Following an early suggestion by Dirac, contemporary quantum mechanics (QM) and measurement theory are used to stepwise construct a conceptual framework to chemistry. In QM arbitrary physical quantum states are represented by linear superpositions. Base sets and quantum states are clearly distinguished; the latter are sets of ordered complex numbers. The generator of time evolution \(\fancyscript{H}\) is shown to have besides the molecular hamiltonian H=H C+K N, the electron–phonon and spin–orbit operators.H is shown diagonal in a product base set formed with generalized electronic diabatic (GED) and nuclear wave functions; the latter represented in a plane wave base set and unique inertial frame; these functions form the GEDM base set. Chemical species are assigned to particular GED base functions and a chemical quantum state is given as a linear superposition in the GEDM base set. Thus, given a fixed number of electrons and nuclei, the GEDM base set includes all electronuclear quantum states from clusters, supermolecule, molecular aggregates, asymptotic states, and ionized states (continuum electron states) to all plasma states. Experimentally measurable quantum states are given by linear superpositions. A chemical process is sensed by amplitude changes involving different electronic states in the linear superposition; vibration states intervene in excitation–relaxation processes; a time evolution of a global quantum 1-system is the feature. If sufficient time is allowed to an isolated system, with a given total energy E, unitary time evolution with \(\fancyscript{H}\) (but not H) ensures that the system will evolve from the initial state to get amplitudes different from zero for all energy conserving final states. Response towards external dynamic couplings, e.g. electromagnetic fields, is given by changes of amplitudes and expressed in correlation functions. For a quantum state, the amplitude at a given base function reflects the possibility for the system submitted to excitation sources to respond with its spectral signatures; if the experiment is done, and the amplitude is different from zero, then, there will be a response. Algorithms permitting to relate Hilbert space to real space events are discussed. A chemical compound (analyte) is identified to (i) a fixed electronic quantum state; (ii) linear nuclear base states superpositions; (iii) zero amplitude for all other electronic base states. To get this implies either the action of a chemist introducing constraints to bottle the analyte or an accidental change of external (to the box) conditions producing spontaneous separations.
Similar content being viewed by others
References
Schatz G.C., and Ratner M.A. (1993). Quantum Mechanics in Chemistry. Prentice Hall, Englewood Cliffs
Dirac P.A.M. (1929). Proc. Roy. Soc. (London) 123:714
Meyer H. (2002). Ann. Rev. Phys. Chem 53:141
Roos B.O. (1992). Lecture Notes in Quantum Chemistry. Springer-Verlag, Berlin
Dirac P.A.M. (1947). The Principles of Quantum Mechanics. Clarendon Press, Oxford
von Neumann J. (1955). Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton
Sakurai J.J. (1994). Modern Quantum Mechanics. Benjamin/Cummings, Menlo Park
Primas H. (1981). Chemistry, Quantum Mechanics and Reductionism. Springer-Verlag, Berlin
Fidder H., and Tapia O. (2004). Int. J. quantum chem. 97:670
Greiner W. (1987). Relativistic Quantum Mechanics. Wave Equations. Springer-Verlag, Berlin
Greiner W., and Müller B. (1994). Quantum Mechanics. Symmetries. Springer, Heidelberg
Wigner E. (1939). Ann. Math 40:149
Wigner E. (1959). Group Theory. Academic Press, New York
Ballentine L.E. (1998). Quantum Mechanics: A Modern Development. World Scientific, Singapore
Weinberg S. (1995). The Quantum Theory of Fields. Cambridge Univerty Press, New York
Cohen S., Judd D.L., and Rindell J.J.R. (1960). Phys. Rev 119:384
Pauncz R. (1979). Spin Eigenfunctions. Plenum Press, New York
Kato T. (1951). Trans. Am. Math. Soc 70:195
Zeh H.D. (1970). Found Phys 1:69
Zewail A.H. (1994). Femtochemistry. Ultrafast Dynamics of the Chemical Bond. World Scientific, Singapore
Isham C.J. (1995). Quantum Theory. Imperial College Press, London
Mukamel S. (1995). Nonlinear Optical Spectroscopy. Oxford University Press, New York
