Chemistry Net: Physical & Theoretical Chemistry

Physical & Theoretical Chemistry

Physical & Theoretical Chemistry















Theoretical chemistry is a diverse field of chemistry that uses physics, mathematics and computers to help us understand molecular behavior, to simulate molecular phenomena, and to predict the properties of new molecules. It is common to hear this discipline referred to as theoretical and computational chemistry.

The advent of computers and the development of software which is increasingly easy to use has revolutionized the approach toward understanding chemistry at a fundamental level and an increase is observed in the number of people interested in theoretical and particularly in computational chemistry.

The term computational chemistry is usually used when a mathematical method is sufficiently well developed that it can be automated for implementation on a computer. Computational chemistry / molecular modeling is therefore the science of representing molecular structures numerically and simulating their behavior with the equations of quantum and classical physics. Computational chemistry programs allow scientists to generate and present molecular data including geometries (bond lengths, bond angles), energies (activation energy, heat of formation), electronic properties (charges, ionization potential, electron affinity), spectroscopic properties (vibrational modes, chemical shifts) and bulk properties (volumes, surface areas, diffusion, viscosity). Over the past ten to twenty years, scientists have used computer models of new drugs to help define biological activity profiles, geometries and reactivities.

Theoretical chemistry may be broadly divided into electronic structure and chemical bonding, reaction dynamics, and statistical mechanics.


 Table I.1: Main sub-branches of Theoretical Chemistry


Chemical Bonding & Electronic Structure lies at the very core of Chemistry. It is what enables about one-hundred elements to form millions of chemical substances. Main sub-branches are: Lewis theory of bonding, valence bond theory, molecular orbital theory, covalent bond distance, computational chemistry, ab initio calculations, semi-empirical calculations, modern valence bond theory, generalized valence bond, quantum chemistry, quantum Monte Carlo, molecular modelling, molecular mechanics, cheminformatics.


Reaction dynamics is a field of chemistry, studying why chemical reactions occur in gases, in liquid, at interfaces and how to predict their behavior and how to control them. The main objectives of reaction dynamics are:

  • The microscopic foundation of chemical kinetics
  • State to state chemistry and chemistry in real time
  • Control of chemical reactions at the microscopic level

Main sub-branches are: Adiabatic, intermolecular, intramolecular reaction dynamics, information theory, kinematics, molecular dynamics.


Statistical mechanics sets out to explain the behavior of macroscopic systems by studying the statistical properties of their microscopic constituents. Applications of the techniques of statistical mechanics include:

  • Applications to physical systems such as solids, liquids and gases
  • Applications to colloids, interfaces, polymers and biopolymers.

Main sub-branches are: Quantum Statistics, Boltzmann average, partition functions, correlation functions, ensembles, pair distribution functions.



  1. P. Atkins, J de Paula,  “Physical Chemistry: Thermodynamics, Structure and Change”, 10th Edition, W. H. Freeman, 2014
  2. D. A. McQuarrie, J. D. Simon,“Physical Chemistry: A Molecular Approach”, 1st Edition, University Science Books, 1997
  3. K. J. Laidler, J.H. Meiser, B.C. Sanctuary, “Physical Chemistry”, 4th Edition, Brooks Cole, 2002
  4. J. Simons, "An Introduction to Theoretical Chemistry", 1st Edition, Cambridge University Press, 2003


  1. Heisenberg's uncertainty principle: Δх * Δр ≥ ħ/2

    The Heisenberg's uncertainty principle is correct, moreover, it is fundamental. If the uncertainty principle is incorrect, then all quantum mechanics is incorrect. Heisenberg's justified the ncertainty principle in order to save quantum mechanics. He understood that if it is possible to measure with every accuracy both the coordinate and momentum of a microparticle, then quantum mechanics will collapse, and therefore further justification was already a technical issue. It is the uncertainty principle that prohibits microparticles in quantum mechanics from having a trajectory. If the coordinates of the electron are measured at definite time intervals Δt, then their results do not lie on some smooth curve. On the contrary, the more accurately the measurements are made, the more "jumpy", chaotic the results will be.

    Heisenberg's formulated the uncertainty principle thus:

    if you are studying a body and you are able to determine the x-component of a pulse with an uncertainty Δp, then you can not simultaneously determine the coordinate x of the body with an accuracy greater than Δx = h / Δp.

