Abstract
Quantum chemical calculations rely on a few fortunate circumstances like usually small relativistic and negligible electrodynamic (QED) corrections and large nuclei-to-electron mass ratio. The fast progress in computer technology revolutionized theoretical chemistry and gave birth to computational chemistry. The computational quantum chemistry provides for experimentalists the ready-to-use tools of new kind offering powerful insight into molecular internal structure and dynamics. It is important for the computational chemistry to elaborate methods, which look at molecule in a multiscale way, which provide first of all its global and synthetic description such as shape and charge distribution, and compare this description with those for other molecules. Only such a picture can free researchers from seeing molecules as a series of case-by-case studies. Chemistry represents a science of analogies and similarities, and computational chemistry should provide tools for seeing this. This is especially useful for the supramolecular chemistry, which allow chemists to planify and study intermolecular interactions. Some of them, involving concave and convex moieties, represent molecular recognition, which assures a perfect fitting of the two molecular shapes. A sequence of molecular recognitions often leads to self-assembling and self-organization, typical to nanostructures.
This is a preview of subscription content, log in via an institution to check access.
Notes
- 1.
Computational chemistry contributed significantly to applied mathematics, because new methods had to be invented in order to treat the algebraic problems of the previously unknown scale (like for M of the order of billions); see, e.g., reference Roos (1972).
- 2.
That is, derived from the first principles of the (nonrelativistic) quantum mechanics
- 3.
It is difficult to define what computational chemistry is. Obviously, whatever involves calculations in chemistry might be treated as part of it. This, however, sounds like a pure banality. The same is with the idea that computational chemistry means chemistry, which uses computers. It is questionable whether this problem needs any solution at all. If yes, the author sticks to the opinion that computational chemistry means quantitative description of chemical phenomena at the molecular/atomic level.
- 4.
The speed as well as the capacity of computer’s memory increased about 100 billion times over the period of 40 years. This means that what now takes an hour of computations would require in 1960 about 10, 000 years of computing.
- 5.
In addition, we assume the computer is so clever that it automatically rejects those solutions, which are not square integrable or do not satisfy the requirements of symmetry for fermions and bosons. Thus, all nonphysical solutions are rejected.
- 6.
Bond patterns are the same for different conformers.
- 7.
For a dipeptide, one has something like ten energy minima, counting only the backbone conformations (and not counting the side-chain conformations for simplicity). For very small protein of, say, a hundred amino acids, the number of conformations is therefore of the order of 10100, a very large number exceeding the estimated number of atoms in the Universe.
- 8.
The low-frequency vibrations may be used as indicators to look at possible instabilities of the molecule, such as dissociation channels, formation of new bonds, etc. Moving all atoms, first according to a low-frequency normal mode vibration and continuing the atomic displacements according to the maximum gradient decrease, we may find the saddle point and then, sliding down, detect the products of a reaction channel.
- 9.
The integration of | Ψ |2 is over the coordinates (space and spin ones) of all the electrons except one (in our case the electron 1 with the coordinates r, σ 1) and in addition the summation over its spin coordinate (σ 1). As a result one obtains a function of the position of the electron 1 in space: ρ(r). The wave function Ψ is antisymmetric with respect to exchange of the coordinates of any two electrons, and, therefore, | Ψ |2 is symmetric with respect to such an exchange. Hence, the definition of ρ is independent of the label of the electron we do not integrate over. According to this definition, ρ represents nothing else but the density of the electron cloud carrying N electrons and is proportional to the probability density of finding an electron at position r.
- 10.
Strictly speaking the nuclear attractors do not represent critical points, because of the cusp condition (Kato 1957). This worry represents rather a pure theoretical problem, when, what is a common practice, one uses Gaussian atomic orbitals as the basis set.
- 11.
Although this is only after assuming a reasonable threshold as a criterion. This is a common situation in chemistry – strictly speaking there is no such thing as chemical bond in a polyatomic molecule.
References
Bader, R. F. W. (1994). Atoms in molecules. A quantum theory. Oxford: Clarendon Press.
Bloch, F. (1928). Uber die Quantenmechanik der Electronen in Kristallgittern. PhD Thesis. University of Leipzig.
Born, M., & Oppenheimer, J. R. (1927). Zur Quantentheorie der Molekeln, Annalen der Physik, 84, 457.
Boys, S. F., Cook, G. B., Reeves, C. M., & Shavitt, I. (1207). Automatic Fundamental Calculations of Molecular Structure. Nature, 178, 1956.
Brown, G. E., & Ravenhall, D. G. (1951). On the interaction of two electrons. Proceedings of the Royal Society A, 208, 552.
Cotton, F. A. (1990). Chemical applications of group theory (3rd ed.). New York: Wiley.
Dirac, P. A. M. (1928). The quantum theory of the electron. Proceedings of the Royal Society of London, A117, 610; (1928) ibid., A118, 351.
Feynman, R. P. (1939). Forces in Molecules. Physical Review, 56, 340.
