Honors & Awards

  • Stanford Science Fellow, School of Humanities and Science, Stanford University. (07/01/2022-06/30/2025)

Professional Education

  • Doctor of Philosophy, University of California Berkeley (2022)
  • Bachelor of Science, Massachusetts Institute of Technology (2016)

Stanford Advisors

Lab Affiliations

All Publications

  • Revisiting the Performance of Time-Dependent Density Functional Theory for Electronic Excitations: Assessment of 43 Popular and Recently Developed Functionals from Rungs One to Four JOURNAL OF CHEMICAL THEORY AND COMPUTATION Liang, J., Feng, X., Hait, D., Head-Gordon, M. 2022; 18 (6): 3460-3473


    In this paper, the performance of more than 40 popular or recently developed density functionals is assessed for the calculation of 463 vertical excitation energies against the large and accurate QuestDB benchmark set. For this purpose, the Tamm-Dancoff approximation offers a good balance between computational efficiency and accuracy. The functionals ωB97X-D and BMK are found to offer the best performance overall with a root-mean square error (RMSE) of around 0.27 eV, better than the computationally more demanding CIS(D) wave function method with a RMSE of 0.36 eV. The results also suggest that Jacob's ladder still holds for time-dependent density functional theory excitation energies, though hybrid meta generalized-gradient approximations (meta-GGAs) are not generally better than hybrid GGAs. Effects of basis set convergence, gauge invariance correction to meta-GGAs, and nonlocal correlation (VV10) are also studied, and practical basis set recommendations are provided.

    View details for DOI 10.1021/acs.jctc.2c00160

    View details for Web of Science ID 000812042100001

    View details for PubMedID 35533317

  • Computing x-ray absorption spectra from linear-response particles atop optimized holes JOURNAL OF CHEMICAL PHYSICS Hait, D., Oosterbaan, K. J., Carter-Fenk, K., Head-Gordon, M. 2022; 156 (20): 201104


    State specific orbital optimized density functional theory (OO-DFT) methods, such as restricted open-shell Kohn-Sham (ROKS), can attain semiquantitative accuracy for predicting x-ray absorption spectra of closed-shell molecules. OO-DFT methods, however, require that each state be individually optimized. In this Communication, we present an approach to generate an approximate core-excited state density for use with the ROKS energy ansatz, which is capable of giving reasonable accuracy without requiring state-specific optimization. This is achieved by fully optimizing the core-hole through the core-ionized state, followed by the use of electron-addition configuration interaction singles to obtain the particle level. This hybrid approach can be viewed as a DFT generalization of the static-exchange (STEX) method and can attain ∼0.6 eV rms error for the K-edges of C-F through the use of local functionals, such as PBE and OLYP. This ROKS(STEX) approach can also be used to identify important transitions for full OO ROKS treatment and can thus help reduce the computational cost of obtaining OO-DFT quality spectra. ROKS(STEX), therefore, appears to be a useful technique for the efficient prediction of x-ray absorption spectra.

    View details for DOI 10.1063/5.0092987

    View details for Web of Science ID 000804940900005

    View details for PubMedID 35649868

  • Relativistic Orbital-Optimized Density Functional Theory for Accurate Core-Level Spectroscopy. The journal of physical chemistry letters Cunha, L. A., Hait, D., Kang, R., Mao, Y., Head-Gordon, M. 2022: 3438-3449


    Core-level spectra of 1s electrons of elements heavier than Ne show significant relativistic effects. We combine advances in orbital-optimized density functional theory (OO-DFT) with the spin-free exact two-component (X2C) model for scalar relativistic effects to study K-edge spectra of third period elements. OO-DFT/X2C is found to be quite accurate at predicting energies, yielding a ∼0.5 eV root-mean-square error versus experiment with the modern SCAN (and related) functionals. This marks a significant improvement over the >50 eV deviations that are typical for the popular time-dependent DFT (TDDFT) approach. Consequently, experimental spectra are quite well reproduced by OO-DFT/X2C, sans empirical shifts for alignment. OO-DFT/X2C combines high accuracy with ground state DFT cost and is thus a promising route for computing core-level spectra of third period elements. We also explored K and L edges of 3d transition metals to identify limitations of the OO-DFT/X2C approach in modeling the spectra of heavier atoms.

