Computational chemistry

Computational chemistry is a branch of chemistry that uses computational models to help study and solve chemical problems through the application of techniques and computational simulations of molecular systems. It uses theories, concepts and models of theoretical chemistry, based on physical treatments of matter from classical physics, quantum and statistical mechanics, incorporated into scientific software specially designed to calculate the structure and/or static and dynamic properties of molecules. and molecular aggregates in the gaseous state and in solution and in solid bodies. While their results complement the information that can be obtained in chemical experiments, they can, in other cases, predict chemical phenomena not observed to date, guiding the design of new experimental activity or replacing the absence of other empirical knowledge in problems where the experimental design has associated with a high economic cost and/or the empirical experiment is impracticable in current terms. Computational chemistry has been widely used for several decades in the design of new drugs and materials.

Examples of molecular properties studied in this field are the molecular structure at the atomic level (i.e. the position of the constituent atoms of the molecules in space, which define their molecular architecture) and electronic (i.e., the distribution of electronic charge in the molecule, which completes the definition of the molecular shape), absolute and relative energy (associated with the stability of the molecular system under study), electrical properties such as the electric dipole and higher order multipole moments, vibrational frequencies that allow studying the infrared spectrum of molecules and other spectral magnitudes and cross sections for collision with other particles. Additionally, it is possible to anticipate the interaction capacity of the molecules that determine molecular recognition (this can be described with classical methods or molecular mechanics, MM, and with quantum chemistry, QM methods), anticipate their general and specific chemical reactivity based on different indicators derived from the electronic structure (this requires QM quantum chemistry methods or mixed QM/MM methods) and also analyze reaction mechanisms.

The methods used cover static and dynamic situations. In all cases, there are associated computational requirements (computational cost of the study) that include computation time (which increases rapidly as the size of the studied system grows and/or more sophisticated models and methods are used, which allow us to describe the system with a greater degree of detail, something that is not always necessary, depending on the properties to be studied) and the information storage capacity of the hardware used. The system under study can be a single isolated molecule or a group of these in different states of aggregation or a solid body. In general, there is a tension between the size of the system under study and the degree of detail that can be achieved in it. All computational chemistry methods imply some degree of approximation in their formulation, which therefore implies strengths and weaknesses that must be known when selecting an appropriate method to study a system and its specific properties. The methods used to study the structure can be classified into a first major division into classical methods or molecular mechanics (MM) and quantum methods (QM). While the former only go as far as atomic detail, the latter go as far as electronic detail. Within quantum methods, we can distinguish the so-called ab initio methods, (at first principles) and semi-empirical methods, which introduce a greater number of approximations and parameters. (which can be derived from empirical information or from higher level calculations) in your formulation.

History

Based on discoveries and theory in the history of quantum mechanics, the first theoretical calculations in chemistry were those of Walter Heitler and Fritz London in 1927. Books that influenced the early days of computational quantum chemistry include: Introduction to Quantum Mechanics – with Applications to Chemistry by Linus Pauling and E. Bright Wilson, 1935; Quantum Chemistry by Henry Eyring, John Walter, and George Kimball, 1944; Elementary Wave Mechanics – with Applications to Quantum Chemistry by Walter Heitler, 1945 and later the book Valence by Charles Coulson, both of which served as the primary reference for chemists in later decades.

With the development of efficient computer technology, in the 40' solutions of elaborate wave equations for complex atomic systems begin to be an achievable goal. In the early 50's The first semi-empirical atomic orbital calculations were carried out. Theoretical chemists became a large number of users of the first digital computers. A very detailed description of that use in the UK is given by Smith and Sutcliffe. The first ab initio calculation was the Hartree-Fock method on diatomic molecules, which was carried out in 1956. at MIT using a set of basis functions of the Slater orbital type. For diatomic molecules, a systematic study using a minimal basis set and the first calculations of the largest basis sets were published by Ransil and Nesbet respectively in 1960. The first polyatomic calculations using Gaussian functions were carried out in the late 1950s. 39;. The first configuration interaction calculations were performed at Cambridge on the EDSAC computer in the 1950's. by S. Francis Boys and coworkers, using Gaussian functions. In 1971, when a bibliography of ab initio calculations was published, the largest molecules included were naphthalene and azulene. Summaries of many of the early developments in ab initio theory have been published by Schaefer.

