Semiempirical Methods in Computational Chemistry

Introduction

Computational chemistry is a division of chemistry that uses methods of programing in

computer science to help in solving chemistry problems and designing models for chemists to

use in solving future problems.1 It is commonly applied in physical chemistry, solving

properties and structure of chemicals. Examples of these properties are, amongst other;

electronic charge distribution, energies, dipoles and spectroscopic values.2

Computational chemistry also has subdivisions that apply different methods of computions to

solve chemical problems. One example is the application of semiempirical methods in

computational chemistry problems. The word empirical means the method is based on or

characterized by observation and experiment instead of theory.3 Therefore by inference, a

semiempirical method is a method that is used to come to scientific conclusions based on

experimental observations and theory. There is a number of semiempirical methods that are

being used in computational chemistry, some of which I will discuss in this paper. These

methods run on computer programs and therefore there is also a wide variety of software that

I will briefly discuss that is also being used to solve computational chemistry problems

semiempirically.

Types of semiempirical methods and their uses

Semiempirical methods are largely based on the Hartree-Fock formalism (a quantum

calculation based on the Schródinger equation), however they obtain some factors from

empirical data. Semiempirical calculation are an advantage because they run much faster as

compared to other initial methods. There are many semiempirical methods available and each

has its own parameters that it operates under and different types of calculations. Some

examples are methods such as;

The PPP method (Pariser-Parr-Pople) which is used to provide approximations of the -

electronic excited states.4 This method is no longer widely used if used at all because of

the advancement of computer technology.

Several methods that use valence electrons to provide approximations of the molecular

excited states. Some of these are the CNDO/2, INDO and NDDO. The research into these

methods was proved by John Pople who was aslo involved in the development of the PPP

method. Likewise, these methods have also been largely abandoned.5

Michael Dewar, a theoretical chemist of the ninteenth centuary, famous for developing

the semiempirical quantum chemistry methods between the 1970s and the 1980s, is

accredited with the development of the MINDO, MNDO, AM1 and the PM3 methods,

that operate under the MOPAC computer program, a program designed to run

semiempirical quantum chemistry algorithms.6

The RM1 semiempirical method which runs in the SPARTAN computer program.

The Sparkle or AM1 methods, whose purpose is calculate geometries of coordination

compounds.

The ZINDO and SINDO semiempirical methods, for calculating excited states and

electronic sprectra calculation.7

Semiempirical methods currently in use

In an article by F. K. Karataeva et al., studies of the three isomers of p-tert-Butyl-Substituted

Thiacalix[4]arenes in conformations of partial cone, 1,3-alternant and cone were conducted.8

The compounds used were 5,11,17,23-tetra-tert-butyl-25,26,27-trihydroxy-28- and

5,11,17,23-tetra-tert-butyl-25,26-dihydroxy-27,28-[N-(4'-nitrophenyl)aminocarbonylmethoxy

] thiacalix[4]arenes (I, II). For the analysis during the studies; 1D and 2D (NOESY) 1H NMR

and 13

C NMR spectroscopies (a spectroscopic analytical method) along with the

semiempirical quantum chemical PM3 calculation (semiempirical method) were used. The

PM3 method was used to calculate the theoretical heats of formation and interproton

distances of compound I in the conformations cone, partial cone, 1,2-, and 1,3-alternate with

the Hyperchem Professional 7 program.8 The results of this PM3 method are presented (Table

1) as adopted from Karataeva. The geometries and heats of formations were also assessed by

the PM3 semiempirical method in the structural investigation on ion-selective ionophoric

properties of armed 12-oxacrown-3 derivatives, compounds which are know as crown ethers.

The calculations were performed using the software package SPARTAN’04 for windows (v

1.0.1).9

Table 1. Heat of formation of compound I calculated by РМ3 method8

Conformation ∆H°, kJ mol-1

Cone

Partial Cone

1,2-Alternate

1,3-Alternate

-12041.5993

-12040.5186

-12033.0890

-12041.5909

In the PM3 study, they were able to achieve the calculation of energy and interproton

distances of the compound I by using PM3 as their method of choice. PM3 stands for

parameterized model number 3. It is based on the neglect of differential atomic overlap

integral approximation.10

In the pharmaceutical industry, the quantitative structure-activity relationship (QSAR) plays a

vitally important role in the studies of drug discovery and design. Studies such as ligand-

based drug discovery and design are important when other structure determining methods like

NMR are unavailable. In a study by K Tsai et al., a number of semi-empirical and empirical

charge-assigning methods, AM1, AM1-BCC, CFF, Del-Re, Formal, Gasteiger, Gasteiger–

Hu¨ ckel, Hu¨ ckel, MMFF, PRODRG, Pullman, and VC2003 charges, were compared for

their performances in programs such as CoMFA and CoMSIA by application of standard

datasets. Comparative Molecular Field Analysis (CoMFA) and Comparative Molecular

Similarity Indices Analysis (CoMSIA) are two of the most used QSAR methods in drug

discovery, they play an important role in determining how steric and electrostastic properties

of a drug will affect its intended active site.11

The CoMFA method calculates the steric and electrostatic potential energies of biological

molecules interms of Lennard-Jones and Coulombic potentials, respectively.11

The

conformations and spacial alignments of such molecules are needed for CoMFA. CoMSIA is

used as a congruent technique. Therefore, in this study, semiempirical methods were used to

assign charge to molecules. The results showed that semiempirical methods like AM1 and

