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How does changing the geometry and size of a molecule affect its electronic excited states and optical properties, and how can this information be accurately calculated using quantum chemistry methods?

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Changing the geometry and size of a molecule can significantly affect its electronic excited states and optical properties. This is because the spatial arrangement of atoms and the overall size of the molecule influence the distribution of electrons and their energy levels, which in turn determine the molecule's electronic and optical behavior. Here are some ways in which these properties can be affected:1. Conjugation and delocalization: When a molecule has an extended system of alternating single and double bonds  conjugation , the electrons can delocalize over the entire system. This delocalization lowers the energy gap between the highest occupied molecular orbital  HOMO  and the lowest unoccupied molecular orbital  LUMO , leading to a redshift in the absorption and emission spectra.2. Steric effects: The geometry of a molecule can also affect the electronic excited states through steric effects. For example, when two chromophores are in close proximity, their electronic states can interact, leading to changes in the energy levels and optical properties.3. Size and polarizability: Larger molecules generally have more polarizable electron clouds, which can lead to stronger interactions with light and other electromagnetic radiation. This can result in increased absorption and scattering, as well as changes in the refractive index.To accurately calculate the electronic excited states and optical properties of molecules using quantum chemistry methods, several approaches can be employed:1. Time-Dependent Density Functional Theory  TD-DFT : TD-DFT is a widely used method for calculating the electronic excited states of molecules. It involves solving the time-dependent Kohn-Sham equations to obtain the excitation energies and transition dipole moments, which can then be used to compute the absorption and emission spectra.2. Configuration Interaction  CI  methods: CI methods involve the diagonalization of the electronic Hamiltonian in a basis of Slater determinants, which are constructed from molecular orbitals. By including higher excitations in the CI expansion, more accurate excited state energies and wavefunctions can be obtained.3. Coupled Cluster  CC  methods: CC methods are based on the exponential ansatz for the wavefunction, which provides a more accurate description of electron correlation effects. By including higher-order excitations in the CC expansion, accurate excited state energies and properties can be calculated.4. Quantum Monte Carlo  QMC  methods: QMC methods involve the stochastic sampling of the many-electron wavefunction, which can provide highly accurate excited state energies and properties for a wide range of molecular systems.In summary, changing the geometry and size of a molecule can significantly affect its electronic excited states and optical properties. Accurate calculations of these properties can be performed using various quantum chemistry methods, such as TD-DFT, CI, CC, and QMC. These methods can provide valuable insights into the relationship between molecular structure and electronic/optical behavior, which can be useful for designing new materials with desired properties.
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