Molecular modeling

Three-dimensional representation of a molecule

Under molecular modeling ( English molecular modeling (AE) or molecular modeling (BE)) are techniques for computer-assisted modeling of chemical molecules summarized. The design of new molecules and their modeling is a branch of molecular modeling ( computer-aided molecular design , CAMD).

description

In addition to the spatial representation of the simplest to the most complex molecules, these techniques also enable the calculation of their physicochemical properties. In medicinal chemistry in particular, it is used to optimize structures for new active ingredients (homology modeling). In this area, molecular modeling is increasingly being supplemented by combinatorial chemistry ( Virtual Screening , QSAR , CoMFA , CoMSIA ).

Mechanistic (semi- empirical ) and statistical approaches ( molecular dynamics , Monte Carlo simulation ) are more suitable for very large molecules or interactions between a large number of molecules; quantum chemical calculation methods, on the other hand, are far more precise, but only for smaller and smaller molecules due to the higher computational effort medium size first choice. Molecular modeling benefits from the steadily growing computing power of modern computers.

Programs

• Ghemical open source methods and GAMESS frontend
• Jmol
• PyMOL
• RasMol
• BALL open source with integrated BALLView molecule viewing program
• Visual Molecular Dynamics

Molecular dynamics

• GROMOS forerunner of GROMACS
• GROMACS
• NAMD

Ab initio methods

• GAMESS
• GAUSSIAN

Potential hypersurface

The potential energy surface (PES) is a representation in which the potential energy and the structure of a molecule span a multi-dimensional space. The energy of a molecule is shown as a function of its nuclear coordinates.

Coordinate systems

The choice of a suitable coordinate system is important in molecular modeling. A general distinction is made between global and local coordinate systems. The global coordinate systems include e.g. B. the orthonormal Cartesian coordinates and the crystal coordinates . In contrast to Cartesian coordinates, the angles in crystal coordinates are not 90 °. The local coordinate systems are always related to certain atoms or the relationships of the atoms to one another (e.g. symmetry properties). a. to name the Z matrix or the normal coordinates of the molecular vibrations.

optimization

According to Roland W. Kunz, optimization is the finding of an advantageous state of a system, i.e. the search for a local minimum near a given starting point. In general, the term optimization is used to search for critical points close to the initial structure. Minima, maxima and saddle points of the potential hypersurface are called critical points.

Most optimization methods determine the closest critical point, but a multidimensional function can contain very many different critical points of the same type.

Optimizing general functions: Finding minima

The minimum with the lowest value is called the global minimum, while all others are local minima.

Steepest descent / gradient methods

The steepest descent method , also known as the gradient method , uses the differential properties of the objective function. The search direction is defined by a defined negative gradient (differential property of the hypersurface). The optimization takes place here in the direction of the negative gradient, which indicates the direction of the steepest descent from an initial value until no further improvement can be achieved.

Since the potential energy forms the PES as a function of the core coordinates, the derivatives of the core coordinate functions are particularly important for the critical points. Within the gradient method, a distinction is made between numerical and analytical gradients. In practice you should only work with methods for which an analytical gradient is available.

When running the gradient method, no information from previous search steps is used.

Methods

A main problem of molecular modeling is not the lack of a suitable method for calculating the molecular properties, but rather too many methods. Therefore, the choice of method for a particular problem should be made carefully.

Methods of density functional theory

The goal of density functional theory is to find a suitable (energy) functional of density. The possible functionals are limited to three dimensions, regardless of the size of the molecule.

The performance of various density functional theory (DFT) methods is similar to the Hartree-Fock (HF) results (see below).

B3LYP / 6-31G *

One of the most commonly used methods for geometry optimization is B3LYP / 6-31G * . In B3LYP (short for: Becke, three parameters, Lee-Yang-Parr) is an approximation for the exchange-correlation energy functional in density functional theory (DFT) B3LYP therefore available for the chosen method. The further designation 6-31G refers to the basic set used by John Pople . The general designation of the basic sets is X-YZG. The X stands for the number of primitive Gaussians ( primitive Gaussian functions ) that comprise each core atomic orbital basis function . Y and Z indicate that the valence orbitals are each composed of two basis functions. The first basis function consists of a linear combination of Y primitive Gaussian functions. The second basis function accordingly consists of a linear combination of Z primitive Gaussian functions. The use of linear combinations is necessary, since the primitive Gaussians show a different behavior than atomic orbitals in the vicinity of the nucleus. This error is minimized by the linear combination. In this case, the presence of two numbers after the hyphen implies that this base set is a split valence base set.

A 6-31G basis set thus describes the inner orbitals as a linear combination of six primitive Gaussian functions that are contracted into one. Valence orbitals are correspondingly described by two contracted Gaussian functions. One of the contracted Gaussian functions is a linear combination of three primitive Gaussian functions and the other is a linear combination with a primitive Gaussian function.

The asterisk in 6-31G * indicates a correction for the spatial dependence of the charge distribution in the molecule. This is done using so-called polarization functions.

