9.4.1. Basic concepts and methods of quantum chemistry.

The historical significance of quantum mechanics is also determined by the fact that it radically transformed the system of chemical knowledge, raised this system from the level of empirical and semi-empirical knowledge, which it had essentially been since the time of Lavoisier, to the theoretical level. Quantum mechanics led to the creation of quantum chemistry and thus acted as a theoretical basis for the modern chemical picture of the world.

As you know, the basic concepts and objects of chemistry are the atom and the molecule. Atom - the smallest particle of a chemical element, which is the carrier of its properties. A chemical element, in turn, can be defined as a type of atom, characterized by a certain set of properties and designated by a certain symbol. The combination of atoms with the help of chemical bonds form molecules. Molecules - the smallest particle of a substance that has its basic chemical properties.

Only slightly more than 100 types of atoms are known; as many as chemical elements. But there are more than 18 million molecules. Such a rich diversity is determined by two circumstances. Firstly, by the fact that almost all types of atoms, interacting with each other, are able to unite into molecules. And, secondly, the fact that molecules can contain a different number of atoms. So, the molecules of noble gases are monatomic, the molecules of such substances as hydrogen, nitrogen are diatomic, water is triatomic, etc. Molecules of the most complex substances - higher proteins and nucleic acids - are built from such a number of atoms, which is measured in hundreds of thousands (macromolecules). The atoms in a molecule are interconnected in a certain sequence and arranged in a certain way in space. It is also important that such sequences and spatial arrangements can be different for the same composition of atoms. Therefore, with a relatively small number of chemical elements, the number of different chemical substances is very large.

Quantum chemistry is a field of modern chemistry in which the principles and concepts of quantum mechanics and statistical physics are applied to the study of atoms, molecules, and other chemical entities and processes. The basic method of quantum chemistry is the application of the Schrödinger equation for atoms and molecules. In this case, all types of energy of the particles that make up the system are taken into account (kinetic, energy of interaction of atomic nuclei and electrons, energy of interaction with external fields). The solution of such an equation determines the values ​​of the wave functions ψ, gives knowledge of the total energy of the system and its states, their dependence on spatial coordinates, spin characteristics of particles, etc. All this makes it possible in principle to determine the quantitative characteristics of the system (atom, molecule, etc.). At the same time, the mathematical side here is quite complicated, so exact solutions are possible only for the simplest system - the hydrogen atom. For the theoretical description of more complex systems, approximate methods and laborious calculations are used. The use of computers made it possible to obtain calculations of atomic, molecular systems, systems of activated complexes, etc., with an accuracy quite sufficient for predicting their most important characteristics - spectra, geometric structure, physical and chemical properties. In recent decades, quantum approaches in chemistry have made it possible to solve even more complex problems, primarily related to the analysis of systems that change in time (during chemical reactions, decay, absorption and emission of light, etc.).

ChapterI.1.

Introduction to Quantum Chemistry Course

Quantum chemistry is a science that studies the nature of the chemical bond in molecules and solids. Unfortunately, the overwhelming majority of chemists are currently unaware of the paradoxical nature of the chemical bond.

First of all, the nature of the bonding, in many cases, which will be discussed below, of atoms into molecules and solids is not clear, since physics, as well as chemistry, in fact, does not single out any specific interactions responsible for chemical bonding. What's more, if you think rationally, atoms can't form more complex structures like molecules and solids! Indeed, if molecules and solids consist of negatively charged electrons and positively charged nuclei, then at first glance, any substances (as well as creatures, for example, you and me) cannot exist in principle: despite the fact that that nuclei and electrons are attracted to each other, all nuclei are positively charged, which means that they repel each other, which means they tend to fly apart as far as possible from each other, electrons should also behave similarly.

Thus, we see that the force of attraction between nuclei and electrons is opposed at once by two "black" forces of electrostatic repulsion of nuclei and electrons from each other. Thus, common sense denies the right of existence to molecular bodies of any complexity.

Now let's conduct a thought experiment: Imagine that we nailed three charges to this board with nails - two positive, at a distance 2a and one negative - just in the middle between them. Let us now write down the well-known Coulomb's law for this system:

Thus, we see that for such a simple system, including two positive charges and one negative, the forces of Coulomb attraction between them are eight times greater than the forces of Coulomb repulsion. This is the crudest idea of ​​the binding of nuclei and electrons in molecular systems.