    View details for DOI 10.1021/acs.jpclett.2c00578

    View details for PubMedID 35412838

  • Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package JOURNAL OF CHEMICAL PHYSICS Epifanovsky, E., Gilbert, A. B., Feng, X., Lee, J., Mao, Y., Mardirossian, N., Pokhilko, P., White, A. F., Coons, M. P., Dempwolff, A. L., Gan, Z., Hait, D., Horn, P. R., Jacobson, L. D., Kaliman, I., Kussmann, J., Lange, A. W., Lao, K., Levine, D. S., Liu, J., McKenzie, S. C., Morrison, A. F., Nanda, K. D., Plasser, F., Rehn, D. R., Vidal, M. L., You, Z., Zhu, Y., Alam, B., Albrecht, B. J., Aldossary, A., Alguire, E., Andersen, J. H., Athavale, V., Barton, D., Begam, K., Behn, A., Bellonzi, N., Bernard, Y. A., Berquist, E. J., Burton, H. A., Carreras, A., Carter-Fenk, K., Chakraborty, R., Chien, A. D., Closser, K. D., Cofer-Shabica, V., Dasgupta, S., de Wergifosse, M., Deng, J., Diedenhofen, M., Do, H., Ehlert, S., Fang, P., Fatehi, S., Feng, Q., Friedhoff, T., Gayvert, J., Ge, Q., Gidofalvi, G., Goldey, M., Gomes, J., Gonzalez-Espinoza, C. E., Gulania, S., Gunina, A. O., Hanson-Heine, M. D., Harbach, P. P., Hauser, A., Herbst, M. F., Vera, M., Hodecker, M., Holden, Z. C., Houck, S., Huang, X., Hui, K., Huynh, B. C., Ivanov, M., Jasz, A., Ji, H., Jiang, H., Kaduk, B., Kaehler, S., Khistyaev, K., Kim, J., Kis, G., Klunzinger, P., Koczor-Benda, Z., Koh, J., Kosenkov, D., Koulias, L., Kowalczyk, T., Krauter, C. M., Kue, K., Kunitsa, A., Kus, T., Ladjanszki, I., Landau, A., Lawler, K., Lefrancois, D., Lehtola, S., Li, R. R., Li, Y., Liang, J., Liebenthal, M., Lin, H., Lin, Y., Liu, F., Liu, K., Loipersberger, M., Luenser, A., Manjanath, A., Manohar, P., Mansoor, E., Manzer, S. F., Mao, S., Marenich, A., Markovich, T., Mason, S., Maurer, S. A., McLaughlin, P. F., Menger, M. J., Mewes, J., Mewes, S. A., Morgante, P., Mullinax, J., Oosterbaan, K. J., Paran, G., Paul, A. C., Paul, S. K., Pavosevic, F., Pei, Z., Prager, S., Proynov, E., Rak, A., Ramos-Cordoba, E., Rana, B., Rask, A. E., Rettig, A., Richard, R. M., Rob, F., Rossomme, E., Scheele, T., Scheurer, M., Schneider, M., Sergueev, N., Sharada, S. M., Skomorowski, W., Small, D. W., Stein, C. J., Su, Y., Sundstrom, E. J., Tao, Z., Thirman, J., Tornai, G. J., Tsuchimochi, T., Tubman, N. M., Veccham, S., Vydrov, O., Wenzel, J., Witte, J., Yamada, A., Yao, K., Yeganeh, S., Yost, S. R., Zech, A., Zhang, I., Zhang, X., Zhang, Y., Zuev, D., Aspuru-Guzik, A., Bell, A. T., Besley, N. A., Bravaya, K. B., Brooks, B. R., Casanova, D., Chai, J., Coriani, S., Cramer, C. J., Cserey, G., DePrince, A., DiStasio, R. A., Dreuw, A., Dunietz, B. D., Furlani, T. R., Goddard, W. A., Hammes-Schiffer, S., Head-Gordon, T., Hehre, W. J., Hsu, C., Jagau, T., Jung, Y., Klamt, A., Kong, J., Lambrecht, D. S., Liang, W., Mayhall, N. J., McCurdy, C., Neaton, J. B., Ochsenfeld, C., Parkhill, J. A., Peverati, R., Rassolov, V. A., Shao, Y., Slipchenko, L., Stauch, T., Steele, R. P., Subotnik, J. E., Thom, A. W., Tkatchenko, A., Truhlar, D. G., Van Voorhis, T., Wesolowski, T. A., Whaley, K., Woodcock, H., Zimmerman, P. M., Faraji, S., Gill, P. W., Head-Gordon, M., Herbert, J. M., Krylov, A. 2021; 155 (8)

    View details for DOI 10.1063/5.0055522

    View details for Web of Science ID 000687352200007

  • Exploring spin symmetry-breaking effects for static field ionization of atoms: Is there an analog to the Coulson-Fischer point in bond dissociation? JOURNAL OF CHEMICAL PHYSICS Cunha, L. A., Lee, J., Hait, D., McCurdy, C., Head-Gordon, M. 2021; 155 (1): 014309


    Löwdin's symmetry dilemma is an ubiquitous issue in approximate quantum chemistry. In the context of Hartree-Fock (HF) theory, the use of Slater determinants with some imposed constraints to preserve symmetries of the exact problem may lead to physically unreasonable potential energy surfaces. On the other hand, lifting these constraints leads to the so-called broken symmetry solutions that usually provide better energetics, at the cost of losing information about good quantum numbers that describe the state of the system. This behavior has previously been extensively studied in the context of bond dissociation. This paper studies the behavior of different classes of HF spin polarized solutions (restricted, unrestricted, and generalized) in the context of ionization by strong static electric fields. We find that, for simple two electron systems, unrestricted Hartree-Fock (UHF) is able to provide a qualitatively good description of states involved during the ionization process (neutral, singly ionized, and doubly ionized states), whereas RHF fails to describe the singly ionized state. For more complex systems, even though UHF is able to capture some of the expected characteristics of the ionized states, it is constrained to a single Ms (diabatic) manifold in the energy surface as a function of field intensity. In this case, a better qualitative picture can be painted by using generalized Hartree-Fock as it is able to explore different spin manifolds and follow the lowest solution due to lack of collinearity constraints on the spin quantization axis.

    View details for DOI 10.1063/5.0054387

    View details for Web of Science ID 000692098500005

    View details for PubMedID 34241406

  • Revealing the nature of electron correlation in transition metal complexes with symmetry breaking and chemical intuition JOURNAL OF CHEMICAL PHYSICS Shee, J., Loipersberger, M., Hait, D., Lee, J., Head-Gordon, M. 2021; 154 (19): 194109


    In this work, we provide a nuanced view of electron correlation in the context of transition metal complexes, reconciling computational characterization via spin and spatial symmetry breaking in single-reference methods with qualitative concepts from ligand-field and molecular orbital theories. These insights provide the tools to reliably diagnose the multi-reference character, and our analysis reveals that while strong (i.e., static) correlation can be found in linear molecules (e.g., diatomics) and weakly bound and antiferromagnetically coupled (monometal-noninnocent ligand or multi-metal) complexes, it is rarely found in the ground-states of mono-transition-metal complexes. This leads to a picture of static correlation that is no more complex for transition metals than it is, e.g., for organic biradicaloids. In contrast, the ability of organometallic species to form more complex interactions, involving both ligand-to-metal σ-donation and metal-to-ligand π-backdonation, places a larger burden on a theory's treatment of dynamic correlation. We hypothesize that chemical bonds in which inter-electron pair correlation is non-negligible cannot be adequately described by theories using MP2 correlation energies and indeed find large errors vs experiment for carbonyl-dissociation energies from double-hybrid density functionals. A theory's description of dynamic correlation (and to a less important extent, delocalization error), which affects relative spin-state energetics and thus spin symmetry breaking, is found to govern the efficacy of its use to diagnose static correlation.

