arXiv subjects

Jae Woo Park

Publications and source records attributed to Jae Woo Park.

10 recordsLinked to original sources

arXiv2022

Analytical Gradient Theory for Spin-Free State-Averaged Second-Order Driven Similarity Renormalization Group Perturbation Theory (SA-DSRG-MRPT2) and Its Applications for Conical Intersection Optimizations

The second-order multireference driven similarity renormalization group perturbation theory (DSRG-MRPT2) theory provides an efficient means of correcting the dynamical correlation with the multiconfiguration reference function. The state-averaged DSRG-MRPT2 (SA-DSRG-MRPT2) method is the simplest means of treating the excited states with DSRG-MRPT2. In this method, the Hamiltonian dressed with dynamical correlation is diagonalized in the CASCI state subspace (SA-DSRG-MRPT2c) or the configuration subspace (SA-DSRG-MRPT2). This work develops the analytical gradient theory for spin-free SA-DSRG-MRPT2(c) with the density-fitting (DF) approximation. We check the accuracy of the analytical gradients against the numerical gradients. We present applications for optimizing minimum energy conical intersections (MECI) of ethylene and retinal model chromophores (PSB3 and RPSB6). We investigate the dependence of the optimized geometries and energies on the flow parameter and reference relaxations. The smoothness of the SA-DSRG-MRPT2(c) potential energy surfaces near the reference (CASSCF) MECI is comparable to the XMCQDPT2 one. These results render the SA-DSRG-MRPT2(c) theory a promising approach for studies of conical intersections.

physics.chem-ph↗

arXiv2021

Recent results on Choi's orthogonal Latin squares

Choi Seok-Jeong studied Latin squares at least 60 years earlier than Euler although this was less known. He introduced a pair of orthogonal Latin squares of order 9 in his book. Interestingly, his two orthogonal non-double-diagonal Latin squares produce a magic square of order 9, whose theoretical reason was not studied. There have been a few studies on Choi's Latin squares of order 9. The most recent one is Ko-Wei Lih's construction of Choi's Latin squares of order 9 based on the two $3 \times 3$ orthogonal Latin squares. In this paper, we give a new generalization of Choi's orthogonal Latin squares of order 9 to orthogonal Latin squares of size $n^2$ using the Kronecker product including Lih's construction. We find a geometric description of Choi's orthogonal Latin squares of order 9 using the dihedral group $D_8$. We also give a new way to construct magic squares from two orthogonal non-double-diagonal Latin squares, which explains why Choi's Latin squares produce a magic square of order 9.

math.CO↗

arXiv2021

Analytical Gradient Theory for Resolvent-Fitted Second-Order Extended Multiconfiguration Perturbation Theory (XMCQDPT2)

We present the formulation and implementation of an analytical gradient algorithm for extended multiconfiguration quasidegenerate perturbation theory (XMCQDPT2) with the resolvent-fitting approximation by Granovsky. This algorithm is powerful when optimizing molecular configurations with a moderate-sized active space and many electronic states. First, we present the powerfulness and accuracy of resolvent-fitting approximations compared to the canonical XMCQDPT2 theory. Then, we demonstrate the utility of the current algorithm in frequency analyses, optimizing the minimum energy conical intersection (MECI) geometries of the retinal chromophore model RPSB6, and evaluating nuclear gradients when there are many electronic states. Furthermore, we parallelize the algorithm using the OpenMP/MPI hybrid approach. Additionally, we report the computational cost and parallel efficiency of the program.

physics.chem-ph↗

arXiv2021

Near-Exact CASSCF-Level Geometry Optimization with a Large Active Space using Adaptive Sampling Configuration Interaction Self-Consistent Field Corrected with Second-Order Perturbation Theory (ASCI-SCF-PT2)

An accurate description of electron correlation is one of the most challenging problems in quantum chemistry. The exact electron correlation can be obtained by means of full configuration interaction (FCI). A simple strategy for approximating FCI at a reduced computational cost is selected CI (SCI), which diagonalizes the Hamiltonian within only the chosen configuration space. Recovery of the contributions of the remaining configurations is possible with second-order perturbation theory. Here, we apply adaptive sampling configuration interaction (ASCI) combined with molecular orbital optimizations (ASCI-SCF) corrected with second-order perturbation theory (ASCI-SCF-PT2) for geometry optimization by implementing the analytical nuclear gradient algorithm for ASCI-PT2 with the Z-vector (Lagrangian) formalism. We demonstrate that for phenalenyl radicals and anthracene, optimized geometries and the number of unpaired electrons can be obtained at nearly the CASSCF accuracy by incorporating PT2 corrections and extrapolating them. We demonstrate the current algorithm's utility for optimizing the equilibrium geometries and electronic structures of 6-ring-fused polycyclic aromatic hydrocarbons and 4-periacene.

physics.chem-ph↗

arXiv2019

Analytical Gradient Theory for Strongly Contracted (SC-) and Partially Contracted (PC-) N-Electron Valence State Perturbation Theory (NEVPT2)

