Nonlinear response theory with relaxation: the first-order hyperpolarizability.

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Computational Chemistry

Background:

• The Ehrenfest theorem provides a foundation for describing the time evolution of quantum mechanical expectation values.
• Previous methods for calculating response functions could diverge in resonant regions, limiting their applicability.
• Phenomenological sum-over-states expressions offer a way to model optical properties but lack a rigorous theoretical basis in some contexts.

Purpose of the Study:

• To derive a novel equation of motion within wave-function theory that includes relaxation effects.
• To develop response functions that remain non-divergent across both off-resonant and resonant optical frequency regimes.
• To establish a theoretical framework for calculating electric dipole properties, including polarizabilities and hyperpolarizabilities.

Main Methods:

• Utilized the Ehrenfest theorem to formulate an equation of motion for wave-function theory.
• Incorporated relaxation effects into the theoretical framework.
• Derived response functions applicable to single- and multideterminant reference states.
• Applied the theory to electric dipole properties, linking it to established sum-over-states models.
• Developed a universal dispersion formula for the complex second-order response function.

Main Results:

• A new equation of motion was derived, accounting for relaxation and yielding non-divergent response functions.
• The derived response functions were shown to be equivalent to the Orr and Ward sum-over-states expressions for electric dipole properties.
• A universal dispersion formula for the complex second-order response function was successfully derived.
• Computational calculations were performed for lithium hydride and para-nitroaniline.

Conclusions:

• The developed wave-function theory approach provides a robust method for calculating optical properties, overcoming limitations of previous theories.
• The non-divergent response functions are applicable to a wide range of optical frequencies, including resonant regions.
• The theoretical framework offers a rigorous basis for understanding and predicting phenomena like the electro-optical Kerr effect and second-harmonic generation.