Ab initio quantum chemistry methods



Ab initio quantum chemistry methods are Robert Parr claims in an interview that the term was first used in letter to him by David Craig and was put into the manuscript of their paper on the excited states of benzene published in 1950.[2] [3]

The simplest type of ab initio electronic structure calculation is the Multi-configurational self-consistent field and methods have been developed that use these multi-determinant references for improvements.[5]

Almost always the electronic molecular Hamiltonian, with a discrete set of solutions.

Classes of methods

The most popular classes of ab initio electronic structure methods:

Hartree-Fock methods

  • Hartree-Fock (HF)
  • Restricted Open-shell Hartree-Fock (ROHF)
  • Unrestricted Hartree-Fock (UHF)

Post-Hartree-Fock methods

Multi-reference methods

Example: Is Si2H2 like acetylene (C2H2)?

  A series of ab initio studies of Si2H2 shows clearly the power of ab initio computational chemistry. They go back over 20 years, and most of the main conclusions were reached by 1995. The methods used were mostly Hartree-Fock energy hypersurface. The new isomer is a planar structure with one bridging hydrogen atom and one terminal hydrogen atom, cis to the bridging atom. Its energy is above the ground state but below that of the other isomers.[8] Similar results were later obtained for Ge2H2.[9] More interestingly, similar results were obtained for Al2H2[10] (and then Ga2H2)[11] which has two electrons less than the Group 14 molecules. The only difference is that the four-membered ring ground state is planar and not bent. The cis-mono-bridged and vinylidene-like isomers are present. Experimental work on these molecules is not easy, but matrix isolation spectroscopy of the products of the reaction of hydrogen atoms and silicon and aluminium surfaces has found the ground state ring structures and the cis-mono-bridged structures for Si2H2 and Al2H2. Theoretical predictions of the vibrational frequencies were crucial in understanding the experimental observations of the spectra of a mixture of compounds. This may appear to be an obscure area of chemistry, but the differences between carbon and silicon chemistry is always a lively question, as are the differences between group 13 and group 14 (mainly the B and C differences). The silicon and germanium compounds were the subject of a Journal of Chemical Education article.[12]

Accuracy and scaling

Ab initio electronic structure methods have the advantage that they can be made to converge to the exact solution, when all approximations are sufficiently small in magnitude. In particular configuration interaction where all possible configurations are included (called "Full CI") tends to the exact non-relativistic solution of the Schrödinger equation. The convergence, however, is usually not monotonic, and sometimes the smallest calculation gives the best result for some properties. The downside of ab initio methods is their computational cost. They often take enormous amounts of computer time, memory, and disk space. The HF method scales nominally as N4 (N being the number of basis functions) – i.e. a calculation twice as big takes 16 times as long to complete. However in practice it can scale closer to N³ as the program can identify zero and extremely small integrals and neglect them. Correlated calculations scale even less favorably - MP2 as N5; MP4 as N6 and coupled cluster as N7. DFT methods scale in a similar manner to Hartree-Fock but with a larger proportionality term. Thus DFT calculations are always more expensive than an equivalent Hartree-Fock calculation.

Linear scaling approaches

The problem of computational expense can be alleviated through simplification schemes.[13] In the density fitting scheme, the four-index integrals used to describe the interaction between electron pairs are reduced to simpler two- or three-index integrals, by treating the charge densities they contain in a simplified way. This reduces the scaling with respect to basis set size. Methods employing this scheme are denoted by the prefix "df-", for example the density fitting biologically-sized molecules. Methods employing this scheme are denoted by the prefix "L", e.g. LMP2. Both schemes can be employed together, as in the recently developed df-LMP2 and df-LCCSD(T0) methods. In fact, df-LMP2 calculations are faster than df-Hartree-Fock calculations and thus are feasible in nearly all situations in which also DFT is.

Valence bond methods

Valence bond (VB) methods are generally ab initio although some semi-empirical versions have been proposed. Current VB approaches are[1]:-

Quantum Monte Carlo methods

A method that avoids making the variational overestimation of HF in the first place is Monte Carlo integration. Such calculations can be very time-consuming, but they are probably the most accurate methods known today.

See also

References

  1. ^ a b Levine, Ira N. (1991). Quantum Chemistry. Englewood Cliffs, New jersey: Prentice Hall, 455 - 544. ISBN 0-205-12770-3. 
  2. ^ History of Quantum Chemistry: Robert G. Parr
  3. ^ Parr, Robert G.; Craig D. P,. and Ross, I. G (1950). "Molecular Orbital Calculations of the Lower Excited Electronic Levels of Benzene, Configuration Interaction included". Journal of Chemical Physics 18: 1561 - 1563.
  4. ^ Cramer, Christopher J. (2002). Essentials of Computational Chemistry. Chichester: John Wiley & Sons, Ltd., 153 - 189. ISBN 0-471-48552-7. 
  5. ^ a b Cramer, Christopher J. (2002). Essentials of Computational Chemistry. Chichester: John Wiley & Sons, Ltd., 191 - 232. ISBN 0-471-48552-7. 
  6. ^ Jensen, Frank (2007). Introduction to Computational Chemistry. Chichester, England: John Wiley and Sons, 98 - 149. ISBN 0470011874. 
  7. ^ Colegrove, B. T.; Schaefer, Henry F. III (1990). "Disilyne (Si2H2) revisited". Journal of Physical Chemistry 94: 5593.
  8. ^ Grev, R. S.; Schaefer, Henry F. III (1992). "The remarkable monobridged structure of Si2H2". Journal of Chemical Physics 97: 7990.
  9. ^ Palágyi, Zoltán; Schaefer, Henry F. III, Kapuy, Ede (1993). "Ge2H2: A Molecule with a low-lying monobridged equilibrium geometry". Journal of the American Chemical Society 115: 6901 - 6903.
  10. ^ Stephens, J. C.; Bolton, E. E.,Schaefer, H. F. III, and Andrews, L. (1997). "Quantum mechanical frequencies and matrix assignments to Al2H2". Journal of Chemical Physics 107: 119 - 223.
  11. ^ Palágyi, Zoltán; Schaefer, Henry F. III, Kapuy, Ede (1993). "Ga2H2: planar dibridged, vinylidene-like, monobridged and trans equilibrium geometries". Chemical Physics Letters 203: 195 - 200.
  12. ^ DeLeeuw, B. J.; Grev, R. S. and Schaefer, Henry F. III (1992). "A comparison and contrast of selected saturated and unsaturated hydrides of group 14 elements". Journal of Chemical Education 69: 441.
  13. ^ Jensen, Frank (2007). Introduction to Computational Chemistry. Chichester, England: John Wiley and Sons, 80 - 81. ISBN 0470011874. 
 
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