arXiv subjects

Younghwan Kim

Publications and source records attributed to Younghwan Kim.

3 recordsLinked to original sources

arXiv2025

MC-PDFT Nuclear Gradients and L-PDFT Energies with Meta and Hybrid Meta On-Top Functionals for Ground- and Excited-State Geometry Optimization and Vertical Excitation Energies

Multiconfiguration pair-density functional theory (MC-PDFT) is a post-MCSCF multireference electronic-structure method that explicitly models strong electron correlation, and linearized pair-density functional theory (L-PDFT) is a recently developed multi-state extension that can accurately model conical intersections and locally-avoided crossings. Because MC-PDFT and L-PDFT rely on an on-top energy functional, their accuracy depends on the quality of the on-top functional used. Recent work has introduced translated meta-gradient-approximation (meta-GA) on-top functionals, and specifically the MC23 hybrid meta-GA on-top functional, which is the first on-top functional specifically optimized for MC-PDFT. Here we report the derivation and implementation of analytic nuclear gradients for MC-PDFT calculations using meta-GA and hybrid meta-GA on-top functionals. This development also enables analytic nuclear gradients for the widely successful tPBE0 hybrid on-top functional. Because MC-PDFT nuclear-gradient calculations involve the derivative of the on-top functional, this development also enables the use of meta-GA on-top functionals in L-PDFT single-point energy calculations. We use the new capabilities to test MC23 for ground-state geometries, excited-state geometries, and vertical excitation energies of s-trans-butadiene and benzophenone as well as to test MC23, another hybrid meta-GA, and seven other meta-GA on-top functionals for 441 vertical excitation energies. We find MC23 performs the best of all nine meta and hybrid meta functionals for vertical excitation energies and is comparable in accuracy to tPBE0 and to the NEVPT2 multireference wave function method. Additionally, we directly compare our MC-PDFT vertical excitation results to previously computed TD-DFT values and find that MC-PDFT outperforms even the best performing Kohn-Sham density functional.

physics.chem-ph↗

arXiv2020

Diameters of Graphs on Reduced Words of 12 and 21-Inflations

It is a classical result that any permutation in the symmetric group can be generated by a sequence of adjacent transpositions. The sequences of minimal length are called reduced words, and in this paper we study the graphs of these reduced words, with edges determined by relations in the underlying Coxeter group. Recently, the diameter has been calculated for the longest permutation $n\ldots 21$ by Reiner and Roichman as well as Assaf. In this paper we find inductive formulas for the diameter of the graphs of 12-inflations and many 21-inflations. These results extend to the associated graphs on commutation and long braid classes. Also, these results give a recursive formula for the diameter of the longest permutation, which matches that of Reiner, Roichman and Assaf. Lastly, We make progress on conjectured bounds of the diameter by Reiner and Roichman, which are based on the underlying hyperplane arrangement, and find families of permutations that achieve the upper bound and lower bound of the conjecture. In particular permutations that avoid 312 or 231 have graphs that achieve the upper bound.

math.CO↗

arXiv2019

Identifiability of Gaussian Structural Equation Models with Homogeneous and Heterogeneous Error Variances

In this work, we consider the identifiability assumption of Gaussian linear structural equation models (SEMs) in which each variable is determined by a linear function of its parents plus normally distributed error. It has been shown that linear Gaussian structural equation models are fully identifiable if all error variances are the same or known. Hence, this work proves the identifiability of Gaussian SEMs with both homogeneous and heterogeneous unknown error variances. Our new identifiability assumption exploits not only error variances, but edge weights; hence, it is strictly milder than prior work on the identifiability result. We further provide a structure learning algorithm that is statistically consistent and computationally feasible, based on our new assumption. The proposed algorithm assumes that all relevant variables are observed, while it does not assume causal minimality and faithfulness. We verify our theoretical findings through simulations and real multivariate data, and compare our algorithm to state-of-the-art PC, GES and GDS algorithms.

stat.ML↗