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# Aron Cohen

#### Dr Aron Cohen

## Interests and expertise (Subject groups)

## Grants awarded

#### Development and Application of Density Functional Theory

#### Development and Application of Density Functional Theory

#### Development and application of density functional theory

#### Development and application of density functional theory

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Research Fellow

**Scheme: **University Research Fellowship

**Organisation: **University of Cambridge

**Dates: **Oct 2013-Sep 2016

**Value: **£290,087.37

**Summary: **From the simplest molecules in the chemical universe such as hydrogen and water to more complicated systems such as enzymes and drug molecules to semiconductors and superconductors everything is made up of atoms consisting of nuclei with electrons. This complexity of these electrons is at the base and challenge of understanding chemistry and physics of materials. The basic equation for understanding the quantum behaviour of electrons is given by the Schrödinger equation from 1926. If we could solve this equation it would tell us all we wanted to know about chemistry however its solution is extremely complex as summarised by Paul Dirac in the following quote:
``The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved.''
This is due to the exponential scaling of the the problem and even today with the worlds largest supercomputers and massive advances in algorithms we can still only find the exact solution of this equation for a system with around 10 electrons, one water molecule. A different view of the problem came with the introduction of Density Functional Theory (DFT). In the 1960s Walter Kohn along with his coworkers established that to get the exact energy of the Schrödinger equation one does not need to go for a direct solution but instead can use a physical observable, the electron density. However the key of DFT is that although this established that it is possible, the exact way to use the density is unknown. All the unknown complexity and many-body quantum effects are placed into one term, the exchange-correlation functional. The massive computational challenge of a direct solution of the Schrödinger equation attacking the wavefunction of has been turned in to a true theoretical challenge of developing an exchange-correlation functional.

**Scheme: **University Research Fellowship

**Organisation: **University of Cambridge

**Dates: **Jan 2009-Sep 2013

**Value: **£465,516

**Summary: **From the simplest molecules in the chemical universe such as hydrogen and water to more complicated systems such as enzymes, drug molecules, semiconductors and superconductors everything is made up of atoms consisting of nuclei with electrons. The complexity of these electrons is the challenge of understanding chemistry and physics of materials. The basic equation for understanding the quantum behaviour of electrons is given by the Schrodinger equation from 1926. If we could solve this equation it would tell us all we wanted to know about chemistry however its solution is extremely complex as summarized by Paul Dirac in the following quote:
``The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved.''
This is due to the exponential scaling of the the problem and even today with the worlds largest supercomputers and massive advances in algorithms we can still only find the exact solution of this equation for a system with around 10 electrons, one water molecule. A different view of the problem came with the introduction of Density Functional Theory (DFT). In the 1960s Walter Kohn along with his coworkers established that to get the exact energy of the Schrodinger equation one does not need to go for a direct solution but instead can use a physical observable, the electron density. However the key of DFT is that although this established that it is possible, the exact way to use the density is unknown. All the unknown complexity and many-body quantum effects are placed into one term, the exchange-correlation functional. The massive computational challenge of a direct solution of the Schrodinger equation attacking the wavefunction of has been turned in to a true theoretical challenge of developing an exchange-correlation functional.

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