In fact, as we shall see below, the nature of chemical bonding is much more complex. This is due to the fact that both nuclei and electrons are microparticles, for which the laws of behavior are much more complex than the laws of classical mechanics. First of all, electrons in atoms and molecules do not behave like particles, their behavior is somewhat similar to the behavior of a charged gas. As we saw from the above formulas, a system consisting of three point charges is unstable - it tends to stick together. Molecules do not behave this way due to the fact that the electron gas cannot be completely concentrated exactly in the middle between the nuclei, but is blurred over the entire volume of the molecule and, therefore, the entire system cannot stick together, as it should happen in the case of point charges. We will touch on other differences between the microcosm and the macrocosm later.

At present, quantum chemistry is the theoretical basis for all branches of chemistry - organic and inorganic, physical chemistry, various types of spectroscopy, etc. Quantum chemistry successfully solves many scientific problems - in conjunction with many types of spectroscopy, it is used to study the structure of matter, to study the mechanisms of chemical reactions, including those on the surface, to study biological and biologically active substances, the useful or lethal properties of which are often, if not to say - almost always associated with their atomic and electronic structure, the study of the structure of new highly promising materials, such as, for example, high-temperature superconductors, forms of elemental carbon, transition metal complexes, the dynamic properties of atoms and ions in various crystalline and molecular structures, and many, many more.

The result of the application of quantum chemistry methods is information on the densities of electronic states, the distribution of electron density, potential reaction surfaces and rearrangement barriers, the calculation of various spectroscopic quantities, such as vibrational spectra, electronic and X-ray spectra, optical spectra, parameters of nuclear and electronic magnetic resonance spectra.

At present, quantum chemistry is perhaps the cheapest, most accessible and universal method for studying the atomic and electronic structures of matter. True, it must be understood that humanity, nevertheless, cannot completely abandon expensive experimental methods for studying matter, since the results of quantum chemical research must be confirmed by key experiments.

It should be noted that, nevertheless, there is one significant difference between the experimental methods and the theoretical quantum-chemical method: If the methods of quantum chemistry and molecular mechanics can equally well investigate both real and hypothetical structures, then in the experiment it is possible to investigate only that that really exists. Thus, the calculation of the tetrahedran molecule can be carried out as easily as the similar calculation of the butane molecule, while tetrahedran cannot be experimentally studied, since it has not yet been obtained in its pure form (only one of its derivatives is known - tetra-tert-butyl).

Nevertheless, it is necessary to note a number of brilliant theoretical predictions of quantum chemists in recent years - the work of Bochvar and Halpern, who theoretically predicted fullerene and calculated its electronic structure, Kornilov, who predicted nanotubes. These structures were discovered experimentally twenty years later, first from the ultraviolet spectra of interstellar gas, and then synthesized in the laboratory. In 1996, Kretschmer and Smalley were awarded the Nobel Prize in Chemistry for this work.

However, the Nobel Prizes were also awarded to other quantum chemists - Polling - for the theory of hybridization and Hoffmann - for the theory of upper filled and lower vacant orbitals. These beautiful and extremely important views for chemists will be considered in detail later.

At present, the theoretical models and methods of quantum chemistry, in comparison with the 50-70 years, when the above works were made, have become much more complicated. At present, modern quantum-chemical programs based on modern elemental base make it possible to calculate unique objects, such as proteins, forms of elemental carbon, including hundreds and thousands of atoms, molecules and solids, which include atoms of transition elements, lanthanides and actinides.

Nevertheless, the methods of quantum chemistry are rapidly becoming cheaper. This is due, first of all, to the progress of the element base of computer technology. Compare - modern synchrotrons - sources of electrons, protons, X-ray and ultraviolet synchrotron radiation cost several billion dollars apiece, while mass computers - several thousand dollars, workstations - tens of thousands, and, in extreme cases, large supercomputers - up to a million dollars.

At present, however, the overwhelming majority of calculations are aimed at obtaining additional information about already known and actually existing objects. But even taking into account this circumstance, the information content of theoretical methods is much higher! Is it possible to obtain an equilibrium atomic structure, dipole moment, heat of formation, ionization potentials, charge distribution, bond orders, spin density, study the spectroscopic characteristics of a substance in one experiment? Of course, there is a certain limitation on the reliability of the results obtained, however, the limitations of quantum chemistry methods are known, which in many cases makes it possible to realistically assess their accuracy and adequacy. In a number of cases, the reliability of the obtained quantum-chemical data is even higher than that of the experimental ones. So, the experimental determination of the heat of formation of a polycyclic alkane is a long, expensive, complex and multi-stage procedure, while the calculation will take several seconds on a cheap computer, and the accuracy will be even higher than in the experiment!

