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).

Coherent Switching with Decay of Mixing Provides an Accurate Description of Intersystem Crossing

March 5, 2021

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.

Yinan Shu Receives Wiley Computers in Chemistry Outstanding Postdoc Award

February 25, 2021

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.

Jie Bao Successfully Defends Thesis on MC-PDFT

January 29, 2021

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).   

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

     The density matrix renormalization group (DMRG) [White and Martin 1999; Chan and Head-Gordon 2002; Ma, Knecht, Keller, and Reiher 2017] is a variational electronic structure method converging in principle to full configuration interaction (as one increases the bond dimension M) by using a sweep algorithm to optimize a matrix-product-state representation of the wave function. It allows one to use active spaces about six times larger than conventional CASSCF. But DMRG (like conventional CASSCF) is energetically unreliable without a post-SCF calculation of external correlation. In this paper we presented an inexpensive way to calculate dynamic correlation energy starting from a DMRG wave function by using pair-density functional theory (PDFT).

     In the Chemical Science paper, we applied this new approach, called DMRG-PDFT, to study singlet–triplet gaps in polyacenes and polyacetylenes that require active spaces larger than the feasibility limit of the conventional CASSCF method. The results matched reasonably well with the most reliable literature values, and they have only a moderate dependence on the compression of the initial DMRG wave function. Furthermore, DMRG-PDFT is significantly more affordable than other commonly applied way of adding additional correlation to DMRG, such as DMRG followed by multireference perturbation theory.

Structure of n-acenes and n-polyacetylene

(a) n-acenes, (b) n-polyacetylene

     More recently, our group has applied the DMRG-PDFT method to free-base iron porphyrin, Fe(P):

“Multiconfiguration Pair-Density Functional Theory for Iron Porphyrin with CAS, RAS, and DMRG Active Spaces,” C. Zhou, L. Gagliardi, and D. G. Truhlar, Journal of Physical Chemistry A 123, 3389-3394 (2019).

In this paper, we used MC-PDFT to calculate the energetic order of four states of Fe(P) with active spaces ranging from 8 active electrons in  6 active orbitals to 34 active electrons in  35 active orbitals, and the largest active space is only affordable for DMRG-PDFT. DMRG-PDFT gives the correct ground state, regardless of the selection of active space, and it provides an efficient and accurate approach to treat electron correlation in large molecules like for iron porphyrin.

     A third application of DMRG-PDFT will be published shortly:

“Magnetic Coupling in a Tris-hydroxobridged Chromium Dimer Occurs Through Ligand-Mediated Superexchange in Conjunction with Through-Space Coupling,” by P. Sharma, D. G. Truhlar, and L. Gagliardi, to be published.

     DMRG-PDFT calculations are performed with the OpenMolcas 8.3 software package using an implementation based on the QCMaquis software suite in OpenMolcas 8.3. To carry out the calculations, one has to enable the DMRG function while compiling. When one installs OpenMolcas and enables DMRG, one automatically downloads the source files and necessary libraries of QCMaquis.


August 5, 2020

Yinan Shu

Link to the Department of Chemistry News

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

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.

July 22, 2020

The potential energy surface for high energy N2–N2 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 N4,” J. D. Bender, S. Doraiswamy, D. G. Truhlar, and G. V. Candler, Journal of Chemical Physics 140, article 054302 (2014).

[2] “An Improved Potential Energy Surface and Multi-Temperature Quasiclassical Trajectory Calculations of N2 + N2 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).

[3] “Many-Body Permutationally-Invariant-Polynomial Neural-Network Potential Energy Surface for N4,” J. Li, Z. Varga, D. G. Truhlar, and H. Guo, Journal of Chemical Theory and Computation 16, 4822-4832 (2020).

Neural Networks Provide Accurate Potential Energy Surfaces

July 1, 2020

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).

Minnesota Density Functionals and CASPT2.5 Predict Accurate Spin Splitting Energies of Transition Metals

June 15, 2020

The languages that physicists and chemists use in regarding the HOMO-LUMO gaps, HOCO-LUCO gaps, band gaps, fundamental gaps, and optical excitation thresholds can be quite different, and the difference in language has the very serious consequence that it changes the way that different communities interpret their calculations.  We studied the relations between these kinds of quantities for a large number of  exchange-correlation functionals. Surprisingly, despite large differences in functional forms, a consistent relation with the percentage of Hartree-Fock exchange was discovered. Furthermore, we concluded that with presently available functionals the orbital energies should be treated as intermediate mathematical variables in the calculation of excitation energies rather than as the energies of independent-particle reference states for quasiparticle theory.

“Relationships between Orbital Energies, Optical AND fundamental Gaps, Exciton Shifts in Approximate Density Functional Theory and Quasiparticle Theory” Y. Shu, and D. G. Truhlar, Journal of Chemical Theory and Computation 16, 7 (2020). doi,org/10.1021/acs.jctc.0c00320

Relations Between Orbital Energies, Fundamental Gaps, Exciton Shifts, Quasiparticle Shifts, and Excitation Energies Have Been Elucidated

May 26, 2020

When two electronic states of the same symmetry are close in energy, they have strong interactions, and they cannot be treated separately – one must use multi-state methods. To incorporate state interactions in multiconfiguration pair-density functional theory (MC-PDFT), we have developed two new multi-state (MS) methods, namely extended multi-state PDFT (XMS-PDFT) and variational multi-state PDFT (VMS-PDFT. The new methods have been tested successfully for eight systems exhibiting locally avoided crossings among two to six states. Since both XMS-PDFT and VMS-PDFT are much less expensive than XMS-CASPT2, they will allow well-correlated calculations on large systems for which perturbation theory is undoable. The figure shows schematically how nonphysical results are obtained for potential curves when they are treated separately – on the left, and how this is remedied when they are treated together by a multi-state method – on the right.

“Multi-state pair-density functional theory,” J. J. Bao, C. Zhou, Z. Varga, S. Kanchanakungwankul, L. Gagliardi and D. G. Truhlar, Faraday Discussions 224, 348-372 (2020).

Multi-State Pair-Density Functional Theory Provides Consistent Excited-State Energies for Strongly Interacting States

May 7, 2020

A key issue in chemical kinetics is advancing the theoretical framework to handle reactions beyond the domain of textbook transition state theory by including – for example – anharmonicity, barrierless transition states, transition states in series, and the effect of conformational flexibility on equilibrium constants. Other key issues are validating affordable electronic structure methods for direct dynamics and the direct calculation of high-pressure limiting rate constants, which are often obtainable experimentally only by extrapolation. We have addressed all these issues in a study of the prototype radical–molecule barrierless association reaction Cl + C2H2, and this work  demonstrates the ability of recent advances in theoretical methods, when combined, to provide rate constants even for a difficult class of reactions in cases where experimental data are uncertain or missing.

“Association of Cl with C2H2 by Unified Variable-Reaction-Coordinate and Reaction-Path Variational Transition State Theory,” L. Zhang, D. G. Truhlar, and S. Sun, Proceedings of the National Academy of Sciences U.S.A. 117, 5610-5616 (2020).

Barrierless Association Reactions with Transition States in Series are Treated by Combining VRC-VTST and RP-VTST

March 2, 2020