# Truhlar Research Group News

Our new computer program, *TUMME*, solves the master equation by the method of chemically significant eigenmodes to calculate temperature- and pressure-dependent rate constants for thermal unimolecular chemical reactions and chemical activation reactions. A paper describing the program is now published:

R. M. Zhang, X. Xu, and D. G. Truhlar, TUMME: Tsinghua University Minnesota Master Equation program, Computer Physics Communications **270**, 108140/1-17 (2021).

doi.org/10.1016/j.cpc.2021.108140

Share link for free access (expires Oct. 30, 2021):

https://authors.elsevier.com/a/1djlI2OIngMWU

The program, which includes a detailed manual, is available free of charge at https://comp.chem.umn.edu/tumme

*TUMME* calculates microcanonical flux coefficients (which are inputs to the master equation) by multi-structural variational transition state theory with small-curvature tunneling (MS-VTST/SCT) or by conventional transition state theory or RRKM theory (which is conventional transition state theory applied to unimolecular reactions) by using data read from output files of *Gaussian*, *Polyrate*, and/or *MSTor*.

The program is written in double precision with Python 3, and quadruple and octuple precision are also available for some subtasks in C++ (the higher precision is often necessary at low temperature or for competing reactions). The Python code can run in serial or parallel (multithreading and MPI), and the C++ code can run on a single processor or on multiple processors with OpenMP.

Weighted flux coefficients *k*_{X,wt} for unimolecular dissociation of 2-methylhexyl radicals at 700 K and 10^{-6} torr; *E _{η}* is internal energy, and X equal to A, B, or C denotes one of three possible products. Double precision refers to 8 bytes per word, and quadruple precision refers to 16 bytes per word.

Dayou Zhang is the recipient of the 2021-2022 Robert and Jill DeMaster Excellence Fellowship. This is a very competitive fellowship and is a strong endorsement of his accomplishments so far in our graduate program.

Dayou’s work has already led to four publications:

1. “Spin Splitting Energy of Transition Metals: A New, More Affordable Wave Function Benchmark Method and Its Use to Test Density Functional Theory,” D. Zhang and D. G. Truhlar, Journal of Chemical Theory and Computation **16**, 4416-4428 (2020). doi.org/10.1021/acs.jctc.0c00518

2. “Unmasking Static Correlation Error in Hybrid Kohn–Sham Density Functional Theory,” D. Zhang and D. G. Truhlar, Journal of Chemical Theory and Computation **16**, 5432-5440 (2020). doi.org/10.1021/acs.jctc.0c00585

3. “Multiconfigurational Effects on the Density Coherence,” D. Zhang and D. G. Truhlar, Journal of Chemical Theory and Computation **16**, 6915-6925 (2020). doi.org/10.1021/acs.jctc.0c00903

4. “Multiconfiguration Density-Coherence Functional Theory,” D. Zhang, M. R. Hermes, L. Gagliardi, and D. G. Truhlar, Journal of Chemical Theory and Computation **17**, 2775-2782 (2021). doi.org/10.1021/acs.jctc.0c01346

Paper 1 presents a new algorithm, CASPT2.5, for accurate calculations on strongly correlated systems. It also tests this algorithm and several other multireference methods on transition metal spin-splitting energies for which the standard CCSD(T) method fails. The CASPT2.5 method is found to be very accurate with an affordable cost for small molecules and it is used to provide benchmark spin-splitting energies and geometries for transition metal complexes. These were used to test 60 exchange-correlation functionals. The MN15-L method was validated to perform very well for spin splitting. We believe that CASPT2.5 and MN15-L can be very useful for calculating spin splittings, which are important for many technical applications.