However, it is clear that this is a rare case. In the vast majority of cases, the quality of the results is largely determined by the adequacy of the chosen model. So, as an example, we can cite the study of the potential curve of formation/dissociation of the hydrogen molecule.

The first curve is obtained when a singlet is chosen as the wave function of the system, i.e. when the electron spins are antiparallel. As we can see, this wave function describes the experimental curve well only in the region of its minimum. The second potential curve corresponds to the triplet wave function (the spins are parallel). As we see, it describes well only the dissociation limit with actually non-interacting hydrogen atoms. As we can see, the real system must be investigated using the wave function built from a singlet and a triplet.

From the point of view of a chemist, the presented reaction is unique - the recombination of atomic hydrogen on the surface of iron is the "hottest" chemical reaction, during which ten thousand degrees can be reached!

As mentioned above, quantum chemistry is based on the laws of quantum mechanics, which describes the behavior of microparticles. The nature of the microcosm is essentially different from the nature of the macrocosm. Mankind began to realize this at the end of the past - the beginning of this century. It was at this time that the “non-classical” (i.e., not ancient Greek) doctrine of atomism began to develop, the structure of some molecules and solids became known. The fundamental difference between metals, which have free electrons, and dielectrics, which do not have them, was revealed.

In turn, the charge of the electron, equal to -4.77 * 10 -23 CGSE, its mass - 9.1066 * 10 -28 g, the mass of the hydrogen atom - 1.6734 * 10 -24 g, and a number of other things became known.

Then it was assumed that micro-objects can be described by classical mechanics in combination with statistics. Thus, for example, the molecular-kinetic theory of heat was created, which well described a number of observed phenomena.

Unlike matter, light was represented as a specific matter, continuously distributed in a certain region of space. Experiments on the diffraction of light revealed its wave properties, and Maxwell's electromagnetic theory revealed the unity of the nature of light, radio waves and X-rays. At that time, it was believed that all changes observed both in matter and in radiation are continuous - particle energies, trajectories, all characteristics do not change abruptly, but continuously. The classical idea of ​​the interaction of light with matter was also built on the principle of continuity. The absorption of light was represented by the “sucking in” of the electromagnetic field by the substance, and the emission, respectively, by the “outflow”. It is known from experiments with macroscopic bodies that an unevenly moving charged body emits electromagnetic waves, gradually losing energy.

However, a number of incomprehensible effects were soon discovered that could in no way be explained from the point of view of classical mechanics and electrodynamics. Thus, the behavior of the heat capacity of crystals at low temperatures turned out to be unclear, it was not clear why free electrons do not contribute to the heat capacity of metals, and finally, a sharp discrepancy was established between the experimental and theoretical patterns of the thermal emission spectrum of atoms (“ultraviolet” and “infrared” catastrophes).

To explain the "ultraviolet" catastrophe, Planck in 1900 proposed the hypothesis that light is emitted/absorbed in discrete portions - quanta. The energy of a quantum is related to its frequency according to the following formula:

Where h = 1.05*10 -27 erg*sec- Planck's constant, - cyclic frequency equal to 2 p n , and the linear frequencyn =1/T, Where T- oscillation period. An amazing fact - Planck until the end of his days could not believe in the revolutionary nature and effectiveness of his own hypothesis and considered it just a kind of curiosity.

But then it got even worse! Einstein, relying on Planck's ideas, suggested that light is not only absorbed and emitted in portions, but also propagates similarly in quanta. A quantum of light was called a photon, whose properties were studied in Vavilov's subtle experiments. Later, a model of a wave packet was proposed, which qualitatively explains the features of the behavior of photons, in particular, the photoelectric effect. Later, the Compton effect was discovered on the elastic scattering of electrons by photons

The conclusion from all these experiments was at first glance strange - a photon can behave both as a particle and as a wave.