    View details for DOI 10.1063/5.0047386

    View details for Web of Science ID 000692560700002

    View details for PubMedID 34240907

  • Two-Coordinate Iron(I) Complexes on the Edge of Stability: Influence of Dispersion and Steric Effects ORGANOMETALLICS Witzke, R. J., Hait, D., Head-Gordon, M., Tilley, T. 2021; 40 (11): 1758-1764
  • Orbital Optimized Density Functional Theory for Electronic Excited States JOURNAL OF PHYSICAL CHEMISTRY LETTERS Hait, D., Head-Gordon, M. 2021; 12 (19): 4517-4529


    Density functional theory (DFT) based modeling of electronic excited states is of importance for investigation of the photophysical/photochemical properties and spectroscopic characterization of large systems. The widely used linear response time-dependent DFT (TDDFT) approach is, however, not effective at modeling many types of excited states, including (but not limited to) charge-transfer states, doubly excited states, and core-level excitations. In this perspective, we discuss state-specific orbital optimized (OO) DFT approaches as an alterative to TDDFT for electronic excited states. We motivate the use of OO-DFT methods and discuss reasons behind their relatively restricted historical usage (vs TDDFT). We subsequently highlight modern developments that address these factors and allow efficient and reliable OO-DFT computations. Several successful applications of OO-DFT for challenging electronic excitations are also presented, indicating their practical efficacy. OO-DFT approaches are thus increasingly becoming a useful route for computing excited states of large chemical systems. We conclude by discussing the limitations and challenges still facing OO-DFT methods, as well as some potential avenues for addressing them.

    View details for DOI 10.1021/acs.jpclett.1c00744

    View details for Web of Science ID 000655640200007

    View details for PubMedID 33961437

  • Too big, too small, or just right? A benchmark assessment of density functional theory for predicting the spatial extent of the electron density of small chemical systems JOURNAL OF CHEMICAL PHYSICS Hait, D., Liang, Y., Head-Gordon, M. 2021; 154 (7): 074109


    Multipole moments are the first-order responses of the energy to spatial derivatives of the electric field strength. The quality of density functional theory prediction of molecular multipole moments thus characterizes errors in modeling the electron density itself, as well as the performance in describing molecules interacting with external electric fields. However, only the lowest non-zero moment is translationally invariant, making the higher-order moments origin-dependent. Therefore, instead of using the 3 × 3 quadrupole moment matrix, we utilize the translationally invariant 3 × 3 matrix of second cumulants (or spatial variances) of the electron density as the quantity of interest (denoted by K). The principal components of K are the square of the spatial extent of the electron density along each axis. A benchmark dataset of the principal components of K for 100 small molecules at the coupled cluster singles and doubles with perturbative triples at the complete basis set limit is developed, resulting in 213 independent K components. The performance of 47 popular and recent density functionals is assessed against this Var213 dataset. Several functionals, especially double hybrids, and also SCAN and SCAN0 predict reliable second cumulants, although some modern, empirically parameterized functionals yield more disappointing performance. The H, Li, and Be atoms, in particular, are challenging for nearly all methods, indicating that future functional development could benefit from the inclusion of their density information in training or testing protocols.

    View details for DOI 10.1063/5.0038694

    View details for Web of Science ID 000630521300005

    View details for PubMedID 33607884

  • Electron-Nuclear Dynamics Accompanying Proton-Coupled Electron Transfer JOURNAL OF THE AMERICAN CHEMICAL SOCIETY Yoneda, Y., Mora, S., Shee, J., Wadsworth, B. L., Arsenault, E. A., Hait, D., Kodis, G., Gust, D., Moore, G. F., Moore, A. L., Head-Gordon, M., Moore, T. A., Fleming, G. R. 2021; 143 (8): 3104-3112


    Although photoinduced proton-coupled electron transfer (PCET) plays an essential role in photosynthesis, a full understanding of the mechanism is still lacking due to the complex nonequilibrium dynamics arising from the strongly coupled electronic and nuclear degrees of freedom. Here we report the photoinduced PCET dynamics of a biomimetic model system investigated by means of transient IR and two-dimensional electronic-vibrational (2DEV) spectroscopies, IR spectroelectrochemistry (IRSEC), and calculations utilizing long-range-corrected hybrid density functionals. This collective experimental and theoretical effort provides a nuanced picture of the complicated dynamics and synergistic motions involved in photoinduced PCET. In particular, the evolution of the 2DEV line shape, which is highly sensitive to the mixing of vibronic states, is interpreted by accurate computational modeling of the charge separated state and is shown to represent a gradual change in electron density distribution associated with a dihedral twist that occurs on a 120 fs time scale.

