We present work exploring the validity of an energy gradient-based target function as the primary optimization target for excited states. This target function can be augmented with desired chemical properties, for example Mulliken charges or dipole moments for specificity and stability. This work aims to describe excited states that are particularly difficult for theory to find and describe due to large correlation effects and degeneracy, both of which can thwart most strategies.<br/>Our target function, known as the Generalized Variational Principle (GVP), is expressed as the square of the gradient of energy with additional terms for the specified chemical properties. We compare these target functions to existing variance minimization target functions. The GVP has previously been applied successfully in an analytical wavefunction method, but has not before been used in a statistical method like QMC. This is a natural next application for the GVP not only because QMC is highly accurate, but also because it is readily able to accommodate new target functions.<br/>QMC provides a platform for optimization of wavefunctions whose forms may not be analytically integrable and which have a large number of parameters. Thus, we can efficiently and explicitly describe dynamic correlation by including a Jastrow factor in our wavefunction ansatz, whereas other methods may rely on perturbation theory or large determinant expansions.<br/>The combination of these two tools is a new way to tackle challenging excited states. The GVP is a highly customizable target function, so it is an excellent complement to the highly flexible wavefunction used in QMC methodology. This method will act as a point of comparison to other existing target functions, and will provide an open-ended mechanism for handling the particularities of chemical systems with degenerate or otherwise challenging excited states.

State-specific targeting of excited states using an energy gradient-based target function in quantum Monte Carlo

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