Then similar results were obtained for electrons. So, Frank and Hertz, measuring the electric current in mercury vapor. The scheme of the experiment was as follows: A stream of electrons was passed through the mercury vapor, the speed of which and, consequently, the energy, gradually increased. Until some time, electrons, colliding with mercury atoms, almost do not lose their energy, that is, the impacts are elastic, so that the electric current corresponds to Ohm's law, approximately equal to the applied potential difference. When the electron energy becomes equal to 4.9 eV, the current drops sharply. This is because the electron loses energy by colliding with the mercury atom, exciting it. Thus, excite a mercury atom by transferring to it an energy of less than 4.9 eV. impossible. It turned out, however, that excitation does not occur even when the electron energy is greater than 4.9 eV.

The discreteness of the possible states of atoms is also indicated by the experiment of Stern and Gerlach, in which a beam of atoms with a magnetic moment is directed into an inhomogeneous magnetic field, which deviates the atom from a straight path in such a way that the angle of deviation depends on the orientation of the magnetic moment of the atom with respect to the field. From the point of view of classical physics, any orientation of the magnetic moment of an atom in the field is possible, therefore, when it hits the screen after passing through the magnetic field, a blurred spot should appear corresponding to the image of the gap that limits the flow at the beginning of the path. In reality, two sharp images of the slit are observed, i.e. the beam is divided into two (generally, several) parts. This can be explained by the fact that the magnetic moment acquires only strictly defined values, thus, the magnetic states of the atom are discrete.

However, the most striking fact, contrary to the laws of classical physics, was the very existence of atoms. In Rutherford's experiment, the nuclear model of the atom was first established: in the center is a very small nucleus (10 -13 cm.), Carrying a positive charge +ze , and around are z negatively charged electrons that fill the space of the atom (10 -8 cm).

The first contradiction of such a picture was the following: according to the theory of electricity, an immobile system of charges cannot be stable. If we assume that the electrons revolve around the nucleus, then, moving with acceleration, they must constantly emit electromagnetic radiation, lose energy and, in the end, fall onto the nucleus.

Another experience that contradicted the traditional picture of the world was the photoelectric effect - the threshold value of the ionization energy of matter, and it clearly indicates the corpuscular nature of the electrons themselves.

On the other hand, irrefutable evidence was obtained that the electron is a wave! These were experiments on the interference of electrons.

The spectra of atoms, which consist of individual lines corresponding to certain excitation frequencies, also turned out to be incomprehensible from the classical point of view. The spectra of hydrogen and hydrogen-like atoms are the simplest, the frequencies of which are described by the formula:

w = const z2 (1/nk 2 - 1/n m 2)

No classical model could explain such a shape of atomic spectra.

In 1913, Niels Bohr proposed the first non-classical model of the atom, the Bohr model of the atom. In this model, electrons were considered to be corpuscles, which at the same time had amazing properties that were defined in the postulates of the model:

1. Electrons can only be in strictly defined orbits - stationary orbits, while the atom does not absorb or emit light.

2. The transfer of electrons can only occur from one stationary orbit to another.

Many important consequences immediately followed from this model: quantum numbers were obtained in this way, with the help of which it was possible to describe the line spectra of atoms, the magnetic moments of atoms, and to estimate the radii of orbits and the speed of rotation of electrons on them. As we shall see later, quantum numbers, first obtained in the Bohr model, have a clear physical meaning.

However, the value of the moment of a univalent atom did not correspond to this picture. Therefore, Yulenbeck and Goudsmit suggested that in creating the magnetic moment of an atom, an essential role is played by the intrinsic moment of the electron, which arises due to the fact that the electron, being a charged ball, rotates around its axis, as a result of which it has mechanical and magnetic moments.

Of course, the Bohr model of the atom could not explain the structure of more complex, non-hydrogen-like atoms.Now this is done within the framework of quantum mechanics, solving the Schrödinger equation for systems of nuclei and electrons. However, nevertheless, often chemists successfully use another simple model approach based on the traditional picture of chemical bonding - molecular mechanics.

In this approach, it is considered that a chemical bond is a spring that can be either stretched or compressed, and a molecule is a set of atoms. Now there are many empirical ways to set the properties of a chemical bond - the so-called valence fields. In general terms, molecular mechanics seeks the minimum of energy using potential curves such as the Morse curve and Hooke's law. Such approaches also take into account the potentials of angular deformations, which, as a rule, are chosen in quadratic form. This approach includes both torsion functions and van der Waals type interactions. Using all these potential functions, the energy of the system is found and then the configuration with the lowest energy is sought, optimizing the problem in 3n-6 coordinates. In this approach, the structure of molecules and fragments of solids, the heat of formation, and the energy of steric stress are often obtained with good accuracy.