Cohen-Tannoudji C., Dupont-Roc J. and Grynberg G. (1989). Photons and Atoms Introduction to Quantum Electrodynamics Wiley & Son Inc., New York
Tapia O., and Braña P. (2002). J. Mol. Str. (Theochem) 580:9
Tapia O., Fidder H., Safont V.S., Oliva M. and Andres J. (2002). Int. J. Quantum Chem 88:154
Elbaz E. (1998). Quantum. The Quantum Theory of Particles, Fields, and Cosmology. Springer-Verlag, Berlin
Biedenharn L.C., and Van Dam H. (1965). Quantum Theory of Angular Momentum. Academic Press, New York
Condon E.U., and Shortley G.H. (1977). The Theory of Atomic Spectra. Cambridge University Press, London
Wolf S.A., Awschalom D.D., Buhrman R.A., Daughton J.M., von Molnár S., Roukes M.L., Chtchelkanova A.Y., and Treger D.M. (2001). Science 294:1488
Preskill J. (1999). Nature 402:357
Feynman R.P. (1961). Quantum Electrodynamics. Benjamin Inc., New York
Arteca G.A., and Tapia O. (2004). J. Math. Chem 35:1
Arteca G.A., and Tapia O. (2004). J. Math. Chem 35:159
Born M. and Oppenheimer J. (1927). Ann Physik. 84:457
Born M. and Huang K. (1954). Dynamical Theory of Crystal Lattices. Clarendon, Oxford
Herzberg G. and Teller E. (1933). Z Physik Chem B21:410
Longuet-Higgins H.C. (1961). Adv. Spectry 2:429
Martín F. (1999). J. Phys. B 32:R197
Tapia O. and Arteca G.A. (2003). Internet Electron. J. Mol. Des 2:454
Tapia O. (2004). Int. J. Quantum Chem. 97:637
Tapia O. and Arteca G.A. (2004). Adv Quantum Chem. 47:273
Kiselev A.A. (1970). J. Phys. B: Atom Molec. Phys 3:904
Jasper A.W., Zhu C., Nangia S. and Truhlar D.G. (2004). Faraday Discuss. 127:1
Byron F.W. Jr. and Fuller R.W. (1970). Mathematics of Classical and Quantum Physics. Dover Publications Inc., New York
Child M.S. (eds). (2004). Faraday Discussions 127:473
Goscinski O. and Mujica V. in: Density Matrices and Density Functionals, eds. R. Erdahl and Smith V.H., Jr, (Reidel, Dordrecht 1987) p. 597
Woolley R.G., and Sutcliffe B.T. (1977). Chem Phys Lett 45:393
Moffitt W. and Liehr A.D. (1957). Phys Rev 106:1195
Abragam A. and Bleaney B. (1986). Electron Paramagnetic Resonance of Transition Ions. Dover Publications Inc., New York
Ham F.S., and Slack G.A. (1971). Phys. Rev. B 4:777
Pople J.A., and Longuet-Higgins H.C. (1958). Mol Phys 1:372
Pople J.A. (1959). Mol. Phys 2:16
Yarkony D.R. (1998). Acc. Chem. Res 31:511
Loudon R. (1986). The Quantum Theory of Light. Clarendon Press, Oxford
Friedrich D.M., and McClain W.M. (1980). Ann Rev Phys Chem 31:559
Shapiro M. and Brumer P. (2000). Adv. Atom Mol. Opt. Phys 42:287
Courtade E., Anderlini M., Ciampini D., J.H. Müller, Morsch O., Arimondo E., Aymar M. and Robinson E.J. (2004). J. Phys. B: At. Mol. Opt. Phys. 37:967
Zewail A.H. (1988). Science 242:1645
Kreyszig E. (1978). Introductory Functional Analysis with Applications. John Wiley & Sons, New York
Thirring W.E. in: Schrödinger, Kilmister C.W., ed. (Cambridge University Press, Cambridge, 1987) p. 65.
Tapia O. (2004). Int. J. Quantum Chem. 99:373
Pauling L. (1935). Introduction to Quantum Mechanics. McGraw-Hill, New York
Kroto H.W. (1992). Molecular Rotation Spectra. Dover Publications Inc., New York
Aparicio F., Ireta J., Rojo A., Escobar L., Cedillo A., Galván M. (2003). J. Phys. Chem. B 107:1692
Tapia O., in: Quantum Systems in Chemistry and Physics, Vol II: Advanced Problems and Complex Systems, eds. A. Hernandez-Laguna, Maruani J., R. McWeeny and S. Wilson (Kluwer, Dordrecht, 2000) p. 193.
Tapia O., in: New Trends in Quantum Systems in Chemistry and Physics, eds. Maruani J., S. Wilson and Y. G. Smeyers (Kluwer, Dordrecht, 2000) p. 23
Tapia O. (2001). Adv. Quantum Chem. 40:103
Mead C.A., and Truhlar D.G. (1982). J. Chem. Phys 77:6090
Nakamura H. and Truhlar D.G. (2001). J. Chem. Phys 115:10353
Langhoff P.W., Hinde R.H., Boatz J.A., and Sheehy J.A. (2002). Chem Phys Lett 358:231
Bayfield J.E. (1999). Quantum Evolution. John Wiley & Sons, New York
Bartels L., Wang F. Möller D., Knoesel E. and Heinz T. (2004). Science 305:648
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tapia, O. Can chemistry be derived from quantum mechanics? Chemical dynamics and structure. J Math Chem 39, 637–669 (2006). https://doi.org/10.1007/s10910-005-9012-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-005-9012-6