Accurately treating strongly correlated systems is a challenging task for Kohn–Sham density functional theory (KS theory). The factors underlying its inaccuracy are only partly clear, especially regarding static correlation. To unmask the static correlation error, paper 2 compares the potential energy curves of four diatomic molecules, namely H_{2}, F_{2}, HF, and NaF, using restricted and unrestricted KS theory. With the aid of restricted KS theory calculations, Dayou found that limiting the percentage of Hartree–Fock exchange significantly reduces the static correlation error in Hartree–Fock theory. This work extends and builds upon a stimulating paper of Nobel Laureate Martin Karplus. Dayou showed that utilizing restricted KS calculations is a useful tool to elucidate the origin of static correlation error in KS theory. One reviewer commented, “It is useful that it is brought home to the readers that there may be important drawbacks to the inclusion of exact exchange, and what the problems are exactly.” Another reviewer said, “I think this is a very interesting perspective on static correlation and I think the authors do a good job of supporting their claims with calculations.”

Paper 3 is a study of density coherences in multiconfiguration self-consistent field theory and Kohn−Sham density functional theory. The density coherences under study here are the off-diagonal elements of the one-body density matrix. Although the one-body density matrix is a central quantity in wave function and density functional methods, it has not been nearly as widely studied as the density itself, which is the diagonal part of the density matrix in the coordinate representation. Dayou compared CASSCF, Hartree–Fock, local Kohn–Sham theory, and hybrid Kohn–Sham theory for the density coherence. The quantitative conclusions are quite striking, showing larger deviations among the methods than one might have expected. We expect that there will be much more emphasis on the density matrix in the near future, and this study can lay a groundwork for general expectations and thereby help guide the development work.

Paper 4 describes a new theory — multiconfiguration density coherence functional theory — and it demonstrates its promise for representing the correct physics of static and dynamic correlation. Potentially it allows new strategies for designing density matrix functionals that take advantage of the physical interpretation of the number of unpaired electrons rather than unphysical effective spin densities. Dayou’s paper shows that already with just two parameters he can get good results for bond energies, equilibrium distances, vibrational frequencies, and potential curves.

In addition to his published work, Dayou has completed a fifth project and has a sixth in progress. Project 5 analyzes static and dynamic electron correlation by decomposing the total electronic energy of calculations by restricted Hartree–Fock (RHF) theory, complete active space self-consistent field (CASSCF) theory, and multireference configuration interaction (MRCI). Dayou is using two different schemes to break down the total energy contributions to the potential energy curves for the dissociation of diatomic molecules. He finds that a significant portion of the static correlation comes from the part of the energy that is not expressible in terms of the one-body reduced density matrix. He also finds that negligible static correlation is included in the sum of the effective one-electron energy and the classical two-electron energy, which provides a way to understand the success of multiconfiguration pair-density functional theory (MC-PDFT) and multiconfiguration density coherence functional theory (MC-DCFT). This kind of analysis of energetic contributions to the total energy in terms of different components of the two-body reduced density matrix has never been done before, and it leads to fundamental understanding.

In project 6, Dayou is developing new strategies for multi-parameter optimization of density coherence functionals.

Jiaxin Ning has been awarded the 2021 John Overend Award for Graduate Research in Physical Chemistry. Jiaxin was given this award in recognition of her outstanding work on the following two research articles:

“The Valence and Rydberg States of Dienes,” J. Ning and D. G. Truhlar, Physical Chemistry Chemical Physics **22**, 6176-6183 (2020). doi.org/10.1039/c9cp06952f

“Spin-Orbit Coupling Changes the Identity of the Hyper-Open-Shell Ground State of Ce^{+}, and the Bond Dissociation Energy of CeH^{+} Proves to be Challenging for Theory,” J. Ning and D. G. Truhlar, Journal of Chemical Theory and Computation **17**, 1421−1434 (2021). doi.org/10.1021/acs.jctc.0c01124

Polychromophoric assemblies are widespread in both biological systems and functional materials, and 1,3-cyclohexadiene and 1,4-cyclohexadiene are classic prototypes for investigating the electronic structures of molecules with interacting conjugated and unconjugated double bonds, respectively. The existence of Rydberg states interspersed with the valence states makes the quantum mechanical calculation of their spectra very challenging and has led to uncertainty about the extent of valence–Rydberg mixing. This paper, for the first time, demonstrates that one can calculate the whole spectrum of valence and Rydberg states in a consistent fashion; the agreement of theory with experiment is remarkable. A special characteristic of Jiaxin’s analysis is the calculation of the second moments of the excited-state orbitals. These moments give a more accurate picture of the diffuseness of the excited-state orbitals in these prototype molecules than had previously been available.

