Complete basis set orbital representation for DMRG using multiwavelets

Wavelets and multiwavelets recently emerged in the multi-resolution analysis framework as a promising representation method of chemical systems [1, 2]. Unlike the traditional basis sets (Gaussian atomic orbitals and plane waves), they can provide a high precision and local description of molecular systems by adaptively refining the underlying multi-resolution representation.

In our work, we combine this framework with the Density Matrix Renormalization Group (DMRG) method. In particular, we self-consistently refine the molecular orbitals through constrained optimization (as inspired by [3]) and the calculation of the orbitals’ gradients. We test our methods on small molecules.

[1] R. J. Harrison, G. I. Fann, T. Yanai, Z. Gan, and G. Beylkin, Multiresolution quantum chemistry: Basic theory and initial applications, The Journal of Chemical Physics 121, 11587 (2004).

[2] B. Alpert, G. Beylkin, D. Gines, and L. Vozovoi, Adaptive solution of partial differential equations in multiwavelet bases, Journal of Computational Physics 182, 149 (2002).

[3] E. F. Valeev, R. J. Harrison, A. A. Holmes, C. C. Peterson, and D. A. Penchoff, Direct determination of optimal real-space orbitals for correlated electronic structure of molecules, Journal of Chemical Theory and Computation 19, 7230 (2023).