Minimal Active Space: NOSCF and NOSI in Multistate Density Functional Theory

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Current methods in wave function theory often require expanding active space sizes to approximate wave functions.
• Multistate density functional theory (MSDFT) offers a framework for studying multiple electronic states simultaneously.
• Accurate calculation of molecular eigenstates, including excited states, is crucial for understanding chemical phenomena.

Purpose of the Study:

• To introduce a minimal active space (MAS) for MSDFT, providing an upper bound for calculating N-dimensional matrix density functions.
• To develop computational approaches for optimizing the MAS and calculating eigenstate energies and diabatic states.
• To stimulate the development of approximate multistate density functionals for both ground and excited states.

Main Methods:

• Introduction of a minimal active space (MAS) comprising no more than N^2 nonorthogonal Slater determinants for N eigenstates.
• Partitioning of the total Hamiltonian matrix functional into orbital-dependent and correlation matrix functional parts.
• Derivation of nonorthogonal multistate self-consistent-field (NOSCF) equations and introduction of a multistate correlation potential.
• Description of a nonorthogonal state interaction (NOSI) procedure for separate optimization of determinant functions.

Main Results:

• The MAS approach provides an upper bound for the N-dimensional matrix density function in MSDFT.
• The NOSCF and NOSI computational methods are presented for variational optimization and calculation of eigenstate energies.
• The developed methods are capable of constructing variational diabatic states when the universal correlation matrix functional is known.

Conclusions:

• The minimal active space (MAS) in MSDFT provides a computationally tractable and accurate method for determining molecular eigenstates.
• The proposed NOSCF and NOSI methods offer practical pathways for implementing MSDFT calculations.
• This work is expected to foster advancements in approximate multistate density functionals for diverse chemical applications.