arXiv subjects

Martin Head-Gordon

Publications and source records attributed to Martin Head-Gordon.

At least 55 records · Page 3Linked to original sources

arXiv2023

Repartitioned Brillouin-Wigner Perturbation Theory with a Size-Consistent Second-Order Correlation Energy

Second-order Møller-Plesset perturbation theory (MP2) often breaks down catastrophically in small-gap systems, leaving much to be desired in its performance for myriad chemical applications such as noncovalent interactions, thermochemistry, and dative bonding in transition metal complexes. This divergence problem has reignited interest in Brillouin-Wigner perturbation theory (BWPT), which is regular at all orders but lacks size-consistency and extensivity, severely limiting its application to chemistry. In this work, we propose an alternative partitioning of the Hamiltonian that leads to a regular BWPT perturbation series that, through second order, is size-extensive, size-consistent (provided its Hartree-Fock reference is also), and orbital invariant. Our second-order size-consistent Brillouin-Wigner (BW-s2) approach is capable of describing the exact dissociation limit of H$_2$ in a minimal basis set regardless of the spin-polarization of the reference orbitals. More broadly, we find that BW-s2 offers improvements relative to MP2 for covalent bond breaking, noncovalent interaction energies, and metal/organic reaction energies, while rivaling coupled-cluster with single and double substitutions (CCSD) for thermochemical properties.

physics.chem-ph↗

arXiv2023

Even Faster Exact Exchange for Solids via Tensor Hypercontraction

Hybrid density functional theory (DFT) remains intractable for large periodic systems due to the demanding computational cost of exact exchange. We apply the tensor hypercontraction (THC) (or interpolative separable density fitting) approximation to periodic hybrid DFT calculations with Gaussian-type orbitals. This is done to lower the computational scaling with respect to the number of basis functions ($N$), and $\mathbf k$-points ($N_k$). Additionally, we propose an algorithm to fit only occupied orbital products via THC (i.e. a set of points, $N_\text{ISDF}$) to further reduce computation time and memory usage. This algorithm has linear scaling cost with $\mathbf k$-points, no explicit dependence of $N_\text{ISDF}$ on basis set size, and overall cubic scaling with unit cell size. Significant speedups and reduced memory usage may be obtained for moderately sized systems, with additional gains for large systems. Adequate accuracy can be obtained using THC-oo-K for self-consistent calculations. We perform illustrative hybrid density function theory calculations on the benzene crystal in the basis set and thermodynamic limits to highlight the utility of this algorithm.

physics.comp-ph↗

arXiv2023

Analytical harmonic vibrational frequencies with VV10-containing density functionals: Theory, efficient implementation, and benchmark assessments

VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, ωB97X-V and the hybrid mGGA, ωB97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and efficient implementation of the analytical second derivatives of the VV10 energy. The additional compute cost of the VV10 contributions to analytical frequencies is shown to be small in all but the smallest basis sets for recommended grid sizes. This study also reports the assessment of VV10-containing functionals for predicting harmonic frequencies using the analytical second derivative code. The contribution of VV10 to simulating harmonic frequencies is shown to be small for small molecules but important for systems where weak interactions are important, such as water clusters. In the latter cases, B97M-V, ωB97M-V, and ωB97X-V perform very well. The convergence of frequencies with respect to grid size and atomic orbital basis set size is studied and recommendations reported. Finally, scaling factors to allow comparison of scaled harmonic frequencies with experimental fundamental frequencies and to predict zero-point vibrational energy are presented for some recently developed functionals (including r2SCAN, B97M-V, ωB97X-V, M06-SX, and ωB97M-V).

physics.chem-ph↗

arXiv2022

Femtosecond Symmetry Breaking and Coherent Relaxation of Methane Cations at the Carbon K-Edge

Understanding the relaxation pathways of photoexcited molecules is essential to gain atomistic level insight into photochemistry. Herein, we perform a time-resolved study of ultrafast molecular symmetry breaking via geometric relaxation (Jahn-Teller distortion) on the methane cation. Attosecond transient absorption spectroscopy with soft X-rays at the carbon K-edge reveals that the distortion occurs within $10\pm 2$ femtoseconds after few-femtosecond strong-field ionization of methane. The distortion activates coherent oscillations in the scissoring vibrational mode of the symmetry broken cation, which are detected in the X-ray signal. These oscillations are damped within $58\pm13$ femtoseconds, as vibrational coherence is lost with the energy redistributing into lower-frequency vibrational modes. This study completely reconstructs the molecular relaxation dynamics of this prototypical example and opens new avenues for exploring complex systems.

physics.chem-ph↗

arXiv2022

Ultrafast X-ray Spectroscopy of Intersystem Crossing in Hexafluoroacetylacetone: Chromophore Photophysics and Spectral Changes in the Face of Electron Withdrawing Groups

Intersystem crossings between singlet and triplet states represent a crucial relaxation pathway in photochemical processes. Herein, we probe the intersystem crossing in hexafluoro-acetylacetone with ultrafast X-ray transient absorption spectroscopy at the carbon K-edge. We observe the excited state dynamics following excitation with 266 nm UV light to the $^1ππ^{*}$ (S$_2$) state with element and site-specificity using a broadband soft X-ray pulse produced by high harmonic generation. These results are compared to X-ray spectra computed from orbital optimized density functional theory methods. It is found that the electron withdrawing fluorine atoms decongest the X-ray absorption spectrum by enhancing separation between features originating from different carbon atoms. This facilitates the elucidation of structural and electronic dynamics at the chromophore. The evolution of the core-to-valence resonances at the carbon K-edge reveals an ultrafast population transfer between the $^1nπ^{*}$ (S$_1$) and $^3ππ^{*}$ (T$_1$) states on a $1.6\pm0.4$ ps timescale, which is similar to the 1.5 ps timescale earlier observed for acetylacetone [J. Am. Chem. Soc. 139, 16576 (2017)]. It therefore appears that terminal fluorination has little influence on the intersystem crossing rate of the acetylacetone chromophore. In addition, the significant role of hydrogen-bond opened and twisted rotational isomers is elucidated in the excited state dynamics by comparison of the experimental transient X-ray spectra with theory.