In 1964, calculations of the Hückel method, which are a simple CLOA method for determining the energy of electrons of molecular orbits of π π {displaystyle pi } electrons in combined hydrocarbon systems, ranging from simple systems such as butadiene or benzene to the oval with 10 rings fused from 6 to 6 were generated in computers in Berkeley and Oxford. These empirical methods were replaced in the 60's by semi-empirical methods such as CNDO.

In the early 1970s, efficient ab initio computer programs such as ATMOL, Gaussian, IBMOL and POLYAYTOM began to be used to speed up ab initio computations. of molecular orbits. Of these programs only Gaussian, massively expanded, is still in use, being one of many used today. At the same time, molecular mechanics methods, such as MM2, were mainly developed by Norman Allinger.

One of the first times the term "computational chemistry" was mentioned can be found in the 1970 book Computers and Their Role in the Physical Sciences, written by Sidney Fernbach and Abraham Haskell Taub, where they say: "It appears, therefore, that the 'computational chemistry' may finally be more and more a reality'. During the 1970s, different methods began to be seen as part of a new emerging discipline of computational chemistry. of computational chemistry was published in 1980.

Concepts

The term "theoretical chemistry" can be defined as a mathematical description of chemistry or, more broadly, encompassing the entire conceptual scaffolding that runs through theories, concepts and models of chemistry (this is a matter of debate within the field of philosophy of chemistry), while the term "computational chemistry " It is usually used when a physical-mathematical method is sufficiently well developed for its application to molecular systems in a relatively automated way, implemented in a computational package. Although very few aspects of chemistry can be calculated exactly, these methodologies have fairly well-defined errors against existing experimental data, which allow the determination of molecular properties to within what is known as "chemical precision".;. However, almost any aspect of chemistry can be described qualitatively, semi-quantitatively, or even quantitatively using a computational scheme.

The molecules are made up of atomic nuclei and electrons, so that the theory and models of quantum mechanics can be applied to their description. Most often, computational chemicals plan and resolve the unrelativized Schrödinger equation, incorporating a posteriori relativistic corrections when this is indispensable for obtaining a correct system description. Theoretically, it is possible to solve exactly the equation of Schrödinger molecular, either in its time-dependent form or in its time-independent form, but in practice this is only possible for very small systems. Therefore, a wide variety of approximate methods have been developed to achieve the best balance between the feasibility of the calculation, its cost and the accuracy of the result obtained. Precision can always be improved by increasing the computational cost. Current computational chemistry allows to routinely calculate the properties of molecules containing hundreds of atoms (and corresponding electrons), with errors for energy that may be below 1 kcal/mol. In terms of structural aspects at the atomic level (molecular geometry) it is possible to predict link lengths with errors of a few picmeters (pm) and link angles with errors of the order 0.5or{displaystyle 0.5^{text{o}}}. Treatment of large molecules is computationally approachable by other approaches such as those based on the theory of functional density (DFT, English) density functional theory). There is some controversy in the field about whether theoretical methods are sufficiently accurate to describe complex chemical reactions, such as those involved in biochemical problems. Macromolecules can be studied through semi-empirical quantum methods or by methods of classical mechanics, also called molecular mechanic methods.(MM).

In theoretical chemistry, chemists, physicists, mathematicians, and computer scientists develop models, algorithms, and software to predict atomic and molecular properties and to find mechanisms of chemical reactions. Rather, computational chemists use existing software and methodologies to answer specific chemical questions.