    View details for DOI 10.1021/jacs.0c10626

    View details for Web of Science ID 000626325000014

    View details for PubMedID 33601880

  • Third-Order Moller-Plesset Theory Made More Useful? The Role of Density Functional Theory Orbitals JOURNAL OF CHEMICAL THEORY AND COMPUTATION Rettig, A., Hait, D., Bertels, L. W., Head-Gordon, M. 2020; 16 (12): 7473-7489


    The practical utility of Møller-Plesset (MP) perturbation theory is severely constrained by the use of Hartree-Fock (HF) orbitals. It has recently been shown that the use of regularized orbital-optimized MP2 orbitals and scaling of MP3 energy could lead to a significant reduction in MP3 error [Bertels, L. W.; J. Phys. Chem. Lett. 2019, 10, 4170 4176]. In this work, we examine whether density functional theory (DFT)-optimized orbitals can be similarly employed to improve the performance of MP theory at both the MP2 and MP3 levels. We find that the use of DFT orbitals leads to significantly improved performance for prediction of thermochemistry, barrier heights, noncovalent interactions, and dipole moments relative to the standard HF-based MP theory. Indeed, MP3 (with or without scaling) with DFT orbitals is found to surpass the accuracy of coupled-cluster singles and doubles (CCSD) for several data sets. We also found that the results are not particularly functional sensitive in most cases (although range-separated hybrid functionals with low delocalization error perform the best). MP3 based on DFT orbitals thus appears to be an efficient, noniterative O(N6) scaling wave-function approach for single-reference electronic structure computations. Scaled MP2 with DFT orbitals is also found to be quite accurate in many cases, although modern double hybrid functionals are likely to be considerably more accurate.

    View details for DOI 10.1021/acs.jctc.0c00986

    View details for Web of Science ID 000598208600021

    View details for PubMedID 33161713

  • The Ground State Electronic Energy of Benzene JOURNAL OF PHYSICAL CHEMISTRY LETTERS Eriksen, J. J., Anderson, T. A., Deustua, J., Ghanem, K., Hait, D., Hoffmann, M. R., Lee, S., Levine, D. S., Magoulas, I., Shen, J., Tubman, N. M., Whaley, K., Xu, E., Yao, Y., Zhang, N., Alavi, A., Chan, G., Head-Gordon, M., Liu, W., Piecuch, P., Sharma, S., Ten-No, S. L., Umrigar, C. J., Gauss, J. 2020; 11 (20): 8922-8929


    We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground-state energy of the benzene molecule in a standard correlation-consistent basis set of double-ζ quality. As a broad international endeavor, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around -863 mEH. However, we find the root-mean-square deviation of the energies from the studied methods to be considerable (1.3 mEH), which in light of the acclaimed performance of each of the methods for smaller molecular systems clearly displays the challenges faced in extending reliable, near-exact correlation methods to larger systems. While the discrepancies exposed by our study thus emphasize the fact that the current state-of-the-art approaches leave room for improvement, we still expect the present assessment to provide a valuable community resource for benchmark and calibration purposes going forward.

    View details for DOI 10.1021/acs.jpclett.0c02621

    View details for Web of Science ID 000582569600064

    View details for PubMedID 33022176

  • Accurate prediction of core-level spectra of radicals at density functional theory cost via square gradient minimization and recoupling of mixed configurations JOURNAL OF CHEMICAL PHYSICS Hait, D., Haugen, E. A., Yang, Z., Oosterbaan, K. J., Leone, S. R., Head-Gordon, M. 2020; 153 (13): 134108


    State-specific orbital optimized approaches are more accurate at predicting core-level spectra than traditional linear-response protocols, but their utility had been restricted due to the risk of "variational collapse" down to the ground state. We employ the recently developed square gradient minimization [D. Hait and M. Head-Gordon, J. Chem. Theory Comput. 16, 1699 (2020)] algorithm to reliably avoid variational collapse and study the effectiveness of orbital optimized density functional theory (DFT) at predicting second period element 1s core-level spectra of open-shell systems. Several density functionals (including SCAN, B3LYP, and ωB97X-D3) are found to predict excitation energies from the core to singly occupied levels with high accuracy (≤0.3 eV RMS error) against available experimental data. Higher excited states are, however, more challenging by virtue of being intrinsically multiconfigurational. We thus present a configuration interaction inspired route to self-consistently recouple single determinant mixed configurations obtained from DFT, in order to obtain approximate doublet states. This recoupling scheme is used to predict the C K-edge spectra of the allyl radical, the O K-edge spectra of CO+, and the N K-edge of NO2 with high accuracy relative to experiment, indicating substantial promise in using this approach for the computation of core-level spectra for doublet species [vs more traditional time dependent DFT, equation of motion coupled cluster singles and doubles (EOM-CCSD), or using unrecoupled mixed configurations]. We also present general guidelines for computing core-excited states from orbital optimized DFT.

    View details for DOI 10.1063/5.0018833

    View details for Web of Science ID 000577136500008

    View details for PubMedID 33032432

  • Bimetallic Mechanism for Alkyne Cyclotrimerization with a Two-Coordinate Fe Precatalyst ACS CATALYSIS Witzke, R. J., Hait, D., Chakarawet, K., Head-Gordon, M., Tilley, T. 2020; 10 (14): 7800-7807
  • Generalized single excitation configuration interaction: an investigation into the impact of the inclusion of non-orthogonality on the calculation of core-excited states PHYSICAL CHEMISTRY CHEMICAL PHYSICS Oosterbaan, K. J., White, A. F., Hait, D., Head-Gordon, M. 2020; 22 (15): 8182-8192


    In this paper, we investigate different non-orthogonal generalizations of the configuration interaction with single substitutions (CIS) method for the calculation of core-excited states. Fully non-orthogonal CIS (NOCIS) has been described previously for species with singlet and doublet ground states, and this paper reports the extension to molecules in their triplet ground state. In addition to NOCIS, we present a novel method, one-center NOCIS (1C-NOCIS), for open-shell molecules which is intermediate between NOCIS and the computationally less demanding static exchange approximation (STEX). We explore this hierarchy of spin-pure methods for core excitations of molecules with singlet, doublet, and triplet ground states. We conclude that, while NOCIS provides the best results and preserves the spatial symmetry of the wavefunction, 1C-NOCIS retains much of the accuracy of NOCIS at a dramatically reduced cost. For molecules with closed-shell ground states, STEX and 1C-NOCIS are identical.