AM1-BCC charges offer the more precise results as compared to Gasteiger–Húckel charge.11

In the study for the approximate switching algorithms for trajectory surface hopping, a

semiempirical MNDO method was used to analys data to study surface hopping molecular

dynamics.12

MNDO is Modified Intermediate Neglect of Differential Overlap, a

semiempirical method for the quantum calculation of molecular electronic structures in

computational chemistry.13

This method was also used used in another study to find the heat

capacities of wulfenite in the temperature range from (0 to 55) K calculated by the

semiempirical method MNDO using the program package on quantum chemical calculation

MOPAC25 allowing calculations for crystalline material.14

Another type of semiempirical

quantum chemical method, SAM1 for the calculation of energy in the ground electronic state,

was combined with INDO for calculation of the excitation energy for the torsional surfaces in

the study of light-driven molecular motors.15

Semiempirical quantum methods also often

have shortcomings in terms of macromolecular calculation, whereby the molecules are larger

and more complicated. In order to model such large systems, empirically corrected

semiempirical methods appear to be an attractive alternative. In one such study, the widely

used semiempirical methods like AM1 were unable to model long-range dispersion and

consequently an experiential improvement term was desirable. A new experimentally

modified AM1 method that applies two empirical correction terms for dispersion and

hydrogen bonding interactions, was presented and designated AM1-FS1.16

Although this is

one of their shortcomings amongst others.

Conclusion

This paper has managed discribe and contrast between empirical and semiempirical methods

as applied in computational chemistry and also explicitly define computional chemistry

through the citing of research papers. An adequate number of research papers from current

publications (2006-present) were used to discuss semiempirical methods in computational

chemistry, however, a a few publications from past decades were also included for the

literature backround of this topic.

Bibliography

1. S. J. Smith and B T Sutcliffe. The development of computational chemistry in the United

Kingdom. London : s.n., Reviews in Computational Chemistry, 1997, Vol. 70, pp. 271-290.

2. S. T. Fernbach and A. Haskell. Computers and their role in the physical sciences. s.l. :

Routledge, 1970. pp. 1-10. 0677140304.

3. T. Engel and P. Reid. Physical Chemistry. Molecular Structure and Energy Levels for

Polyatomic Molecules. 1. San Francisco : Pearson Education, Inc., 2006, 25, p. 564.

4. R. Pariser and R. Parr. Journal of Chemical Physics, 1953, Vol. 21, no 466, p. 767.

5. I. Levine. Quantum Chemistry. 4. s.l. : Prentice Hall, 1991. pp. 579-580.

6. D. Young. Computational Chemistry. s.l. : Wiley-Interscience, 2001. p. 342.

7. M Zerner. New York : s.n., Reviews in Computational Chemistry, 1991, Vol. 2, No 313

8. F. K. Karataeva, M. V. Rezepova, A. Y. Zhukov, I. I. Stoikov, I. S. Antipin and V. V

Klochkov. Structure of the Stereoisomers of Tetrasubstituted p-t-Butylcalix[4]arene

Containing a Morpholine Fragment: Data of 1D and 2D (NOESY) NMR Spectroscopy.

Kazan : Pleiades Publishing, Ltd., Russian Journal of General Chemistry, 2009, Vol. 79,No 9

pp. 1495-1503. 1070-3632.

9. T. Moriuchi-Kawakami, T. Yokou, H. Tsujioka, R. Aoki, K. Fujimori and Y. Shibutani.

Structural investigation on ion-selective ionophoric properties of armed 12-oxacrown-3

derivatives. s.l. : Elsevier, Analytica Chemica Acta, 2006, Vol. 562, pp. 59-65.

10. J. J. J. Stewart. Optimization of parameters for the semiempirical methods IV: extension

of MNDO, AM1 and PM3 to more main group elements. Journal of Molecular Modeling,

2004, Vol. 10, pp. 155-164.

11. K. Tsai, Y. Chen, N. Hsiao, C. Wang, C. Lin, Y. Lee, M. Li, and B. Wang. A comparison

of different electrostatic potentials on prediction accuracy in CoMFA CoMSIA studies. s.l. :

Elsevier, European Journal of Medicinal Chemistry, 2010, Vol. 45, pp. 1544-1551.

12. E. Fabiano, G. Groenhof and W. Thiel. Approximate switching algorithms for trajectory

surface hopping. s.l. : Elvsevier, Chemical Physics, 2008, Vol. 351, pp. 111-116.

13. R. C. Bingham, M. J. S Dewar and D. H. Lo. Ground states of molecules. XXV.

MINDO/3. Improved version of the MINDO semiempirical SCF-MO method. Journal of the

American Chemical Society, 1975, Vol. 97, No 6, pp. 1285-1293.

14. M. R. Bessingaliyeva, M. A. Bespyatov, and D. B Gogol. Experimental measurement and

calculation of mole heat capacity and thermodynamic functions of wulfenite PbMoO4.

Novosibirsk : Journal of Chemical Engineering Data, 2010, Vol. 55, No 9, pp. 2974-2979.

15. N. M. Albu, E. Bergin and D. J. Yaron. Computational design of a light-driven molecular

motor. Pennsylvania : Journal of Physical Chemistry, 2009, Vol. 113, No 25 pp. 7090-7096.

16. M. E. Foster and K. Sohlberg. A new empirical correction to the AM1 method for

macromolecular complexes.. Pennsylvania : Journal of Chemical Theory and Computation,

2010, Vol. 6, No 7, pp. 2153-2166.