There are two different types of challenges for computational chemistry:

• Studies aimed at guiding the laboratory synthesis of new substances with desired properties for a particular use or to help to understand more experimentally obtained information (e.g. the position and origin of the spectroscopic signals of a molecule).
• Studies aimed at predicting molecules to date totally unknown, properties that cannot be experimentally determined or explored reaction mechanisms that to date has not been easy to determine by experiments.

Thus, computational chemistry can help experimental chemists in their work or challenge them to find entirely new chemical objects.

Within computational chemistry, important areas stand out:

• The prediction of molecular structure at the atomic level by using classical methods or reaching electronic detail through the methods of quantum chemistry. This is done by locating stationary points (nut gradient) on the potential energy hypersurface corresponding to the system that is explored by varying the position of the atomic nuclei (procedure known as geometry optimization).
• Storage and data search in chemical entities.
• Determination of correlations between the chemical structure and properties of chemical and/or biological interest that allow to build quantitative predictive models (QSPR and QSAR).
• Computer modelling work to help efficient component synthesis.
• In silic design work of molecules capable of interacting specifically with other molecules (e.g. drug design).

Methods

The same molecular formula can represent a large number of isomers. Each isomer corresponds to a local minimum of the potential energy surface of the molecular system (resulting from considering the energy of the electrons plus the nuclear repulsion energy) as a function of the nuclear coordinates. A stationary point corresponds to a geometry such that the derivative of the energy with respect to all displacements of the nuclei is zero. A local minimum (of molecular potential energy) is a stationary point for which all nuclear displacements lead to an increase in energy, therefore they are associated with stable forms of the system. The lowest energy local minimum is called the global minimum and corresponds to the most stable isomer. When a change in a particular coordinate of the structure leads to a decrease in the total energy in both directions, the stationary point corresponds to a transition state and the coordinate for which it is a maximum is the reaction coordinate. This process of determining stationary points is called geometric optimization.

The determination of molecular structure via geometric optimization became routine only when efficient methods for calculating the first derivative of energy with respect to all atomic coordinates were available. The evaluation of the second derivatives allows the prediction of the vibrational frequencies assuming harmonic movements. The frequencies are related to the eigenvalues of the second derivative matrix (the Hessian matrix). If the eigenvalues are all positive, then the frequencies are all real and the stationary point is a local minimum. If an eigenvalue is negative (an imaginary frequency), the stationary point is a transition state. If more than one eigenvalue is negative, the stationary point is even more complex, and usually of little interest. When it is found, it is necessary to move the search outside of it, if looking for a local minimum and a transition state.

The total energy is determined by an approximate solution of the time-dependent Schrödinger equation, usually including non-relativistic terms, and making use of the Born-Oppenheimer approximation, which, based on the highest velocities of electrons compared to nuclei, allowing the separation of electronic and nuclear motions, simplifying the Schrödinger equation. This leads to the evaluation of the total energy as a sum of the electronic energy at the fixed positions of the nucleus plus the repulsion energy of the nucleus. A notable exception is provided by approaches called direct quantum chemistry, which treat electrons and nuclei equally. Density functional methods and semi-empirical methods are variants of the main theme. For each large system, the relative total energy can be compared using molecular mechanics. The ways to determine the total energy to predict the molecular structure are:

Ab initio quantum methods (HF SCF)

The programs used in computational chemistry are based on different methods of quantum chemistry that solve the Schrödinger equation associated with the molecular Hamiltonian. Methods that do not include any empirical or semi-empirical parameters in their equations (being derived directly from theoretical principles, without the inclusion of experimental data), are called ab initio methods. This does not imply that the solution is exactly one; they are all rough calculations of quantum mechanics. This means that an approximation is rigorously defined based on first principles (quantum theory) and its resolution is with a margin of error that is qualitatively known in advance. If iterative numerical methods have been employed, the goal is to iterate to the maximum precision that the machine can give (the best that is possible with a finite computer word size and with the mathematical and/or physical approximations made).