    View details for DOI 10.1039/c9cp06592j

    View details for Web of Science ID 000529178800048

    View details for PubMedID 32249856

  • Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method JOURNAL OF CHEMICAL THEORY AND COMPUTATION Tubman, N. M., Freeman, C., Levine, D. S., Hait, D., Head-Gordon, M., Whaley, K. 2020; 16 (4): 2139-2159


    Recent advances in selected configuration interaction methods have made them competitive with the most accurate techniques available and, hence, creating an increasingly powerful tool for solving quantum Hamiltonians. In this work, we build on recent advances from the adaptive sampling configuration interaction (ASCI) algorithm. We show that a useful paradigm for generating efficient selected CI/exact diagonalization algorithms is driven by fast sorting algorithms, much in the same way iterative diagonalization is based on the paradigm of matrix vector multiplication. We present several new algorithms for all parts of performing a selected CI, which includes new ASCI search, dynamic bit masking, fast orbital rotations, fast diagonal matrix elements, and residue arrays. The ASCI search algorithm can be used in several different modes, which includes an integral driven search and a coefficient driven search. The algorithms presented here are fast and scalable, and we find that because they are built on fast sorting algorithms they are more efficient than all other approaches we considered. After introducing these techniques, we present ASCI results applied to a large range of systems and basis sets to demonstrate the types of simulations that can be practically treated at the full-CI level with modern methods and hardware, presenting double- and triple-ζ benchmark data for the G1 data set. The largest of these calculations is Si2H6 which is a simulation of 34 electrons in 152 orbitals. We also present some preliminary results for fast deterministic perturbation theory simulations that use hash functions to maintain high efficiency for treating large basis sets.

    View details for DOI 10.1021/acs.jctc.8b00536

    View details for Web of Science ID 000526313000013

    View details for PubMedID 32159951

  • CASSCF with Extremely Large Active Spaces Using the Adaptive Sampling Configuration Interaction Method JOURNAL OF CHEMICAL THEORY AND COMPUTATION Levine, D. S., Hait, D., Tubman, N. M., Lehtola, S., Whaley, K., Head-Gordon, M. 2020; 16 (4): 2340-2354


    The complete active space self-consistent field (CASSCF) method is the principal approach employed for studying strongly correlated systems. However, exact CASSCF can only be performed on small active spaces of ∼20 electrons in ∼20 orbitals due to exponential growth in the computational cost. We show that employing the Adaptive Sampling Configuration Interaction (ASCI) method as an approximate Full CI solver in the active space allows CASSCF-like calculations within chemical accuracy (<1 kcal/mol for relative energies) in active spaces with more than ∼50 active electrons in ∼50 active orbitals, significantly increasing the sizes of systems amenable to accurate multiconfigurational treatment. The main challenge with using any selected CI-based approximate CASSCF is the orbital optimization problem; they tend to exhibit large numbers of local minima in orbital space due to their lack of invariance to active-active rotations (in addition to the local minima that exist in exact CASSCF). We highlight methods that can avoid spurious local extrema as a practical solution to the orbital optimization problem. We employ ASCI-SCF to demonstrate a lack of polyradical character in moderately sized periacenes with up to 52 correlated electrons and compare against heat-bath CI on an iron porphyrin system with more than 40 correlated electrons.

    View details for DOI 10.1021/acs.jctc.9b01255

    View details for Web of Science ID 000526313000028

    View details for PubMedID 32109055

  • Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory JOURNAL OF CHEMICAL THEORY AND COMPUTATION Hait, D., Head-Gordon, M. 2020; 16 (3): 1699-1710


    We present a general approach to converge excited state solutions to any quantum chemistry orbital optimization process, without the risk of variational collapse. The resulting square gradient minimization (SGM) approach only requires analytic energy/Lagrangian orbital gradients and merely costs 3 times as much as ground state orbital optimization (per iteration), when implemented via a finite difference approach. SGM is applied to both single determinant ΔSCF and spin-purified restricted open-shell Kohn-Sham (ROKS) approaches to study the accuracy of orbital optimized DFT excited states. It is found that SGM can converge challenging states where the maximum overlap method (MOM) or analogues either collapse to the ground state or fail to converge. We also report that ΔSCF/ROKS predict highly accurate excitation energies for doubly excited states (which are inaccessible via TDDFT). Singly excited states obtained via ROKS are also found to be quite accurate, especially for Rydberg states that frustrate (semi)local TDDFT. Our results suggest that orbital optimized excited state DFT methods can be used to push past the limitations of TDDFT to doubly excited, charge-transfer, or Rydberg states, making them a useful tool for the practical quantum chemist's toolbox for studying excited states in large systems.

    View details for DOI 10.1021/acs.jctc.9b01127

    View details for Web of Science ID 000519337700029

    View details for PubMedID 32017554

  • Highly Accurate Prediction of Core Spectra of Molecules at Density Functional Theory Cost: Attaining Sub-electronvolt Error from a Restricted Open-Shell Kohn-Sham Approach JOURNAL OF PHYSICAL CHEMISTRY LETTERS Hait, D., Head-Gordon, M. 2020; 11 (3): 775-786


    We present the use of the recently developed square gradient minimization (SGM) algorithm for excited-state orbital optimization to obtain spin-pure restricted open-shell Kohn-Sham (ROKS) energies for core excited states of molecules. The SGM algorithm is robust against variational collapse and offers a reliable route to converging orbitals for target excited states at only 2-3 times the cost of ground-state orbital optimization (per iteration). ROKS/SGM with the modern SCAN/ωB97X-V functionals is found to predict the K-edge of C, N, O, and F to a root mean squared error of ∼0.3 eV. ROKS/SGM is equally effective at predicting L-edge spectra of third period elements, provided a perturbative spin-orbit correction is employed. This high accuracy can be contrasted with traditional time-dependent density functional theory (TDDFT), which typically has greater than 10 eV error and requires translation of computed spectra to align with experiment. ROKS is computationally affordable (having the same scaling as ground-state DFT and a slightly larger prefactor) and can be applied to geometry optimizations/ab initio molecular dynamics of core excited states, as well as condensed phase simulations. ROKS can also model doubly excited/ionized states with one broken electron pair, which are beyond the ability of linear response based methods.

