A new dipole-free sum-over-states expression for the second hyperpolarizability

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Nonlinear Optics

Background:

• Traditional sum-over-states (SOS) expressions for second hyperpolarizability rely on dipolar terms.
• Studying nondipolar systems (quadrupolar, octupolar, dodecapolar) with traditional methods presents challenges.
• Accurate calculation of molecular electronic properties is crucial in various scientific fields.

Purpose of the Study:

• To derive a new, equivalent sum-over-states (SOS) expression for second hyperpolarizability that eliminates dipolar terms.
• To provide a more suitable method for investigating the second hyperpolarizability of nondipolar molecular systems.
• To explore the potential of the new expression in developing simplified models for third-order susceptibility and as a computational convergence test.

Main Methods:

• Utilized generalized Thomas-Kuhn sum rules to reformulate the traditional SOS expression.
• Derived a novel dipole-free SOS expression for second hyperpolarizability.
• Applied and compared the new and traditional expressions to model systems (particle in a box, clipped harmonic oscillator) and for molecular orbital calculation convergence testing.

Main Results:

• A new, equivalent dipole-free SOS expression for second hyperpolarizability was successfully derived.
• The new expression demonstrates applicability to nondipolar systems.
• Both expressions yield identical fundamental limits for off-resonance second hyperpolarizability and exhibit the same frequency dependence in model systems.

Conclusions:

• The derived dipole-free SOS expression offers an alternative for calculating second hyperpolarizability, particularly for nondipolar molecules.
• The new expression, combined with the standard SOS approach, can facilitate a three-state model for third-order susceptibility dispersion.
• Comparing the two SOS expressions serves as a valuable convergence test for molecular orbital calculations of second hyperpolarizability.