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Buldakov Mikhail A. - Interaction-induced Electric Properties of van der Waals Complexes

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Buldakov Mikhail A. Interaction-induced Electric Properties of van der Waals Complexes

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Introduction -- Theoretical Backgrounds of Interaction-induced Theory -- Interaction-Induced Dipole Moment -- Interaction-induced Polarizability -- Interaction-induced Hyperpolarizability -- Conclusion.;This brief explains the theory of the interaction-induced electrical properties of van der Waals complexes. It focuses on the interaction-induced electrical dipole moments, polarizabilities and first hyperpolarizabilities of atom-atomic, atom-molecular and molecular-molecular van der Waals complexes.

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The Author(s) 2017
Victor N. Cherepanov , Yulia N. Kalugina and Mikhail A. Buldakov Interaction-induced Electric Properties of van der Waals Complexes SpringerBriefs in Molecular Science 10.1007/978-3-319-49032-8_1
1. Introduction
Victor N. Cherepanov 1 , Yulia N. Kalugina 1 and Mikhail A. Buldakov 2
(1)
Department of Physics, Tomsk State University, Tomsk, Russia
(2)
Institute of Monitoring of Climatic and Ecological Systems of the Siberian Branch of the Russian Academy of Science, Tomsk, Russia
Victor N. Cherepanov
Email:
Van der Waals complexes. Well-known, that all atoms and molecules can interact together to form either a new molecule or a molecular cluster []. As a result, the van der Waals complexes are intensively studied in the last decades. And in the book some aspects of electrical properties of van der Waals complexes, which are not delighted enough in scientific literature, are discussed.
Classification of intermolecular interactions. In this small book the two-body interactions, which are the strongest, are only considered for study the electrical properties of van der Waals complexes. Particularities of many-body interactions may be found, for example, in []. Usually, the intermolecular interactions, the physical nature of which is electromagnetic one, are classified according to the distance R between interacting molecules (or atoms). They are the long-range interactions when the interaction energy has a form Interaction-induced Electric Properties of van der Waals Complexes - image 1 and the short-range interactions Interaction-induced Electric Properties of van der Waals Complexes - image 2 . The main long-range contributions to the energy and electric properties of interacting molecules are as follows: electrostatic (multipole-multipole), polarization (induction and dispersion), resonance, relativistic, magnetic and retardation. The short-range interactions include the direct electrostatic, exchange, repulsion, change transfer effects. Note that the long-range interactions can be well described in an analytical form using classical electrodynamics for some approximation of the perturbation theory. In turn, for short distances the methods of quantum chemistry are only effective. In part of analytical theory for large R this book will only focus on interaction-induced theory.
References
A. van der Avoid, P.E.S. Wormer, R. Moszynski, From intermolecular potentials to the spectra of van der Waals molecules, and vice versa. Chem. Rev. , 19311974 (1994) CrossRef
P.E.S. Wormer, A. van der Avoid, Internuclear potentials, internal motions, and spectra of van der Waals and hydrogen-bonded complexes. Chem. Rev. , 41094143 (2000) CrossRef
G. Chalasinski, M.M. Szczesniak, State of the art and challenges of the ab initio theory of intermolecular interactions. Chem. Rev. (1), 42274252 (2000) CrossRef
K. Mller-Dethlefs, P. Hobza, Noncovalent interactions: a challenge for experiment and theory. Chem. Rev. (11), 143167 (2000) CrossRef
B. Pullman (ed.), Molecular associations in biology (Academic Press, New York, 1968)
A.D. Buckingham, in Intermolecular Interaction: From Diatomic to Biopolymers , ed. by B. Pullman (Wiley, New York, 1978), pp. 168
S. Kielich, Molekularna Optyka Nieliniowa (Nonlinear Molecular Optics) (Naukowe, Warszawa-Poznan, 1977)
D. Pugh, Electric multipoles, polarizabilities and hyperpolarizabilities, in Chemical Modelling: Applications and Theory , vol. 1. The Royal Society of Chemistry, London, pp. 137 (2000)
W. Klemperer, V. Vaida, Molecular complexes in close and far away. Proc. Natl. Acad. Sci. U.S.A (PNAS) (28), 1058410588 (2006) CrossRef
G. Maroulis, Interaction-induced electric properties, in Chemical Modelling; Applications and Theory , vol. 9, ed. by M. Springborg. The Royal Society of Chemistry, London, pp. 2560 (2012)
J. Stone, The Theory of Intermolecular Forces (Clarendon Press, Oxford, 2002)
I.G. Kaplan, Intermolecular Interactions: Physical Picture, Computational Methods and Model Potentials (Wiley, Chichester, 2006) CrossRef
The Author(s) 2017
Victor N. Cherepanov , Yulia N. Kalugina and Mikhail A. Buldakov Interaction-induced Electric Properties of van der Waals Complexes SpringerBriefs in Molecular Science 10.1007/978-3-319-49032-8_2
2. Theoretical Backgrounds of Interaction-induced Theory
Victor N. Cherepanov 1 , Yulia N. Kalugina 1 and Mikhail A. Buldakov 2
(1)
Department of Physics, Tomsk State University, Tomsk, Russia
(2)
Institute of Monitoring of Climatic and Ecological Systems of the Siberian Branch of the Russian Academy of Science, Tomsk, Russia
Victor N. Cherepanov
Email:
At present, a lot of fine manuals and books may be recommended to study the theoretical backgrounds of interaction of atoms and molecules [], however, that is a special topic. In the short book it is not possible to describe in details the modern interaction-induced theory of molecules. Nevertheless, the general backgrounds of this theory are needed to be given to facilitate the reading of the book. In the next sections of this chapter some main definitions and formulas used in the book are given.
2.1 Multipole Electrical Moments
2.1.1 Coordinate System
In the book we will use for all molecular van der Waals complexes the Cartesian coordinate system (X, Y, Z) related to the complex (Fig. ). The origin of this coordinate system (OA) is usually placed on the molecule A. The vector R is directed from the point OA of the molecule A to any point OB of the molecule B. The relative orientation of molecules in a complex is determined by local coordinate systems ( x A, y A, z A) and ( x B, y B, z B) placed, accordingly, on the separate molecules A and B of the complex. The rotations of the molecules A and B are described by Euler angles, which determine the positions of the local coordinate systems ( x A, y A, z A) and ( x B, y B, z B) with respect to the complex coordinate system (X, Y, Z).
Fig 21 Coordinate system of a molecular complex 212 Cartesian - photo 3
Fig. 2.1
Coordinate system of a molecular complex
2.1.2 Cartesian Definition
In this case the multipole electrical moments of the rank n for any molecule B can be defined in the form (see, for example, [])
211 where the Greek indexes take the values X Y Z the number of Greek - photo 4
(2.1.1)
where the Greek indexes Picture 5 take the values X, Y, Z (the number of Greek indexes equals to n ), Picture 6 is any charge of the molecule B and Picture 7 is the radius-vector of the charge relatively to the origin of local coordinate system OB. The multipole electrical moments in the form (2.1.1) appear when the interaction Hamiltonian is expanded in the Taylor series about the point OB (see Sect. ) if we put in it n = 0, 1 and 2 (analogously, for larger values of n the highest multipole moments can be written in the explicit form):
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