    View details for DOI 10.1021/acs.jpclett.9b03661

    View details for Web of Science ID 000512223400028

    View details for PubMedID 31917579

  • Beyond the Coulson-Fischer point: characterizing single excitation CI and TDDFT for excited states in single bond dissociations PHYSICAL CHEMISTRY CHEMICAL PHYSICS Hait, D., Rettig, A., Head-Gordon, M. 2019; 21 (39): 21761-21775


    Linear response time dependent density functional theory (TDDFT), which builds upon configuration interaction singles (CIS) and TD-Hartree-Fock (TDHF), is the most widely used class of excited state quantum chemistry methods and is often employed to study photochemical processes. This paper studies the behavior of the resulting excited state potential energy surfaces beyond the Coulson-Fischer (CF) point in single bond dissociations, when the optimal reference determinant is spin-polarized. Many excited states exhibit sharp kinks at the CF point, and connect to different dissociation limits via a zone of unphysical concave curvature. In particular, the unrestricted MS = 0 lowest triplet T1 state changes character, and does not dissociate into ground state fragments. The unrestricted MS = ±1 T1 CIS states better approximate the physical dissociation limit, but their degeneracy is broken beyond the CF point for most single bond dissociations. On the other hand, the MS = ±1 T1 TDHF states reach the asymptote too soon, by merging with the ground state from the CF point onwards. Use of local exchange-correlation functionals causes MS = ±1 T1 TDDFT states to resemble their unphysical MS = 0 counterpart. The 2 orbital, 2-electron model system of minimal basis H2 is analytically treated to understand the origin of these issues, revealing that the lack of double excitations is at the root of these remarkable observations. The behavior of excited state surfaces is also numerically examined for species like H2, NH3, C2H6 and LiH in extended basis sets.

    View details for DOI 10.1039/c9cp04452c

    View details for Web of Science ID 000490157000006

    View details for PubMedID 31552963

  • What Levels of Coupled Cluster Theory Are Appropriate for Transition Metal Systems? A Study Using Near-Exact Quantum Chemical Values for 3d Transition Metal Binary Compounds JOURNAL OF CHEMICAL THEORY AND COMPUTATION Hait, D., Tubman, N. M., Levine, D. S., Whaley, K., Head-Gordon, M. 2019; 15 (10): 5370-5385


    Transition metal compounds are traditionally considered to be challenging for standard quantum chemistry approximations like coupled cluster (CC) theory, which are usually employed to validate lower level methods like density functional theory (DFT). To explore this issue, we present a database of bond dissociation energies (BDEs) for 74 spin states of 69 diatomic species containing a 3d transition metal atom and a main group element, in the moderately sized def2-SVP basis. The presented BDEs appear to have an (estimated) 3σ error less than 1 kJ/mol relative to the exact solutions to the nonrelativistic Born-Oppenheimer Hamiltonian. These benchmark values were used to assess the performance of a wide range of standard single reference CC models, as the results should be beneficial for understanding the limitations of these models for transition metal systems. We find that interactions between metals and monovalent ligands like hydride and fluoride are well described by CCSDT. Similarly, CCSDTQ appears to be adequate for bonds between metals and nominally divalent ligands like oxide and sulfide. However, interactions with polyvalent ligands like nitride and carbide are more challenging, with even CCSDTQ(P)Λ yielding errors on the scale of a few kJ/mol. We also find that many perturbative and iterative approximations to higher order terms either yield disappointing results or actually worsen the performance relative to the baseline low level CC method, indicating that complexity does not always guarantee accuracy.

    View details for DOI 10.1021/acs.jctc.9b00674

    View details for Web of Science ID 000489678700018

    View details for PubMedID 31465217

  • Chemoenzymatic Platform for Synthesis of Chiral Organofluorines Based on Type II Aldolases ANGEWANDTE CHEMIE-INTERNATIONAL EDITION Fang, J., Hait, D., Head-Gordon, M., Chang, M. Y. 2019; 58 (34): 11841-11845


    Aldolases are C-C bond forming enzymes that have become prominent tools for sustainable synthesis of complex synthons. However, enzymatic methods of fluorine incorporation into such compounds are lacking due to the rarity of fluorine in nature. Recently, the use of fluoropyruvate as a non-native aldolase substrate has arisen as a solution. Here, we report that the type II HpcH aldolases efficiently catalyze fluoropyruvate addition to diverse aldehydes, with exclusive (3S)-selectivity at fluorine that is rationalized by DFT calculations on a mechanistic model. We also measure the kinetic parameters of aldol addition and demonstrate engineering of the hydroxyl group stereoselectivity. Our aldolase collection is then employed in the chemoenzymatic synthesis of novel fluoroacids and ester derivatives in high stereopurity (d.r. 80-98 %). The compounds made available by this method serve as precursors to fluorinated analogs of sugars, amino acids, and other valuable chiral building blocks.