Fock, V. (1930). Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems. Zeitschrift für Physik, 61, 126; (1930),,Selfconsistent field“ mit Austausch für Natrium. ibid., 62, 795.
Fukui, K., & Fujimoto, H. (1968). An MO-theoretical interpretation of nature of chemical reactions. I. Partitioning Analysis of Interaction Energy. Bulletin of the Chemical Society of Japan, 41, 1989.
Hartree, D. R. (1927). The wave mechanics of an atom with a non-coulomb central field. Part I. Theory and methods. Proceedings of the Cambridge Philosophical Society, 24, 89.
Heitler, W., & London, F. W. (1927). Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik. Zeitschrift für Physik, 44, 455.
Hellmann, H. (1937). Einführung in die Quantenchemie. Leipzig: Deuticke.
Hund, F. (1927). Zur Deutung der Molekelspektren. I- III. Zeitschrift für Physik, 40, 742; (1927) ibid., 42, 93; (1927) ibid., 43, 805.
Hylleraas, E. A. (1929). Neue Berechnung der Energie des Heliums im Grundzustande, sowie des tiefsten Terms von Ortho-Helium. Zeitschrift für Physik, 54, 347.
James, H. M., & Coolidge, A. S. (1933). The ground state of the hydrogen molecule. Journal of Chemical Physics, 1 825.
Jeziorski, B., & Kołos, W. (1977). On Symmetry Forcing in the Perturbation Theory of Weak Intermolecular Forces. International Journal of Quantum Chemistry, 12, 91.
Kato, T. (1957). On the eigenfunctions of many-particle systems in quantum mechanics. Communications on Pure and Applied Mathematics, 10, 151.
Kołos, W., & Roothaan, C. C. J. (1960). Accurate electronic wave functions for the H2 molecule. Reviews of Modern Physics, 32, 219.
Koliński, A., & Skolnick, J. (2004). Reduced models of proteins and their applications. Polymer, 45, 511.
Koopmaans, T. C. (1933/1934). Über die Zuordnung von Wellenfunktionen und Eigenwerten zu den Einzelnen Elektronen Eines Atoms. Physica, 1, 104.
Łach, G., Jeziorski, B., & Szalewicz, K. (2004). Radiative corrections to the polarizability of helium. Physical Review Letters, 92, 233001.
Lee, B., & Richards, F. M. (1971). The interpretation of protein structures. Estimation of static accessibility. Journal of Molecular Biology, 55, 379.
Pestka, G., Bylicki, M., & Karwowski, J. (2008). Dirac- Coulomb equation: Playing with artifacts In S. Wilson, P. J. Grout, J. Maruani, G. Delgado-Berrio, & P. Piecuch (Eds.), Frontiers in quantum systems in chemistry and physics (pp. 215–238). Heidelberg: Springer.
Piela, L. (2002). Deformation methods of global optimization in chemistry and physics. In P. M. Pardalos & H. E. Romeijn (Eds.), Handbook of global optimization (Vol. 2, pp. 461–488). Dordrecht/Boston: Kluwer Academic Publishers.
Piela, L. (2014). Ideas of quantum chemistry (2nd ed.). Amsterdam: Elsevier.
Roos, B. O. (1972). A new method for large-scale CI calculations. Chemical Physics Letters, 15, 153.
Schrödinger, E. (1926). Quantisierung als Eigenwertproblem.I-IV. Annalen der Physik, 79, 361; (1926) ibid., 79, 489; (1926) ibid., 80, 437; (1926) ibid., 81, 109.
Slater, J. (1930). Cohesion in monovalent metals. Physical Review, 35, 509.
Woodward, R. B., & Hoffmann, R. (1965). Selection rules for sigmatropic reactions. Journal of the American Chemical Society, 87, 395, 2511.
Acknowledgements
The author is very indebted to Professor Leszek Z. Stolarczyk, for joy to be with him, discussing all exciting aspects of chemistry, science, and beyond, a part of them included in the present paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media Dordrecht
About this entry
Cite this entry
Piela, L. (2015). Computational Chemistry: From the Hydrogen Molecule to Nanostructures. In: Leszczynski, J. (eds) Handbook of Computational Chemistry. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6169-8_1-2
Download citation
DOI: https://doi.org/10.1007/978-94-007-6169-8_1-2
Received:
Accepted:
Published:
Publisher Name: Springer, Dordrecht
Online ISBN: 978-94-007-6169-8
eBook Packages: Springer Reference Chemistry and Mat. ScienceReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics
Publish with us
Chapter history
-
Latest
Two Photon Absorption in Biological Molecules- Published:
- 14 January 2016
DOI: https://doi.org/10.1007/978-94-007-6169-8_47-1
-
Computational Chemistry: From the Hydrogen Molecule to Nanostructures
- Published:
- 12 January 2016
DOI: https://doi.org/10.1007/978-94-007-6169-8_1-2
-
Original
Theoretical Studies of Structural and Electronic Properties of Clusters- Published:
- 19 December 2015
DOI: https://doi.org/10.1007/978-94-007-6169-8_26-2