Future of Semiempirical Methods

Isotopic substitution effects can be studied using the DRC. This would allow, for example, kinetic isotope effects to be calculated. 

In addition to the reaction coordinate mapped out by the DRC, the minimum energy path from transition state to reactants or products is of interest. As with the DRC originating at the transition state, this path is coordinate-system independent. The calculation to determine the minimum energy path starts in a similar manner to the DRC calculation, only after the initial displacement, all velocities are annulled at every step. This results in the system moving perpendicular to the energy contours in mass-weighted coor nate space. Su di trajectories are time independent, and are called intrinsic reaction coordinates (IRC). For a review of potential energy surfaces for polyatomic reaction dynamics, see ref. 59. 

Care should be exercised in using both IRC and DRC calculations. Certain high-symmetry systems may have bifurcation points on the potential energy surface in which alternative paths are available. If such forks in the reaction coordinate exist, the final geometry resulting from two superficially similar calculations may be very different. 

Over the past three decades, semiempirical methods have changed from being of purely theoretical interest to being eminently practical. To a large measure this has been a result of the shift from atom-centered methods such as CNDO to molecule-centered methods such as PM3. Without the dramatic increase in the availability and power of computers, the improvements in modeling would have been of little use. 

It is desirable and likely that over the next several years a comprehensive compendium of reference data suitable for calibrating and testing molecular mechanics, semiempirical, and ab initio methods will be set up. This data base would initially contain mainly experimental results, but as more very high quality ab initio results become available the data base would become increasingly theoretic. 

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Andrew Holder, The Future of Semiempirical Methods, in THEOCHEM, 401 (3), Elsevier, Amsterdam, 1997. 

This coexistence with higher-level methods represents one of the most promising outlooks for the future of semiempirical methods. At the present and in the near future, there still exists a wide field in which approximate methods can aid the researcher to gain an understanding of the fundamental principles in chemistry and biology. 

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. 

Not so many works have made use of MO methods to study the CD-guest minimum energy conformations [26-40]. It is not the purpose of this work a full analysis of the results for the different complexes but to present the capabilities of the MO methods in this field and analyze the limitations and future trends. Whereas the first works were almost restricted to the use of semiempirical methods, recently the more reliable ab initio or DFT methods have begun to be applied to such large molecular systems. A recent comparative study has shown that the more popular semiempirical methods AMI and PM3 may give unphysical very short H - H distances between the host and guest molecules. 

Here we skim over the field of semiempirical VB theory of the Jt-systems of benzenoids. Primary focus is on a systematic derivational development of a hierarchical sequence of VB models. Different VB-based models are addressed in different sections (2, 3,5, 6) here, and the overall development is summarized in the diagram at the conclusion of Sect. 7. Section 4 serves as an interlude on quantum chemical computational methods, with emphasis on the VB basis and its relationship to chemical structure — this being crucial for the following sections. Along the way we indicate some of the history and general characteristics of the models. The unifying view which emerges not only incorporates many aspects of past work but reveals avenues for future research. 

AMI and PM3 perform similarly and usually give quite good geometries, but less satisfactory heats of formation and relative energies. A modification of AMI called SAMI (semi-ab initio method 1), relatively little-used, is said to be an improvement over AMI. AMI and SAMI represent work by the group of M. J. S. Dewar. PM3 is a version of AMI, by J. J. P. Stewart, differing mainly in a more automatic approach to parameterization. Recent extensions of AMI (RM1) and PM3 (PM6) seem to represent substantial improvements and are likely to be the standard general-purpose semiempirical methods in the near future. 

In conclusion, we share the philosophy H. F. Schaefer III expressed in 1979 (which we believe is still valid in 1986, and very likely to be for the foreseeable future) We have been convinced for about five years that ab initio electronic structure calculations should not even attempt (except for the very simplest systems) to predict the entire potential energy surface . Since the success of a semiempirical method stems from the judicious combination of theory and experiment, we present a brief survey of the main theoretical methods in the remainder of this section. 

To conclude this section, it should be noted that the calculations of the potential energy surfaces for heterogeneous catalytic reactions, even by semiempirical methods, still remain a matter for the future. Insufficient accuracy of the semiempirical methods, the approximate nature of cluster modeling, the large volume of a configurational space, a variety of possible reaction paths, etc., considerably restrict the utility of quantum chemistry as applied to this field. There is, however, no doubt that these difficulties will be successfully overcome. The value of conclusive quantum-chemical calculations can hardly be overestimated. They are able to answer questions which the most sophisticated and refined experiments would fail to answer. 

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. 

In recent years there have been significant advances in ab initio and DFT methods. Many groups (including our own) employ these techniques to compute molecular properties of chemical interest as accurately as presently possible. What are the perspeetives of semiempirical molecular orbital methods under these circumstances Which role can they play in the near future ... 

In the near future, ab initio, DFT, and semiempirical methods are expected to remain the major computational tools of quantum chemistry, with significant improvements in each of these methods. Undoubtedly,... 

A combination of the hard-sphere MSA concept and the chemical model (Section III.D) concept permits correct data reproduction over large concentration ranges, which makes this type of MSA a good candidate for the data reduction in practical problems treated by engineers. It may be expected that in the near future MSA can replace more and more the semiempirical methods commonly installed in process simulators. 

Finally, in the future, semiempirical methods will be applied to a wider and wider range of problems. At present, applications have been made to a wide range of ground-state properties, to vibrational frequencies, and consequently to thermodynamic quantities, such as entropies and heat capacities, to reaction mechanisms and transition states, to polarizabilities and hyperpolarizabilities, to time-dependent phenomena, and to quantum phenomena, such as tunneling, to molecules, ions, enzyme active sites, and to polymer properties including heats of polymerization and elastic moduli. With the passage of time the range of simulations will increase, and with it the ultimate limitations of the methods will become apparent. 

Accurate calculations are still believed to be restricted to light-atom molecules. The 1990s may well become the decade in which computational chemistry conquers the heavy-atom part of the periodic system of the elements Because ab initio calculations may also be used to derive parameters for semiempirical methods and molecular mechanics calculations, the outlook for the future of computational chemistry is bright. 

Certain trends in the development and application of hybrid potentials are evident. Up to now most studies have been done with potentials that use semiempirical methods as the approximation. It is likely that these potentials will remain the most widely used in the future as they are relatively inexpensive to apply, although they will be improved, either by reparametrizing the semiempirical method for each new problem of interest or by using newer semiempirical approximations. Wider application of potentials with ab initio methods is also likely. Particularly promising are hybrid DFT/MM potentials as DFT methods are one of the most inexpensive types of ab initio methods yet they can provide results of an accuracy equivalent to the more expensive correlated molecular orbital methods. 

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