    View details for DOI 10.1002/anie.201906805

    View details for Web of Science ID 000478220900001

    View details for PubMedID 31240790

    View details for PubMedCentralID PMC7224411

  • Well-behaved versus ill-behaved density functionals for single bond dissociation: Separating success from disaster functional by functional for stretched H-2 JOURNAL OF CHEMICAL PHYSICS Hait, D., Rettig, A., Head-Gordon, M. 2019; 150 (9): 094115


    Unrestricted density functional theory (DFT) methods are typically expected to describe the homolytic dissociation of nonpolar single bonds in neutral species with qualitative accuracy, due to the lack of significant delocalization error. We however find that many widely used density functional approximations fail to describe features along the dissociation curve of the simple H2 molecule. This is not a universal failure of DFT in the sense that many classic functionals like PBE and B3LYP give very reasonable results, as do some more modern methods like MS2. However, some other widely used functionals like B97-D (empirically fitted) and TPSS (non-empirically constrained) predict qualitatively wrong static polarizabilities, force constants, and some even introduce an artificial barrier against association of independent H atoms to form H2. The polarizability and force constant prediction failures appear to stem from incomplete spin localization into individual H atoms beyond the Coulson-Fischer point, resulting in "fractionally bonded" species where the ionic contributions to the Slater determinant are not completely eliminated, unlike the case of unrestricted Hartree-Fock. These errors therefore appear to be a consequence of poor self-consistent density prediction by the problematic functional. The same reasons could potentially lead to spurious barriers toward H atom association, indirectly also leading to incorrect forces. These unphysicalities suggest that the use of problematic functionals is probably unwise in ab initio dynamics calculations, especially if strong electrostatic interactions are possible.

    View details for DOI 10.1063/1.5080122

    View details for Web of Science ID 000460786600017

    View details for PubMedID 30849907

  • Delocalization Errors in Density Functional Theory Are Essentially Quadratic in Fractional Occupation Number JOURNAL OF PHYSICAL CHEMISTRY LETTERS Flait, D., Head-Gordon, M. 2018; 9 (21): 6280-6288


    Approximate functionals used in practical density functional theory (DFT) deviate from the piecewise linear behavior of the exact functional for fractional charges. This deviation causes excess charge delocalization, which leads to incorrect densities, molecular properties, barrier heights, band gaps, and excitation energies. We present a simple delocalization function for characterizing this error and find it to be almost perfectly linear vs the fractional electron number for systems spanning in size from the H atom to the C12H14 polyene. This causes the delocalization energy error to be a quadratic polynomial in the fractional electron number, which permits us to assess the comparative performance of 47 popular and recent functionals through the curvature. The quadratic form further suggests that information about a single fractional charge is sufficient to eliminate the principal source of delocalization error. Generalizing traditional two-point information like ionization potentials or electron affinities to account for a third, fractional charge-based data point could therefore permit fitting/tuning of functionals with lower delocalization error.

    View details for DOI 10.1021/acs.jpclett.8b02417

    View details for Web of Science ID 000449308200018

    View details for PubMedID 30339010

  • Bimolecular Reaction Dynamics in the Phenyl-Silane System: Exploring the Prototype of a Radical Substitution Mechanism JOURNAL OF PHYSICAL CHEMISTRY LETTERS Lucas, M., Thomas, A. M., Yang, T., Kaiser, R. I., Mebel, A. M., Hait, D., Head-Gordon, M. 2018; 9 (17): 5135-5142


    We present a combined experimental and theoretical investigation of the bimolecular gas-phase reaction of the phenyl radical (C6H5) with silane (SiH4) under single collision conditions to investigate the chemical dynamics of forming phenylsilane (C6H5SiH3) via a bimolecular radical substitution mechanism at a tetracoordinated silicon atom. Verified by electronic structure and quasiclassical trajectory calculations, the replacement of a single carbon atom in methane by silicon lowers the barrier to substitution, thus defying conventional wisdom that tetracoordinated hydrides undergo preferentially hydrogen abstraction. This reaction mechanism provides fundamental insights into the hitherto unexplored gas-phase chemical dynamics of radical substitution reactions of mononuclear main group hydrides under single collision conditions and highlights the distinct reactivity of silicon compared to its isovalent carbon. This mechanism might be also involved in the synthesis of cyanosilane (SiH3CN) and methylsilane (CH3SiH3) probed in the circumstellar envelope of the carbon star IRC+10216.

    View details for DOI 10.1021/acs.jpclett.8b02303

    View details for Web of Science ID 000444353900050

    View details for PubMedID 30133285

  • How accurate are static polarizability predictions from density functional theory? An assessment over 132 species at equilibrium geometry PHYSICAL CHEMISTRY CHEMICAL PHYSICS Hait, D., Head-Gordon, M. 2018; 20 (30): 19800-19810


    Static polarizabilities are the first response of the electron density to electric fields, and are therefore important for predicting intermolecular and molecule-field interactions. They also offer a global measure of the accuracy of the treatment of excited states by density functionals in a formally exact manner. We have developed a database of benchmark static polarizabilities for 132 small species at equilibrium geometry, using coupled cluster theory through triple excitations (extrapolated to the complete basis set limit), for the purpose of developing and assessing density functionals. The performance of 60 popular and recent functionals are also assessed, which indicates that double hybrid functionals perform the best, having RMS relative errors in the range of 2.5-3.8%. Many hybrid functionals also give quite reasonable estimates with 4-5% RMS relative error. A few meta-GGAs like mBEEF and MVS yield performance comparable to hybrids, indicating potential for improved excited state predictions relative to typical local functionals. Some recent functionals however are found to be prone to catastrophic failure (possibly as a consequence of overparameterization), indicating a need for caution in applying these.

    View details for DOI 10.1039/c8cp03569e

    View details for Web of Science ID 000441583300005

    View details for PubMedID 30028466

  • Communication: xDH double hybrid functionals can be qualitatively incorrect for non-equilibrium geometries: Dipole moment inversion and barriers to radical-radical association using XYG3 and XYGJ-OS JOURNAL OF CHEMICAL PHYSICS Hait, D., Head-Gordon, M. 2018; 148 (17): 171102


    Double hybrid (DH) density functionals are amongst the most accurate density functional approximations developed so far, largely due to the incorporation of correlation effects from unoccupied orbitals via second order perturbation theory (PT2). The xDH family of DH functionals calculate energy directly from orbitals optimized by a lower level approach like B3LYP, without self-consistent optimization. XYG3 and XYGJ-OS are two widely used xDH functionals that are known to be quite accurate at equilibrium geometries. Here, we show that the XYG3 and XYGJ-OS functionals can be ill behaved for stretched bonds well beyond the Coulson-Fischer point, predicting unphysical dipole moments and humps in potential energy curves for some simple systems like the hydrogen fluoride molecule. Numerical experiments and analysis show that these failures are not due to PT2. Instead, a large mismatch at stretched bond-lengths between the reference B3LYP orbitals and the optimized orbitals associated with the non-PT2 part of XYG3 leads to an unphysically large non-Hellman-Feynman contribution to first order properties like forces and electron densities.