The simplest type of ab initio electronic structure calculation is the Hartree-Fock (HF) method, an extension of molecular orbital theory, in which the electron correlation, corresponding to the electron-electron repulsion is not taken into account instantaneously, but its average effect is included in the calculations. As the size of the set bases is increased, the energy and the wave function tend to a limit called the Hartree-Fock limit. Many types of calculations, known as post-Hartree-Fock methods, start with a Hartree-Fock calculation and then correct for electron-electron repulsion, also known as electron correlation. Since these methods are pushed to the limit, the delivered solution approaches the exact solution of the non-relativistic Schrödinger equation. In order to obtain full agreement with the experiments, it is necessary to include relativistic terms and the orbit-spin interaction, both of which are only relevant for heavy atoms. In all these approaches, in addition to the choice of method, it is necessary to choose a base set. This is a set of bases, usually centered around the different atoms in the molecule, which are used to expand the molecular orbits with the CLOA ansatz. Ab initio methods need to define a level of theory (the method) and a base set.

Within the one-electronic model, the Hartree-Fock wave function is described by a single electronic configuration or Slater determinant. Such a description is adequate to represent the ground state nature of molecules, generally close to equilibrium structures of systems. From this single reference, ab initio quantum-chemical methods add the effects of electronic correlation through procedures of interaction of configurations, perturbative or others.

There are many cases in which the HF uniconfigurational description is inadequate to represent the electronic structure of the system, or to study the evolution of the chemical system in different regions of the potential energy surfaces.

Typical situations are the study of the dissociation of the chemical bond, the calculation of the excited electronic state, the description of degenerate situations between states, biradical cases, complex transition states, electronic structure in transition metals, lanthanides or actinides, with many electron shells close in energy, etc. In those situations it is necessary to describe electronic states with more than one electronic configuration through multiconfigurational methods, the best known of which is the CASSCF method. In them both the coefficients of the configurations and the coefficients of the molecular orbitals are optimized simultaneously.

Once again, it will be necessary to include the rest of the electronic correlation from said multiconfigurational wave function. The use of uniconfigurational methods in situations requiring multiconfigurational descriptions generally leads to severely flawed results.

The total molecular energy can be evaluated as a function of the molecular geometry, in other words, the surface potential energy. This surface can be used for a dynamic reaction. Stationary points on the surface lead to the prediction of different isomers and the transition structures for conversion between isomers, but these can be determined without complete knowledge of the entire surface.

An especially important goal, called computational thermochemistry, is to calculate thermochemical quantities such as enthalpy of formation for chemical precision. Chemical precision is the precision required to make realistic chemical predictions and is generally considered to be 1 kcal/mol or 4 kJ/mol. To achieve such precision economically it is necessary to use a series of post Hartree-Fock methods and combine the results. These methods are called compound methods of quantum chemistry.

Quantum methods based on density functional theory

Density Functional Theory (DFT) methods are often considered for ab initio methods to determine molecular electronic structure, even though many of the More common functionals use parameters derived from empirical data, or from more complex calculations. Therefore, they could also be called semi-empirical methods, although it is more appropriate to treat them as a class by themselves. In DFT, the total energy is expressed in terms of the total density instead of the wave function. In these types of calculations, there is an approximate Hamiltonian and an approximate expression for the total electron density. DFT methods can be very accurate for a very low computational cost. The drawback is that, unlike ab initio methods, there is no systematic way to improve the methods by improving the form of the functional. Some methods combine the density functional exchange with the Hartree-Fock term exchange and are known as hybrid functional methods.

Semi-empirical quantum methods

Semi-empirical methods of quantum chemistry are based on the Hartree-Fock formalism, but make many approximations and derive some parameters from empirical data. They are very important in computational chemistry for dealing with large molecules where the full Hartree-Fock method without approximations is very expensive. The use of empirical parameters appears to allow the inclusion of some correlation effects in the methods.