The second paper describes calculations that open new pathways for treating bonds to heavy metals. Because Ce is in the sixth row of the periodic table, relativistic effects must be treated consistently in the molecule and the dissociated ion, and the treatment of Ce^{+} turned out to require the development of new strategies. Jiaxin found that the ground state is different with and without spin-orbit coupling. She also found that the ground doublet state of Ce^{+} is an intra-atomic hyper-open-shell state. Out of 40 multireference and single-reference methods tested, only seven get the identity of the spin-orbit-free ground state right. The dissociation energy calculations show that the quantitative chemistry of bonds to sixth-period metal atoms presents a serious challenge to quantitative quantum chemistry.

Jiaxin is currently working on the simulation of the photodissociation of 2-fluorothiophenol. Because of the unique role of the intramolecular hydrogen bond, photodissociation and internal relaxation of this molecule provide a prototype for understanding substituent effects on the important p → σ* pathway that is key to understanding photostability in biological molecules. Jiaxin is developing a unique computational procedure for using the coherent switching with decay of mixing (CSDM) method in the SHARC program to do the dynamics simulations with the XMS-CASPT2 method for the electronic structure input.

Jiaxin came to our group after earning a bachelor's degree in chemistry from Nankai University in Tianjin, China. We look forward to her continuing contributions to theoretical and computational physical chemistry.

Developing a computational method that is both affordable and accurate for intersystem crossing is a major challenge. In a recent study, we have considered two key issues - the choice of electronic structure method and the treatment of electronic decoherence for the study of intersystem crossing (ISC) nonadiabatic processes. The results showed the successfulness of our coherent switching with decay of mixing (CSDM) nonadiabatic dynamics method and the dramatic effect of electronic decoherence on the buildup of triplet state populations.

“Direct Coherent Switching with Decay of Mixing for Intersystem Crossing Dynamics of Thioformaldehyde: The Effect of Decoherence,” L. Zhang, Y. Shu, S. Sun, and D. G. Truhlar, Journal of Chemical Physics **154**, 094310/1-10 (2021). doi.org/10.1063/5.0037878

Yinan Shu, Ph.D., a postdoctoral research associate in our group, has received the **Wiley Computers in Chemistry Outstanding Postdoc Award **organized by ACS COMP Division, sponsored by Wiley and presented by the International Journal of Quantum Chemistry and the Journal of Computational Chemistry. Yinan will share his work in the COMP Awards Symposium at the Spring 2021 ACS National Meeting, where he will speak on “Diabatization by Machine Intelligence.” The figure illustrates Yinan’s work on permutationally restrained diabatization by a deep neural network.

Jie Bao successfully defended his Ph. D. thesis entitled “Developing a Model Chemistry for Multiconfiguration Pair-Density Functional Theory to Study Photochemistry and Molecular Interactions.” Congratulations Jie! Jie will remain in the Truhlar group as a postdoc. The figure illustrates Jie’s ABC scheme for automatic active space selection for excited-state calculations.