    View details for DOI 10.1063/1.5031027

    View details for Web of Science ID 000431685500002

    View details for PubMedID 29739217

  • How Accurate Is Density Functional Theory at Predicting Dipole Moments? An Assessment Using a New Database of 200 Benchmark Values JOURNAL OF CHEMICAL THEORY AND COMPUTATION Hait, D., Head-Gordon, M. 2018; 14 (4): 1969-1981


    Dipole moments are a simple, global measure of the accuracy of the electron density of a polar molecule. Dipole moments also affect the interactions of a molecule with other molecules as well as electric fields. To directly assess the accuracy of modern density functionals for calculating dipole moments, we have developed a database of 200 benchmark dipole moments, using coupled cluster theory through triple excitations, extrapolated to the complete basis set limit. This new database is used to assess the performance of 88 popular or recently developed density functionals. The results suggest that double hybrid functionals perform the best, yielding dipole moments within about 3.6-4.5% regularized RMS error versus the reference values-which is not very different from the 4% regularized RMS error produced by coupled cluster singles and doubles. Many hybrid functionals also perform quite well, generating regularized RMS errors in the 5-6% range. Some functionals, however, exhibit large outliers, and local functionals in general perform less well than hybrids or double hybrids.

    View details for DOI 10.1021/acs.jctc.7b01252

    View details for Web of Science ID 000430023200013

    View details for PubMedID 29562129

  • A hybrid memory kernel approach for condensed phase non-adiabatic dynamics JOURNAL OF CHEMICAL PHYSICS Hait, D., Mavros, M. G., Van Voorhis, T. 2017; 147 (1): 014108


    The spin-boson model is a simplified Hamiltonian often used to study non-adiabatic dynamics in large condensed phase systems, even though it has not been solved in a fully analytic fashion. Herein, we present an exact analytic expression for the dynamics of the spin-boson model in the infinitely slow-bath limit and generalize it to approximate dynamics for faster baths. We achieve the latter by developing a hybrid approach that combines the exact slow-bath result with the popular non-interacting blip approximation (NIBA) method to generate a memory kernel that is formally exact to second-order in the diabatic coupling but also contains higher-order contributions approximated from the second-order term alone. This kernel has the same computational complexity as the NIBA, but is found to yield dramatically superior dynamics in regimes where the NIBA breaks down-such as systems with large diabatic coupling or energy bias. This indicates that this hybrid approach could be used to cheaply incorporate higher-order effects into second-order methods and could potentially be generalized to develop alternate kernel resummation schemes.

    View details for DOI 10.1063/1.4990739

    View details for Web of Science ID 000405089400057

    View details for PubMedID 28688393

  • Condensed phase electron transfer beyond the Condon approximation JOURNAL OF CHEMICAL PHYSICS Mavros, M. G., Hait, D., Van Voorhis, T. 2016; 145 (21): 214105


    Condensed phase electron transfer problems are often simplified by making the Condon approximation: the approximation that the coupling connecting two charge-transfer diabatic states is a constant. Unfortunately, the Condon approximation does not predict the existence of conical intersections, which are ubiquitous in both gas-phase and condensed-phase photochemical dynamics. In this paper, we develop a formalism to treat condensed-phase dynamics beyond the Condon approximation. We show that even for an extremely simple test system, hexaaquairon(ii)/hexaaquairon(iii) self-exchange in water, the electronic coupling is expected to fluctuate rapidly and non-Condon effects must be considered to obtain quantitatively accurate ultrafast nonequilibrium dynamics. As diabatic couplings are expected to fluctuate substantially in many condensed-phase electron transfer systems, non-Condon effects may be essential to quantitatively capture accurate short-time dynamics.

    View details for DOI 10.1063/1.4971166

    View details for Web of Science ID 000390603500041

    View details for PubMedID 28799393

  • Prediction of Excited-State Energies and Singlet Triplet Gaps of Charge-Transfer States Using a Restricted Open-Shell Kohn-Sham Approach JOURNAL OF CHEMICAL THEORY AND COMPUTATION Hait, D., Zhu, T., McMahon, D. P., Van Voorhis, T. 2016; 12 (7): 3353-3359


    Organic molecules with charge-transfer (CT) excited states are widely used in industry and are especially attractive as candidates for fabrication of energy efficient OLEDs, as they can harvest energy from nonradiative triplets by means of thermally activated delayed fluorescence (TADF). It is therefore useful to have computational protocols for accurate estimation of their electronic spectra in order to screen candidate molecules for OLED applications. However, it is difficult to predict the photophysical properties of TADF molecules with LR-TDDFT, as semilocal LR-TDDFT is incapable of accurately modeling CT states. Herein, we study absorption energies, emission energies, zero-zero transition energies, and singlet-triplet gaps of TADF molecules using a restricted open-shell Kohn-Sham (ROKS) approach instead and discover that ROKS calculations with semilocal hybrid functionals are in good agreement with experiments-unlike TDDFT, which significantly underestimates energy gaps. We also propose a cheap computational protocol for studying excited states with large CT character that is found to give good agreement with experimental results without having to perform any excited-state geometry optimizations.

    View details for DOI 10.1021/acs.jctc.6b00426

    View details for Web of Science ID 000379703800033

    View details for PubMedID 27267803