Abstract
Conceiving a molecule as being composed of smaller molecular fragments, or subunits, is one of the pillars of the chemical and physical sciences and leads to productive methods in quantum chemistry. Using a fragmentation scheme, efficient algorithms can be proposed to address problems in the description of chemical bond formation and breaking. We present a formally exact time-dependent density functional theory for the electronic dynamics of molecular fragments with a variable number of electrons. This new formalism is an extension of previous work [Phys. Rev. Lett. 111, 023001 (2013)]. We also introduce a stable density-inversion method that is applicable to time-dependent and ground-state density functional theories and their extensions, including those discussed in this work.
Highlights
Simple and productive methods to investigate dynamical features of solids and molecules are offered by Time-dependent Density-functional Theory (TDDFT) [1]
The adiabatic local density approximation (ALDA) [4] to the TD XC potential is the simplest, useful approximation to study the dynamics of atoms and solids
We proved that the partition potential is uniquely determined by the TD electronic density of the system, and that it can be expressed as a density-functional
Summary
Simple and productive methods to investigate dynamical features of solids and molecules are offered by Time-dependent Density-functional Theory (TDDFT) [1]. The TD KS equations describe all of the electrons as part of a single entity, imposing a limit on the number of atoms that can be simulated in a reasonable amount of time This limit can be increased by dividing a molecule into fragments and performing inexpensive calculations on each individual fragment. Several approximated methods to investigate the electron dynamics of molecules as composed of fragments are available [5,6,7,8]. These methods typically assign a set of TD single-particle Schrodinger equations (not necessarily TD KS equations) to every fragment in the molecule. The formalism introduced in this paper serves as a theoretical foundation for the development of methods accounting for electronic excitations and electron-transfer processes, without sacrificing explicit use of the electronic density and computational efficiency
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