*Chemical Science*, the flagship journal of the Royal Society of Chemistry, announced today that the article

“Density Matrix Renormalization Group Pair-Density Functional Theory (DMRG-PDFT): Singlet-Triplet Gaps in Polyacenes and Polyacetylenes,” P. Sharma, V. Bernales, S. Knecht, D. G. Truhlar, and L. Gagliardi, Chemical Science 10, 1716-1723 (2019). doi.org/10.1039/C8SC03569E

has been selected for the themed collection Most Popular 2018-2019 Physical and Theoretical Chemistry Articles:

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We are pleased to congratulate Dr. Yinan Shu, a postdoctoral associate in our group, who has just been awarded the Robin Hochstrasser Young Investigator Award. The Robin Hochstrasser Young Investigator Award was created by Elsevier Publishing to honor Robin Hochstrasser and support young scientists; it is given each year to a scientist working in chemical physics and younger than 40 years of age who does not have permanent professorship. The winner is selected by an international committee of scientists consisting of five members of the editorial board of *Chemical Physics*. Professor Robin Hochstrasser was the Editor of *Chemical Physics* for almost four decades; he was a pioneer in the application of lasers in chemical and biomedical research and among his students was Nobel Laureate Ahmed Zewail.

Yinan Shu was born in Hangzhou, China and obtained his BS degrees in Chemistry and Biological Science from Wuhan University in 2011. In our group he has worked on density functional electronic structure theory, especially for excited electronic states, on understanding complex photochemical and photophysical processes, on nonadiabatic dynamics algorithms, and on machine learning via deep neural networks. His Google Scholar page is

https://scholar.google.com/citations?user=UtZEpfMAAAAJ&hl=en&oi=ao

Yinan won the ACS Physical Chemistry Division Young Investigator Award in April so this is his second major award in a very short period of time.

The potential energy surface for high energy N_{2}–N_{2} collisions was originally [1] fit by moving least squares [1] and by conventional linear regression [2]. Now, in collaboration with Jun Li of Chongqing University and Hua Guo of the University of New Mexico, we have revisited this problem using machine learning, in particular using a neural network (NN) for the fit [3]. Due to the requirement of very complete data coverage of the geometric domain in order to get a physical fit by NN, the number of points in original fitting dataset was extended by about 30% to get 21 406 points. We used several tactical steps to achieve reasonably good data coverage. For the same input data, the NN fit is more accurate than a linear regression fit (denoted MEG in the figure), although using it for trajectory studies is more expensive.

[1] “Potential Energy Surface Fitting by a Statistically Localized, Permutationally Invariant, Local Interpolating Moving Least Squares Method for the Many-Body Potential: Method and Application to N_{4},” J. D. Bender, S. Doraiswamy, D. G. Truhlar, and G. V. Candler, Journal of Chemical Physics **140**, article 054302 (2014). doi.org/10.1063/1.4862157

[2] “An Improved Potential Energy Surface and Multi-Temperature Quasiclassical Trajectory Calculations of N_{2} + N_{2} Dissociation Reactions,” J. Bender, P. Valentini, I. Nompelis, Y. Paukku, Z. Varga, D. G. Truhlar, T. Schwartzentruber, and G. Candler, Journal of Chemical Physics **143**, article 054304 (2015). doi.org/10.1063/1.4927571

[3] “Many-Body Permutationally-Invariant-Polynomial Neural-Network Potential Energy Surface for N_{4},” J. Li, Z. Varga, D. G. Truhlar, and H. Guo, Journal of Chemical Theory and Computation **16**, 4822-4832 (2020). doi.org/10.1021/acs.jctc.0c00430

Our recent benchmark study shows that the Minnesota exchange–correlation density functionals MN15-L, M06-SX, and revM06 can predict highly accurate spin splitting energies for transition metals. The def2-TZVP basis set is found to be the most suitable basis set within our test set to perform these density functional calculations. We also proposed a new wave function method called CASPT2.5, which is performed by taking the average of the CASPT2 and CASPT3 energies. We found that CASPT2.5 extrapolated to a complete basis set is the best wave function method in terms of computational cost and accuracy for spin splittings of transition metals.

“Spin Splitting Energy of Transition Metals: A New, More Affordable Wave Function Benchmark Method and Its Use to Test Density Functional Theory,” D. Zhang and D. G. Truhlar, Journal of Chemical Theory and Computation **16**, 4416-4428 (2020). doi.org/10.1021/acs.jctc.0c00518