A Nonorthogonal State-Interaction Approach for Matrix Product State Wave Functions

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Matrix Product States (MPS) are powerful for describing quantum many-body systems.
• Calculations involving electronic states often require transformations between different molecular orbital bases.
• Nonorthogonal molecular orbital bases present unique challenges in quantum chemical calculations.

Purpose of the Study:

• To develop a novel state-interaction approach for MPS wave functions.
• To enable the calculation of transition and spin-orbit coupling matrix elements between electronic states.
• To adapt existing transformation techniques for MPS wave functions in nonorthogonal bases.

Main Methods:

• A state-interaction approach is formulated for MPS wave functions.
• MPS wave functions are transformed from a nonorthogonal to a biorthonormal molecular orbital basis.
• Nonunitary transformations, based on Malmqvist's proposal, are employed for the basis transformation.

Main Results:

• The developed approach facilitates the computation of matrix elements between arbitrary electronic states.
• The method is applicable when states share the same one-electron basis functions and active orbital space size.
• This work extends the applicability of MPS to systems with nonorthogonal molecular orbital bases.

Conclusions:

• The state-interaction approach provides a robust framework for MPS calculations in nonorthogonal bases.
• This method opens new avenues for accurate computation of electronic properties.
• The adaptation of biorthonormal transformations is key to the success of this approach for MPS.