This and other approaches are currently implemented in a set of computer programs that we will become familiar with later.

Fundamentals of quantum chemistry.

1st idea of ​​quantum chemistry: a) matter discretely; b) energy quantized.

2nd idea of ​​quantum chemistry: corpuscular-wave dualism.

3rd idea of ​​quantum chemistry: probabilistic the nature of the laws of the microworld.

1. discreteness- the substance consists of individual microparticles. It is these particles that quantum chemistry studies. The idea of ​​energy quantization, based on the emission spectra of heated bodies, was put forward by Planck.

2. Wave-particle duality. Microparticles in the microworld have both the properties of a particle and the properties of a wave.

For the first time corpuscular-wave dualism was assumed for light (electromagnetic radiation). On the one hand, light is an electromagnetic wave and it is characterized by such properties as interference and diffraction, and on the other hand, when observing the phenomenon of the photoelectric effect, it was suggested that light is a stream of particles - photons. Even the mass of a photon has been measured. The photon energy is equal to mc 2 .

An electron also has a dual nature: on the one hand, it is a particle with a certain mass and speed, on the other hand, an electron can behave like a wave. For the flow of electrons, the properties of interference and diffraction were discovered.

Electronography- a method of studying the structure of matter, based on the wave properties of the electron flow.

The equation relating corpuscular and wave properties is the de Broglie equation.

E \u003d mc 2; E = hn = h; mc 2 = h ; where l is the wavelength, c is the speed of light, m ​​is the mass of the photon.

- de Broglie's equation for a light wave.

For an electron, the de Broglie equation has the form:

Where u is the speed of an electron. When u ® ¥, l ® 0, l = , n ® ¥.

3. Probabilistic the nature of the laws of the microworld.

In 1927, Heisenberg put forward the uncertainty principle; According to this principle, it is impossible to accurately determine the location of a particle and its momentum at a given time.

Where Dp x - momentum error along the X axis, Dx - coordinate error, - action quantum - constant.

Let Dp x ® 0, then Dx ® ¥, because , and vice versa, if Dx ® 0,

Note. This uncertainty is not related to the inaccuracy of the instruments, it is a consequence of the very nature of the electron.

Consequences of the uncertainty principle:

1. The movement of electrons in an atom is a movement without a trajectory, therefore the concept of “orbit”, put forward by Bohr, is not currently accepted, i.e. one can speak only with varying degrees of probability about finding an electron at a certain distance from the nucleus.

2. Based on the uncertainty principle, it is possible to explain why the electron does not fall on the nucleus.

The laws of motion of microparticles in quantum chemistry are expressed by the Schrödinger equation, which applied the wave function y to describe the motion of an electron in 3-dimensional space.

;

, where Ñ is the “nabla” operator, y is the wave function, E is the total energy, E p is the potential energy, (E - E p) is the kinetic energy.

y 2 dV - probability of finding an electron in an elementary volume dV.

The solution of the Schrödinger equation in the polar coordinate system gives 3 independent quantities, which are called quantum numbers electron: n, l, m e . Enter also m s - spin quantum number, which characterizes the motion of an electron around its axis.

Quantum numbers - space and energy characteristics of an electron. Electrons in an atom form an electron shell, which consists of electron layers, and electron layers consist of atomic orbitals.

An atomic orbital is the region where an electron is most likely to be found.

1).n is the main quantum number, it characterizes the size of the electron cloud, i.e., the distance from the nucleus to the densest part of this cloud. Electrons having clouds of the same size, regardless of shape, make up the electron layer of an atom's shell or energy level.

n takes the values ​​1;2;3;…;¥. n corresponds to the period number.

2). ℓ - orbital quantum number, it characterizes the shape of the electron cloud or the energy sublevel. ℓ takes values ​​from 0 to n - 1.

Electrons with orbital quantum numbers of 0.1, 2, and 3 are called s-electrons, p-electrons, d-electrons, and f-electrons, respectively. For a given value of the principal quantum number n, s-electrons have the lowest energy, followed by p-, d-, and f-electrons.

3). m ℓ - magnetic quantum number, it characterizes the orientation of an electron in the field created by other electrons.

The magnetic quantum number takes the values ​​2ℓ + 1 (- ℓ, … 0, …+ ℓ).

An electron cloud of a certain size (with a certain value of n), a certain shape (with a certain value of ℓ), and in a certain way oriented in space (with a certain value of m) is called an electron orbital and is depicted as a quantum cell.