An analytical gradient theory for single-state N-electron valence state perturbation theory (NEVPT2), using both strongly contracted (SC) and partially contracted (PC) internal contraction schemes, is developed. We demonstrate the utility of the developed algorithm in the optimization of the single-state molecular geometry of acrolein, benzyne, benzene, the retinal chromophore PSB3, the GFP chromophore pHBI, and porphine, with the cc-pVTZ basis sets. The SC-NEVPT2 analytical gradients exhibit numerical instability due to the lack of invariance with respect to the rotations among the inactive orbitals. On the other hand, PC-NEVPT2 gives molecular geometries comparable to CASPT2 in any tested cases. We discuss possible future developments that will make the NEVPT2 gradient algorithm a powerful tool for optimizing the molecular geometries and conducting molecular dynamics simulations of correlated systems.

physics.chem-ph↗

arXiv2019

Multireference electron correlation methods: Journeys along potential energy surfaces

Multireference electron correlation methods describe static and dynamical electron correlation in a balanced way, and therefore, can yield accurate and predictive results even when single-reference methods or multiconfigurational self-consistent field (MCSCF) theory fails. One of their most prominent applications in quantum chemistry is the exploration of potential energy surfaces (PES). This includes the optimization of molecular geometries, such as equilibrium geometries and conical intersections, and on-the-fly photodynamics simulations; both depend heavily on the ability of the method to properly explore the PES. Since such applications require the nuclear gradients and derivative couplings, the availability of analytical nuclear gradients greatly improves the utility of quantum chemical methods. This review focuses on the developments and advances made in the past two decades. To motivate the readers, we first summarize the notable applications of multireference electron correlation methods to mainstream chemistry, including geometry optimizations and on-the-fly dynamics. Subsequently, we review the analytical nuclear gradient and derivative coupling theories for these methods, and the software infrastructure that allows one to make use of these quantities in applications. The future prospects are discussed at the end of this review.

physics.chem-ph↗

arXiv2019

Imaginary shift in CASPT2 nuclear gradient and derivative coupling theory

We report the analytical nuclear gradient theory for complete active space second-order perturbation theory (CASPT2) with imaginary shift, which is commonly used to avoid divergence of the perturbation expression. Our formulation is based on the Lagrangian approach and is an extension of the algorithm for CASPT2 nuclear gradients with real shift. The working equations are derived and implemented into an efficient parallel program. Numerical examples are presented for the ground- and excited-state geometries and conical intersections of a green fluorescent protein model chromophore, $p$-HBDI$^-$. We also report timing benchmarks with adenine, $p$-HBDI$^-$, and iron porphyrin. It is demonstrated that the energies and geometries obtained with the imaginary shift improve accuracy at a minor additional cost which is mainly associated with evaluating the effective density matrix elements for the imaginary shift term.

physics.chem-ph↗

arXiv2018

On the accuracy of retinal protonated Schiff base models

We investigate the molecular geometries of the ground state and the minimal energy conical intersections (MECIs) between the ground and first excited states of the models for the retinal protonated Schiff base in the gas phase using the extended multistate complete active space second-order perturbation theory (XMS-CASPT2). The biggest model in this work is the rhodopsin chromophore truncated between the ε and δ carbon atoms, which consists of 54 atoms and 12-orbital π conjugation. The results are compared with those obtained by the state-averaged complete active space self-consistent field (SA-CASSCF). The XMS-CASPT2 results suggest that the minimum energy conical intersection associated with the so-called 13-14 isomerization is thermally inaccessible, which is in contrast to the SA-CASSCF results. The differences between the geometries of the conical intersections computed by SA-CASSCF and XMS-CASPT2 are ascribed to the fact that the charge transfer states are more stabilized by dynamical electron correlation than the diradicaloid states. The impact of the various choices of active spaces, basis sets, and state averaging schemes is also examined.

physics.chem-ph↗

arXiv2017

On-the-fly CASPT2 surface hopping dynamics

We report the development of programs for on-the-fly surface hopping dynamics simulations in the gas and condensed phases on the potential energy surfaces computed by multistate multireference perturbation theory (XMS-CASPT2) with full internal contraction. On-the-fly nonadiabatic dynamics simulations are made possible by improving the algorithm for XMS-CASPT2 nuclear energy gradient and derivative coupling evaluation. The program is interfaced to a surface hopping dynamics program, Newton-X, and a classical molecular dynamics package, tinker, to realize such simulations. On-the-fly XMS-CASPT2 surface-hopping dynamics simulations of 9H-adenine and an anionic GFP model chromophore (para-hydroxybenzilideneimidazolin-5-one) in water are presented to demonstrate the applicability of our program to sizable systems. Our program is implemented in the bagel package, which is publicly available under the GNU General Public License.

physics.chem-ph↗

arXiv2017

Analytical derivative coupling for multistate CASPT2 theory

The probability of non-radiative transitions in photochemical dynamics is determined by the derivative couplings, the couplings between different electronic states through the nuclear degrees of freedom. Efficient and accurate evaluation of the derivative couplings is, therefore, of central importance to realize reliable computer simulations of photochemical reactions. In this work, the derivative couplings for multistate multireference second-order perturbation theory (MS-CASPT2) and its 'extended' variant (XMS-CASPT2) are studied, in which we present an algorithm for their analytical evaluation. The computational costs for evaluating the derivative couplings are essentially the same as those for calculating the nuclear energy gradients. The geometries and energies calculated with XMS-CASPT2 for small molecules at minimum energy conical intersections (MECIs) are in good agreement with those computed by multireference configuration interaction. As numerical examples, MECIs are optimized using XMS-CASPT2 for stilbene and a GFP model chromophore (the 4-para-hydroxybenzylidene-1,2-dimethyl-imidazolin-5-one anion).

physics.chem-ph↗