Methods according to Hartree-Fock models

In contrast to density functional theory, the Hartree-Fock approximation expresses the many-particle wave function by a Slater determinant of the single-particle states (product states), which means that the Pauli principle is automatically taken into account. The aim is to find a suitable (energy) functional of the wave function, these wave functions are mostly high-dimensional, which results in an increased computational effort compared to DFT. A flaw in the Hartree-Fock product approach to be considered is the assumption that the total probability density is a simple product of the individual probability densities:

${\displaystyle \left|\Psi ^{\text{Hartree-Produkt}}({\vec {r_{1}}}{\vec {r_{2}}})\right|^{2}=\left|\Psi ({\vec {r_{1}}})\right|^{2}\cdot \left|\Psi ({\vec {r_{2}}})\right|^{2}}$

This is a physically questionable assumption, since electrons are treated uncorrelated (i.e. independently of one another). For a closer look, the interactions between the electrons must not be neglected. The electrons are also treated uncorrelated in the form of the Slater determinant .

For geometry optimization at Hartree-Fock level, a. The following basic sets are often used: STO-3G , 3-21G , 6-31G * or 6-31G ** , cc-pVDZ and cc-pVQZ .

Basic rates

The choice of the basic set used and the choice of method (HF, DFT ...) play an important role in molecular modeling. A basis theorem describes a series of basis functions that approximate the total electron wave function by linear combination of the basis functions. Today, the basic functions used are almost exclusively primitive Gaussian functions. This is mainly due to the lower computational effort when using Gaussian functions compared to other basic functions. If other basic functions are to be used, care must be taken to ensure that they exhibit behavior that corresponds to the physics of the problem; it should also be possible to calculate the selected basis function quickly.

A basis set is called minimal if it contains so many basis functions that all electrons of the molecule can be described and only whole sets of basis functions occur.

The basic sets used and the number of basic functions for ${\displaystyle {\ce {H2O}}}$

Base rate	Number of basic functions
3-21G	13
6-31G *	19th
cc-pVDZ	24
cc-pVQZ	115

The basic sets shown here are small, a typical DFT calculation has around 100,000 basic functions.

More terms in molecular modeling

• An adiabatic reaction is a molecular resection that occurs on the same Born-Oppenheimer hypersurface (BO hypersurface) so that one or more trajectories lie on the same BO hypersurface. In contrast, a diabatic reaction leads to a change in the BO hypersurface (e.g. from the ground state of the molecule to an excited state).
  • In general, diabatic reactions are not more difficult to calculate than adiabatic ones, but open shell systems with unpaired electrons can lead to an increased computational effort.

literature

• Roland W. Kunz: Molecular modeling for users. Application of force field and MO methods in organic chemistry . 2nd revised and expanded edition. Teubner, Stuttgart 1997, ISBN 3-519-13511-6 ( Teubner study books: chemistry ).

Individual evidence

1. ↑ ^{a b c d} Kunz, Roland W .: Molecular Modeling for Users: Application of Force Field and MO Methods in Organic Chemistry . 1st edition. Teubner, Stuttgart 1991, ISBN 3-519-03511-1 , pp. 24-35 .
2. ↑ Kunz, Roland W .: Molecular Modeling for Users: Application of Force Field and MO Methods in Organic Chemistry . 1st edition. Teubner, Stuttgart 1991, ISBN 3-519-03511-1 , pp. 35 .
3. ↑ Kunz, Roland W .: Molecular Modeling for Users: Application of Force Field and MO Methods in Organic Chemistry . 1st edition. Teubner, Stuttgart 1991, ISBN 3-519-03511-1 , pp. 50 .
4. ^ ^{A b c} Jensen, Frank: Introduction to computational chemistry . 2nd Edition. John Wiley & Sons, Chichester, England 2007, ISBN 978-0-470-01186-7 , pp. 383-420 .
5. ↑ Kunz, Roland W .: Molecular Modeling for Users: Application of Force Field and MO Methods in Organic Chemistry . 1st edition. Teubner, Stuttgart 1991, ISBN 3-519-03511-1 , pp. 56 .
6. ^ Jensen, Frank: Introduction to computational chemistry . 2nd Edition. John Wiley & Sons, Chichester, England 2007, ISBN 978-0-470-01186-7 , pp. 369 .
7. ^ Aron J. Cohen, Paula Mori-Sánchez, Weitao Yang: Challenges for Density Functional Theory . In: Chemical Reviews . tape 112 , no. 1 , December 22, 2011, ISSN  0009-2665 , p. 289-320 , doi : 10.1021 / cr200107z .
8. ↑ ^{a b} Basic Sets | Gaussian.com. Retrieved July 4, 2018 (American English). 
9. ^ Warren J. Hehre: Ab initio molecular orbital theory . In: Accounts of Chemical Research . tape 9 , no. November 11 , 1976, ISSN  0001-4842 , pp. 399-406 , doi : 10.1021 / ar50107a003 .
10. ^ Jensen, Frank: Introduction to computational chemistry . 2nd Edition. John Wiley & Sons, Chichester, England 2007, ISBN 978-0-470-01186-7 , pp. 360 .
11. ^ Jensen, Frank: Introduction to computational chemistry . 2nd Edition. John Wiley & Sons, Chichester, England 2007, ISBN 978-0-470-01186-7 , pp. 93 ff .