4). m s - spin number.

The spin quantum number reflects the presence of an electron's own moment of motion. The projection of the intrinsic momentum of the electron's momentum onto the chosen direction is called the spin.

m s \u003d ± ½, i.e. electrons can rotate clockwise or counterclockwise. Two electrons with oppositely directed spins can be in one electron orbit.

/ At the forefront of science and technology

Hans Gustavovich Gelman. Pioneer of quantum chemistry

Quantum chemistry fought its way into the laboratory of experimental chemists with great difficulty. It was perceived very skeptically for a long time, since the calculations made on the basis of quantum chemical formulas sometimes did not agree with the results of classical calculations. This is easily explained - after all, the basis of all calculations in quantum mechanics - the Schrödinger equation - can be solved strictly only for systems consisting of one or two particles - even a hydrogen molecule is an unsolvable problem. Therefore, for quantum-chemical calculations, certain assumptions are used that simplify the task, but do not distort the overall picture. Over time, quantum chemical methods have become part of the daily practice of modern chemical research. The impetus was the computerization of research.

However, first things first.

The birth of quantum chemistry

Quantum chemistry originated in the mid-1920s. Its formation went in parallel with the development of quantum mechanics, which serves as the foundation for a promising young science. It is very curious that the main techniques and methods of quantum chemistry implemented in the algorithms of such modern computer programs were developed in a very short period of time - about 10 years. Such a sharp rise is explained by the unique combination of the following circumstances.

The further chemists progressed in studying the structure of matter, the more questions they had. Why do only diatomic molecules form from hydrogen atoms? Why is the H2O molecule shaped like a triangle, while in CO2 all three atoms lie on the same straight line? Why is carbon-based diamond an insulator and graphite a conductor? Such a list can be continued indefinitely, but these questions relate to the properties of already known substances, and the main task of chemistry is to obtain new compounds with predetermined properties that a person needs.

In solving all these problems, an important role is played by a relatively young science - quantum chemistry, which is not just another branch of chemistry (along with inorganic, organic, colloidal and others). It serves as a theoretical foundation for them, and its essence lies in the application of quantum mechanics to determine both the structure of atoms and molecules and their possible transformations.

In principle, the basic equation of quantum mechanics - the Schrödinger equation - can be written for a system consisting of many nuclei and electrons (that is, for atoms, molecules, ions, crystals), and its solution in the form of a wave function will completely determine its structure and behavior. The main obstacle is that even in the case of only two electrons, this equation cannot be solved exactly, and as the number of electrons increases, the difficulties increase manifold.

Therefore, from the very beginning, quantum chemists were faced with the need to introduce some kind of simplifications. They had to create computational methods, often based on lax rules, ingenuity and intuition of their authors. And the effectiveness of the method was judged by its ability to explain already known facts and predict new ones.

At that time there was no unified theory capable of explaining a wide range of chemical phenomena. And so, in cooperation with physics, chemistry began to turn into an exact science, adopting its mathematical apparatus.

Research in quantum chemistry began with the work of Werner Heisenberg in 1926. He carried out a quantum mechanical calculation of the helium atom, showing the possibility of its existence in two different states, introducing the concept of "quantum mechanical resonance".

In 1927, Walter Geitler and Fritz London began to develop a quantum mechanical theory of chemical bonding. They carried out the first approximate calculations of the hydrogen molecule.

In 1928, the future Nobel laureate Linus Pauling proposed the theory of resonance, and also put forward the idea of ​​hybridization of atomic orbitals. The theory of resonance, based on the principles of quantum mechanics, was very accurate in describing molecules that have simple chemical bonds (bonds formed by a single pair of electrons), but it was completely inappropriate for modeling the behavior of molecules with a more complex structure.

World recognition of quantum chemistry

The works of V. Heisenberg (calculation of the helium atom), as well as W. Heitler and F. London (calculation of the hydrogen molecule) served as the basis for the quantum theory of many-electron systems. Linus Pauling, together with John Clark Slater, developed a qualitative chemical theory - the electron pair method (better known as the valence bond method). The main idea of ​​this method is the assumption that during the formation of a molecule, the atoms largely retain their electronic configuration (electrons of the inner shells), and the binding forces between atoms are due to the exchange of electrons in the outer shells as a result of pairing of spins (moments of rotation). He also introduced a new quantitative concept of electronegativity in 1932. His work was awarded the Nobel Prize in 1954.

