Crystal structure prediction
Encyclopedia
Crystal structure prediction (CSP) is the calculation of the crystal structure
s of solids from first principles. Reliable methods of predicting the crystal structure of a compound, based only on its molecular structure, has been a goal of the physical sciences since the 1950s. Computational methods employed include simulated annealing
, evolutionary algorithm
s, distributed multipole analysis
, basin hopping, data mining
, density functional theory
and molecular mechanics
.
, first set out in 1929 by Linus Pauling
. For metals and semiconductors one has different rules involving valence electron concentration. However, prediction and rationalization are rather different things. Most commonly, by crystal structure prediction one understands search for minimum-energy arrangement of the atoms (or, for molecular crystals, of the molecules) in space. The problem has two facets - combinatorial (the "search" problem, in practice most acute for inorganic crystals), and energetic ("ranking", most acute for molecular organic crystals).
For complex non-molecular crystals ("search problem"), major recent advances have been the Martonak version of metadynamics and the Oganov-Glass evolutionary algorithm USPEX. The latter is capable of solving the global optimization problem with up to a few hundred degrees of freedom, while the approach of metadynamics is to reduce all structural variables to a handful of "slow" collective variables (which often works).
s, where understanding polymorphism
is beneficial.
Since 2007, significant progress has been made in the CSP of small organic molecules, with several different methods proving effective. The most widely-discussed method first ranks the energies of all possible crystal structures using a customised MM
force field, and finishes by using a dispersion-corrected DFT
step to estimate the lattice energy
and stability of each short-listed candidate structure.
Crystal structure
In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
s of solids from first principles. Reliable methods of predicting the crystal structure of a compound, based only on its molecular structure, has been a goal of the physical sciences since the 1950s. Computational methods employed include simulated annealing
Simulated annealing
Simulated annealing is a generic probabilistic metaheuristic for the global optimization problem of locating a good approximation to the global optimum of a given function in a large search space. It is often used when the search space is discrete...
, evolutionary algorithm
Evolutionary algorithm
In artificial intelligence, an evolutionary algorithm is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm. An EA uses some mechanisms inspired by biological evolution: reproduction, mutation, recombination, and selection...
s, distributed multipole analysis
Distributed Multipole Analysis
Distributed multipole analysis is a compact and accurate way of describing the spatial distribution of electric charge within a molecule....
, basin hopping, data mining
Data mining
Data mining , a relatively young and interdisciplinary field of computer science is the process of discovering new patterns from large data sets involving methods at the intersection of artificial intelligence, machine learning, statistics and database systems...
, density functional theory
Density functional theory
Density functional theory is a quantum mechanical modelling method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular atoms, molecules, and the condensed phases. With this theory, the properties of a many-electron system can be determined by...
and molecular mechanics
Molecular mechanics
Molecular mechanics uses Newtonian mechanics to model molecular systems. The potential energy of all systems in molecular mechanics is calculated using force fields...
.
History
The crystal structures of simple ionic solids have long been rationalised in terms of Pauling's rulesPauling's rules
Pauling's rules are five rules published by Linus Pauling in 1929 for determining the crystal structures of complex ionic crystals.-First rule:...
, first set out in 1929 by Linus Pauling
Linus Pauling
Linus Carl Pauling was an American chemist, biochemist, peace activist, author, and educator. He was one of the most influential chemists in history and ranks among the most important scientists of the 20th century...
. For metals and semiconductors one has different rules involving valence electron concentration. However, prediction and rationalization are rather different things. Most commonly, by crystal structure prediction one understands search for minimum-energy arrangement of the atoms (or, for molecular crystals, of the molecules) in space. The problem has two facets - combinatorial (the "search" problem, in practice most acute for inorganic crystals), and energetic ("ranking", most acute for molecular organic crystals).
For complex non-molecular crystals ("search problem"), major recent advances have been the Martonak version of metadynamics and the Oganov-Glass evolutionary algorithm USPEX. The latter is capable of solving the global optimization problem with up to a few hundred degrees of freedom, while the approach of metadynamics is to reduce all structural variables to a handful of "slow" collective variables (which often works).
Molecular crystals
The crystal structures of molecular substances, particularly organic compounds, are very hard to predict and rank in stability because the factors that determine them, the intermolecular interactions, are weak and numerous, they act at long range and they have little directionality. Predicting organic crystal structures is important to academic and industrial science, particularly for pharmaceuticals and pigmentPigment
A pigment is a material that changes the color of reflected or transmitted light as the result of wavelength-selective absorption. This physical process differs from fluorescence, phosphorescence, and other forms of luminescence, in which a material emits light.Many materials selectively absorb...
s, where understanding polymorphism
Polymorphism (materials science)
Polymorphism in materials science is the ability of a solid material to exist in more than one form or crystal structure. Polymorphism can potentially be found in any crystalline material including polymers, minerals, and metals, and is related to allotropy, which refers to chemical elements...
is beneficial.
Since 2007, significant progress has been made in the CSP of small organic molecules, with several different methods proving effective. The most widely-discussed method first ranks the energies of all possible crystal structures using a customised MM
Molecular mechanics
Molecular mechanics uses Newtonian mechanics to model molecular systems. The potential energy of all systems in molecular mechanics is calculated using force fields...
force field, and finishes by using a dispersion-corrected DFT
Density functional theory
Density functional theory is a quantum mechanical modelling method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular atoms, molecules, and the condensed phases. With this theory, the properties of a many-electron system can be determined by...
step to estimate the lattice energy
Lattice energy
The lattice energy of an ionic solid is a measure of the strength of bonds in that ionic compound. It is usually defined as the enthalpy of formation of the ionic compound from gaseous ions and as such is invariably exothermic. Lattice energy may also be defined as the energy required to completely...
and stability of each short-listed candidate structure.