for chemistry in the foreseeable future." " So quantum chemistry had to get its main support from the more optimistic international community. Per-Olov Low-din s summer schools held in Uppsala (Sweden) were instrumental in getting young researchers interested in quantum molecular science. Since these schools... 

Topological orbitals... Probably the smartest of our readers have already appreciated the close relationship between the graph theory and the Hiickel method. Actually in quantum chemistry there is a great variety of problems in which the Hamiltonian of a molecule can be written in a matrix form as a one-valued function of the topological matrix of that molecule ... 

By the middle of the 1960s, computers had improved, but they were still incredibly slow by today s standards. Therefore, the quantum chemistry of the time was dominated by semiempirical methods, such as the Pople-Pariser-Parr Method, the Wolfsberg-Helmholtz Method, and the Extended Hiickel Method. 

These successes did not go unnoticed by industry. Several pharmaceutical companies (1963-1964) became interested in applications of it-electron theory to biochemistry. While it was admittedly premature, it was felt that quantum chemistry was both the wave of the future and the very matrix for rational drug design. Hiickel energies of cephalosporins could be correlated with their biological activities.While companies were applying some mathematical methods of correlation techniques in quantitative structure-activity relationships (QSAR), it was chiefly the Hiickel theory and various forms of semiempirical quantum mechanics that was using a large share of computer time on the IBM 7094 mainframe in 1966. 

Theoretical approaches, developed over the past 40 years of quantum chemistry, have recently become very helpful tools for developing an atomic-level understanding of the processes involved in high-temperature carbon chemistry. Interestingly, a combination of two theoretical approaches developed at opposite ends of this time-scale has proven to be extremely fruitful for such studies, namely the relatively new quantum chemical molecular dynamics (QM/MD) approach [14], using improved versions of early-day Extended Hiickel electronic structure method [15-17] for the calculation of potential... 

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