Around the same time, Douglas Hartree, developing the theory of many-electron structures, proposed the self-consistent field method and applied it to the calculation of atoms and atomic spectra. In this method, the state of an individual particle of a complex system (crystal, solution, molecule, etc.) is determined by the average field created by all other particles and depending on the state of each particle. Thus, the state of the system is consistent with the states of its parts (atoms, ions, electrons), which is the reason for the name of the method.

In 1930, Academician Vladimir Aleksandrovich Fok developed the Hartree method, raising the bar for accuracy of calculations.

From atomic orbit to molecular orbit

In the same period, one of the fundamental methods of quantum chemistry, the molecular orbital method, was developed.

The detailed mathematical calculations of quantum chemistry published at that time by Erwin Schrödinger, Max Born, and Werner Heisenberg contained formulas that could be used to describe the behavior of electrons in atoms. Nevertheless, the electronic structure of molecules was very difficult to analyze, and in 1927 R.S. Mulliken, working with F. Hund at the University of Göttingen in Germany, suggested that atoms combine into molecules in a process called chemical bonding, in such a way that their outer electrons are associated with the molecule as a whole. Therefore, the outer electrons of a molecule, which determine many of its important properties, are in molecular orbitals, not in the orbitals of individual atoms. R.S. Mulliken proved that molecular orbitals can be described using precise mathematical formulas, so that the physical and chemical properties of matter can be predicted in great detail. In 1966 R.S. Mulliken was awarded the Nobel Prize in Chemistry "for his fundamental work on chemical bonds and the electronic structure of molecules, carried out using the molecular orbital method." “The molecular orbital method means a completely new understanding of the nature of chemical bonds,” said Inga Fischer-Jalmar in her opening speech on behalf of the Royal Swedish Academy of Sciences. - Previous ideas came from the idea that the formation of chemical bonds depends on the complete interaction between atoms. The method of molecular orbitals, on the contrary, based on the provisions of quantum mechanics, repels from the interaction between all atomic nuclei and all electrons of the molecule. This method has made an extremely important contribution to our understanding of the qualitative aspect of the formation of chemical bonds and the electronic structure of molecules.”

Another gem of quantum chemistry was the theory of the crystal field, proposed by the German scientist Hans Bethe in 1929.

But none of the scientists listed above used the name "quantum chemistry" - for the first time it appeared as the title of a monograph by the great German-Soviet scientist Hans Gustavovich Gelman. Having emigrated from Germany in 1934, already in 1937 he wrote and published the fundamental monograph Quantum Chemistry. Gelman, independently of the Nobel laureate Richard Feynman, derived a number of formulas called the electrostatic Hellmann–Feynman theorem.

Gelman's student, the oldest quantum chemist in Russia, an employee of the Institute of Bioorganic Chemistry Mikhail Kovner (1910–2006) writes that “this theorem has become one of the main tools of quantum chemistry. But in addition to its purely applied significance, it was, one might say, also of philosophical interest. The fact is that Schrödinger, Heisenberg, Dirac paid the main attention to the concept of energy (its definition in classical and quantum mechanics), but they did not have the concept of force. However, from the point of view of the Bohr correspondence principle, there must be a certain connection between classical and quantum quantities. It is the Helman–Feynman theorem that introduces an analog of the concept of force into quantum mechanics and thus fills the indicated gap.”

Hans Gelman was one of the first to suggest using those same "assumptions" to simplify quantum chemical calculations.

One of the most significant difficulties in considering chemical objects from the point of view of quantum mechanics is that the solutions of the Schrödinger equation are very complex. Taking into account the fact that arithmometers were the most advanced computing tools at that time, it is not difficult to imagine what a difficult task it was to obtain an adequate solution: in the course of approximate calculations, errors commensurate with the desired value inevitably accumulated, and the work lost all meaning. Hans Gelman suggested using data taken from the experiment to solve the equations. Thus, it can be said without exaggeration that Hans Gelman was the first to develop a semi-empirical method for solving quantum chemical problems.

Gelman also introduced the concept of a "valence state", into which atoms pass when approaching, which put the theory of chemical reactions on a quantitative basis.