    It should be immediately said that the Heisenberg uncertainty principle inevitably follows from the particle-wave nature of microparticles (there is a corpuscular-wave dualism is the principle of uncertainty, there is no corpuscle-wave dualism - there is no uncertainty principle, and in principle quantum mechanics, too).

    We also need to clearly understand that the Heisenberg's uncertainty principle practically prohibits predicting behavior (in the classical sense, since Newton was able to predict the position of the planets), for example, an electron in the future. This means that if the electron is in a state described by the most complete way possible in quantum mechanics, then its behavior at the following moments is fundamentally ambiguous.

    In the Copenhagen interpretation of quantum mechanics (N. Bohr and followers), the uncertainty principle is adopted at the elementary level, and it is in this interpretation that it is believed that this can not be predicted at all by any method. And it was this interpretation that Einstein questioned when he wrote to Max Born: "God does not play dice." To which Niels Bohr, answered: "Einstein, do not tell to God what to do." Einstein was convinced that this interpretation was erroneous.

    The position of Bohr and Einstein must be viewed as views from different angles of view on one phenomenon (problem), and in the end it may turn out that they are right together. This can be demonstrated by lottery. Despite the fact that theoretically the results of the lottery can be predicted uniquely by the laws of classical mechanics, knowing all the initial conditions (it is necessary only to determine all the forces and perturbations, and to make the necessary calculations), in practice the lottery results are always probabilistic, and only in theory they can be predicted (try win the jackpot :). Even in this simplest case, we will be "inaccessible" to all the initial data for calculations... Moreover, if you think about it, then our world is also probabilistic. It is deterministic only in theory, and practically, in everyday life, we can only predict, for example, tomorrow (or a second, or a year, or 10 years) with a certain probability (who can guarantee the event of tomorrow with 100% probability?). And what is interesting is that only after having lived it (by making a measurement), we can say what probability was realized. Quantum mechanics in action :).

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  2. The present work shows the inapplicability of the Pauli principle to chemical bond, and a new theoretical model of the chemical bond is proposed based on the Heisenberg uncertainty principle.

    See pp. 88 - 104 Review. Benzene on the Basis of the Three-Electron Bond. (The Pauli exclusion principle, Heisenberg's uncertainty principle and chemical bond).

    The Pauli exclusion principle and the chemical bond.

    The Pauli exclusion principle — this is the fundamental principle of quantum mechanics, which asserts that two or more identical fermions (particles with half-integral spin) can not simultaneously be in the same quantum state.

    Wolfgang Pauli, a Swiss theoretical physicist, formulated this principle in 1925 [1]. In chemistry exactly Pauli exclusion principle often considered as a ban on the existence of three-electron bonds with a multiplicity of 1.5, but it can be shown that Pauli exclusion principle does not prohibit the existence of three-electron bonds. To do this, analyze the Pauli exclusion principle in more detail.

    According to Pauli exclusion principle in a system consisting of identical fermions, two (or more) particles can not be in the same states [2]. The corresponding formulas of the wave functions and the determinant are given in the reference (this is a standard consideration of the fermion system), but we will concentrate our attention on the derivation: "... Of course, in this formulation, Pauli exclusion principle can only be applied to systems of weakly interacting particles, when one can speak (at least approximately on the states of individual particles) "[2]. That is, Pauli exclusion principle can only be applied to weakly interacting particles, when one can talk about the states of individual particles.

    But if we recall that any classical chemical bond is formed between two nuclei (this is a fundamental difference from atomic orbitals), which somehow "pull" the electrons one upon another, it is logical to assume that in the formation of a chemical bond, the electrons can no longer be regarded as weakly interacting particles . This assumption is confirmed by the earlier introduced notion of a chemical bond as a separate semi-virtual particle (natural component of the particle "parts" can not be weakly interacting).