Semi-empirical methods are often based on so-called empirical methods where the part of two Hamiltonian electrons is not explicitly included. For systems π π {displaystyle pi }-electron, the method used is that of Hückel, proposed by Erich Hückel, and for all validation electron systems, the Hückel extended method, proposed by Roald Hoffmann.

Classical methods of Molecular Mechanics

In many cases, large molecular systems can be satisfactorily modeled by completely avoiding the computations required by quantum mechanics. Molecular mechanics simulations, for example, use a single expression for the energy of a compound, such as a harmonic oscillator. All constants appearing in the equations should be obtained beforehand by experimental data or ab initio calculations.

The compound database used for parameterization (the resulting set of parameters and functions is called a force field) is crucial to the success of molecular mechanics calculations. A parameterized force field versus a specific class of molecules, eg proteins, is expected to have some relevance when describing other molecules of the same class.

These methods can be applied to proteins and other large biological molecules, and allow the study of approaches and interactions (coupling) of potential drug molecules (eg [1] and [2]).

Methods for solid bodies

Computational chemistry methods can be applied to solid state physics problems. The electronic structure of a crystal is generally described by a band structure, which defines the energy of the electronic orbitals for each point in the Brillouin zone. Ab initio and semi-empirical calculations provide orbital energy, therefore they can be applied to calculations of band structures. Since it is the time consumption to calculate the energy in a molecule, it is even more the consumption time to calculate it for the complete list of points in the Brillouin zone.

Chemical Dynamics

Once the electronic and nuclear variables are separated (under the Born-Oppenheimer representation) in the time-dependent approach, the packet of waves corresponding to the nuclear degrees of freedom is propagated by a time evolution operator associated with the time-dependent Schrödinger equation (for the complete molecular Hamiltonian). In the complementary part of the energy-dependent approach, the time-dependent Schrödinger equation is solved using the scattering theory. The potential representing the interatomic interactions is given by the surface potential energy. In general, the surface potential energies are linked by vibronic coupling terms.

The most popular methods for the propagation of wave packets associated with molecular geometry are:

• the technique of the division operator,
• the Hartree multi-configuration method depends on time and
• semi-classical methods.

Molecular dynamics (MD) examines (using Newton's laws) the behavior of time-dependent systems, including vibrations or Brownian motion, using a classical mechanical description. DM combined with density functional theory leads to the Car-Parrinello method.

Interpretation of molecular wave functions

The model atoms in molecules developed by Richard Bader, was developed in order to effectively unite the quantum mechanical picture of a molecule, as an electronic wave function to the older chemically more widely used models, such as the theory Lewis electron pair theory and valence bond theory. Bader has shown that these empirically useful models are connected to the topology of quantum charge density. This method is an improvement in use over Mulliken's population analysis.

Chemical software

There are many standalones used by computational chemists. Some include many methods covering a wide range of concepts, while others cover only a specific area, and still others even a single method. Details of these can be found at:

• Computational quantum chemistry programs.
• Programs of the theory of functional density.
• Molecular mechanics programs.
• Semi-empirical programs.
• Solid state systems programs with regular edge conditions.
• Programs for valence unions.

Computational Chemistry in Argentina

In Argentina, the High Performance Computing Center (CCAD) of the National University of Córdoba officially inaugurated the "Serafin" (from the Argentine cartoon "Inodoro Pereyra" by the author Roberto Fontanarrosa). Which will provide service to national investigations. One of his most important projects currently covers the research and development of drugs against Covid-19.

The project director, Marcelo Mariscal, declares that:

“There are projects that are very active and need that computing capacity because they launch billions of calculations to find some particular drug that has a specific activity against that virus.”

Marcelo Mariscal

On the other hand, for a decade a group of researchers in bioinformatics from the Faculty of Exact and Natural Sciences of the UBA has been working on the study of the genome of the bacterium that causes tuberculosis. Through bioinformatics techniques, combined with experiments, a key protein of the disease has been precisely identified and the characteristics of the compounds necessary to inhibit it have been detected.