Computer era of quantum chemistry

Student taking an exam in quantum chemistry

After the Second World War began a powerful rise in computing technology. Despite the fact that the computers of the late 40s and early 50s were very cumbersome and slow (in terms of “electronic power” the modern cell phone surpasses all computing facilities taken together at the beginning of the 50s), they had one remarkable feature. (as, indeed, with modern computers): they could perform the same type of operations with arrays of numerical data in volumes unthinkable for a person. This quality was the best suited for the implementation of numerical (approximate) calculations.

Already at that time, two trends began to stand out in quantum chemistry: semi-empirical methods and methods based only on a theoretical basis, without taking into account experimental data.

In semi-empirical methods, complex calculations of “interelectronic interaction integrals” that take up to 70 percent of computer time are replaced by constant values, or these integrals are simply reset to zero. This is called parametrization of integrals.

The quality of semi-empirical methods can be assessed according to two criteria. First, by how many integrals are parameterized. Secondly, according to the level of reliability of the experimental data that are used in the parameterization.

The development of semi-empirical methods took place over a period of 40 years (approximately from 1950 to 1990). It should be noted that semi-empirical methods made it possible at one time to advance in the study of the mechanisms of chemical reactions. With the advent of sufficiently powerful computers, they have become a powerful tool in the study of complex chemical systems.

The second group includes methods in accordance with which the calculation is carried out exclusively on a theoretical basis, that is, without introducing into the calculation scheme any parameters obtained experimentally. In the calculation, all quantities have a specific physical meaning. The advantage of these methods is high accuracy and versatility, but they are extremely complex, so their application has not been wide.

Model instead of sorting through options!

For many decades, chemistry remained a largely experimental science. New substances and new technologies were born in the course of numerous experiments based on the intuition of the researcher. And now modeling with the help of quantum chemical calculations opens up new horizons for chemists, when, perhaps, the chemical laboratory itself will become unnecessary. This applies primarily to the development of efficient and inexpensive catalysts, which are the basis of modern oil and gas chemical technologies.

Understanding the strict relationship between the molecular structure of a substance and its physicochemical properties, including catalytic activity, opens up approaches for the researcher to solve a number of practical problems. As is known, catalytic transformations of organic and inorganic substances underlie most chemical and technological processes. The volumes of production of the target product, the conditions of the process, its hardware design and the features of the technology as a whole directly depend on the catalysts. Often, even the economics of production is determined precisely by the cost of the catalyst and the cost of its maintenance.

In such a situation, one of the priority directions in the development of applied chemistry becomes the development of scientific foundations for the search for the most optimal catalysts for existing industrially important reactions, or, conversely, the selection of a reaction to an already developed catalyst, which results in the formation of one or another target product of the chemical industry with high yield and selectivity. Obviously, a researcher who has set himself such a task in one of its variants will be forced to consider the mechanisms of the elementary stages of chemical processes, as well as the properties and structure of reacting substances and catalysts at the microlevel. The apparatus of quantum chemistry can provide considerable assistance in such work.

Quantum-chemical calculations can confirm or disprove the existence of certain intermediates, since it is determined by the possibility or impossibility of the formation of the corresponding molecular orbitals. Thus, the generalized quantum-chemical principle explains, for example, why ethylene dimerization can proceed only in the presence of catalysts, but is practically impossible without them.

Reference

Intermediate (Latin intermedius - medium) - an intermediate substance with a short life, formed during a chemical reaction and then reacting further to the reaction products. Due to the fact that the intermediates react very quickly, their concentration in the reaction mixture is very low. Therefore, their formation is either theoretically postulated or detected using modern physicochemical methods of analysis.

The methods of quantum chemistry, implemented in computer software products, formed the basis of a new approach to the study of the properties of substances, for which it is not necessary to synthesize or isolate, or to purify from impurities, or to conduct physical and chemical studies to obtain data on the properties of a chemical compound. With this approach to the study of the chemical properties of a substance, even a chemical laboratory as such is not needed. Rapid advances in computer technology and the development of software have led to a scientific revolution in this field, and now it is possible to study unknown molecules, intermediate compounds, transition states during chemical reactions, and even chemical structures that have not yet been synthesized. The experience of carrying out such calculations shows that the results obtained using adequate methods can be trusted, and their experimental verification almost always confirms them.

This year, the Nobel Prize in Chemistry was awarded precisely for modeling complex chemical systems.

In the RN-TSIR laboratories, Rosneft scientists conduct research in the field of quantum chemical modeling. These studies relate to the analysis of chemical reactions on the surface of various promising catalysts.

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