    Representations of the chemical bond given in the chapter "The Principle of Heisenberg's Uncertainty and the Chemical Bond" categorically reject the statements about the chemical bond as a system of weakly interacting electrons. On the contrary, it follows from the above description that in the chemical bond, the electrons "lose" their individuality and "occupy" the entire chemical bond, that is, the electrons in the chemical bond "interact as much as possible", which directly indicates the inapplicability of the Pauli exclusion principle to the chemical bond. Moreover, the quantum-mechanical uncertainty in momentum and coordinate, in fact, strictly indicates that in the chemical bond, electrons are a system of "maximally" strongly interacting particles, and the whole chemical bond is a separate particle in which there is no place for the notion of an "individual" electron, its velocity, coordinate, energy, etc., description. This is fundamentally not true. The chemical bond is a separate particle, called us "semi-virtual particle", it is a composite particle that consists of individual electrons (strongly interacting), and spatially located between the nuclei...

    1. Pauli W. Uber den Zusammenhang des Abschlusses der Elektronengruppen in Atom mit der Komplexstruktur der Spektren, - Z. Phys., 1925, 31, 765-783.

    2. A.S. Davydov. Quantum mechanics. Second edition. Publishing house "Science". Moscow, 1973, p. 334.

  3. Heisenberg's uncertainty principle and chemical bond.

    See pp. 88-104 Review...

    For further analysis of chemical bond, let us consider the Compton wavelength of an electron:

    λc.е. = h/(me*c)= 2.4263 * 10^(-12) m

    ...It is more interesting to consider what happens to an electron in a region with linear dimensions smaller than the Compton wavelength of an electron. According to Heisenberg uncertainty in this area, we have a quantum mechanical uncertainty in the momentum of at least m*c and a quantum mechanical uncertainty in the energy of at least me*c^2 :

    Δp ≥ mе*c and ΔE ≥ me*c^2

    which is sufficient for the production of virtual electron-positron pairs. Therefore, in such a region the electron can no longer be regarded as a "point object", since it (an electron) spends part of its time in the state "electron + pair (positron + electron)". As a result of the above, an electron at distances smaller than the Compton length is a system with an infinite number of degrees of freedom and its interaction should be described within the framework of quantum field theory...

    Now we will try to use all the above-mentioned to describe the chemical bond using Einstein's theory of relativity and Heisenberg's uncertainty principle. To do this, let's make one assumption: suppose that the wavelength of an electron on a Bohr orbit (the hydrogen atom) is the same Compton wavelength of an electron, but in another frame of reference, and as a result there is a 137-times greater Compton wavelength (due to the effects of relativity theory)...

    λb./λc.е.= 137

    Since the De Broglie wavelength in a hydrogen atom (according to Bohr) is 137 times larger than the Compton wavelength of an electron, it is quite logical to assume that the energy interactions will be 137 times weaker (the longer the photon wavelength, the lower the frequency, and hence the energy ). We note that 1 / 137.036 is a fine structure constant, the fundamental physical constant characterizing the force of electromagnetic interaction was introduced into science in 1916 year by the German physicist Arnold Sommerfeld as a measure of relativistic corrections in describing atomic spectra within the framework of the model of the N. Bohr atom.

    To describe the chemical bond, we use the Heisenberg uncertainty principle:

    Δx * Δp ≥ ћ / 2

    Given the weakening of the energy interaction 137 times, the Heisenberg uncertainty principle can be written in the form:

    Δx* Δp ≥ (ћ * 137)/2

    According to the last equation, the quantum mechanical uncertainty in the momentum of an electron in a chemical bond must be at least me * c, and the quantum mechanical uncertainty in the energy is not less than me * c ^ 2, which should also be sufficient for the production of virtual electron-positron pairs.

    Therefore, in the field of chemical bonding, in this case, an electron can not be regarded as a "point object", since it (an electron) will spend part of its time in the state "electron + pair (positron + electron)", and therefore its interaction should be described in the framework of quantum field theory.

    This approach makes it possible to explain how, in the case of many-electron chemical bonds (two-electron, three-electron, etc.), repulsion between electrons is overcome: since the chemical bond is actually a "boiling mass" of electrons and positrons, virtual positrons "help" overcome the repulsion between electrons. This approach assumes that the chemical bond is in fact a closed spatial bag (a potential well in the energy sense), in which "boiling" of real electrons and also virtual positrons and electrons occurs, and the "volume" of this potential bag is actually a "volume" of chemical bond and also the spatial measure of the quantum-mechanical uncertainty in the position of the electron...