# 7.3.2 TDDFT within a Reduced Single-Excitation Space

Much of chemistry and biology occurs in solution or on surfaces. The molecular environment can have a large effect on electronic structure and may change chemical behavior. Q-Chem is able to compute excited states within a local region of a system through performing the TDDFT (or CIS) calculation with a reduced single excitation subspace,Besley:2004a in which some of the amplitudes $\mathbf{x}$ in Eq. (7.15) are excluded. (This is implemented within the TDA, so $\mathbf{y}\equiv\mathbf{0}$.) This allows the excited states of a solute molecule to be studied with a large number of solvent molecules reducing the rapid rise in computational cost. The success of this approach relies on there being only weak mixing between the electronic excitations of interest and those omitted from the single excitation space. For systems in which there are strong hydrogen bonds between solute and solvent, it is advisable to include excitations associated with the neighboring solvent molecule(s) within the reduced excitation space.

The reduced single excitation space is constructed from excitations between a subset of occupied and virtual orbitals. These can be selected from an analysis based on Mulliken populations and molecular orbital coefficients. For this approach the atoms that constitute the solvent needs to be defined. Alternatively, the orbitals can be defined directly. Truncated excitation space within TDDFT/TDA is deployed by activating the TRNSS and TRTYPE keywords. The atoms or orbitals are specified within a $solute block. These approach is implemented within the TDA and has been used to study the excited states of formamide in solution,Besley:2004b CO on the Pt(111) surface,Besley:2005 and the tryptophan chromophore within proteins.Rogers:2005 Restricting excitation space by using TRNSS and$solute can be used to deploy core-valence separationCederbaum:1980 within TDDFT in calculations of core-excited states. Examples 7.3.7 and 7.3.7 illustrate this setup.