physics.chem-ph↗

arXiv2022

Efficient Calculation of NMR Shielding Constants Using Composite Method Approximations and Locally Dense Basis Sets

This paper presents a systematic study of applying composite method approximations with locally dense basis sets (LDBS) to efficiently calculate NMR shielding constants in small and medium-sized molecules. The pcSseg-n series of basis sets are shown to have similar accuracy to the pcS-n series when n $\geq1$ and can slightly reduce compute costs. We identify two different LDBS partition schemes that perform very effectively for density functional calculations. We select a large subset of the recent NS372 database containing 290 H, C, N, and O shielding values evaluated by reference methods on 106 molecules to carefully assess methods of the high, medium, and low compute costs to make practical recommendations. Our assessment covers conventional electronic structure methods (DFT and wavefunction) with global basis calculations, as well as their use in one of the satisfactory LDBS approaches, and a range of composite approaches, also with and without LDBS. Altogether 99 methods are evaluated. On this basis, we recommend different methods to reach three different levels of accuracy and time requirements across the four nuclei considered.

physics.chem-ph↗

arXiv2022

Faster Exact Exchange for Solids via occ-RI-K: Application to Combinatorially Optimized Range-Separated Hybrid Functionals for Simple Solids with Pseudopotentials Near the Basis Set Limit

In this work, we developed and showcased the occ-RI-K algorithm to compute the exact exchange contribution in density functional calculations of solids near the basis set limit. Within the gaussian planewave (GPW) density fitting, our algorithm achieves a 1-2 orders of magnitude speedup compared to conventional GPW algorithms. Since our algorithm is well-suited for simulations with large basis sets, we applied it to 12 hybrid density functionals with pseudopotentials and a large uncontracted basis set to assess their performance on band gaps of 25 simple solids near the basis set limit. The largest calculation performed in this work involves 16 electrons and 350 basis functions in the unit cell utilizing a 6x6x6 k-mesh. With 20-27\% exact exchange, global hybrid functionals (B3LYP, PBE0, revPBE0, B97-3, SCAN0) perform similarly with a root-mean-square-deviation (RMSD) of 0.61-0.77 eV while other global hybrid functionals such as M06-2X (2.02 eV) and MN15 (1.05 eV) show higher RMSD due to their increased fraction of exact exchange. A short-range hybrid functional, HSE achieves a similar RMSD (0.76 eV) but shows a noticeable underestimation of band gaps due to the complete lack of long-range exchange. We found that two combinatorially optimized range-separated hybrid functionals, $ω$B97X-rV (3.94 eV) and $ω$B97M-rV (3.40 eV), and the two other range separated hybrid functionals, CAM-B3LYP (2.41 eV) and CAM-QTP01 (4.16 eV), significantly overestimate the band gap because of their high fraction of long-range exact exchange. Given the failure of $ω$B97X-rV and $ω$B97M-rV, we have yet to find a density functional that offers consistent performance for both molecules and solids. Our algorithm development and density functional assessment will serve as a stepping stone towards developing more accurate hybrid functionals and applying them to practical applications.

physics.chem-ph↗

arXiv2022

The symmetric quasi-classical model using on-the-fly time-dependent density functional theory within the Tamm-Dancoff approximation

The primary computational challenge when simulating nonadiabatic ab initio molecular dynamics is the unfavorable compute costs of electronic structure calculations with molecular size. Simple electronic structure theories, like time-dependent density functional theory within the Tamm-Dancoff approximation (TDDFT/TDA), alleviate this cost for moderately sized molecular systems simulated on realistic time scales. Although TDDFT/TDA does have some limitations in accuracy, an appealing feature is that, in addition to including electron correlation through the use of a density functional, the cost of calculating analytic nuclear gradients and nonadiabatic coupling vectors is often computationally feasible even for moderately-sized basis sets. In this work, some of the benefits and limitations of TDDFT/TDA are discussed and analyzed with regard to its applicability as a "back-end" electronic structure method for the symmetric quasi-classical Meyer-Miller model (SQC/MM). In order to investigate the benefits and limitations of TDDFT/TDA, SQC/MM is employed to predict and analyze a prototypical example of excited-state hydrogen transfer in gas-phase malonaldehyde. Then, the ring-opening dynamics of selenophene are simulated which highlight some of the deficiencies of TDDFT/TDA. Additionally, some new algorithms are proposed that speed up the calculation of analytic nuclear gradients and nonadiabatic coupling vectors for a set of excited electronic states.

physics.chem-ph↗

arXiv2022

Electron-Affinity Time-Dependent Density Functional Theory: Formalism and Applications to Core-Excited States

The particle-hole interaction problem is longstanding within time-dependent density functional theory (TDDFT) and leads to extreme errors in the prediction of K-edge X-ray absorption spectra (XAS). We derive a linear-response formalism that uses optimized orbitals of the n-1-electron system as reference, building orbital relaxation and a proper hole into the initial density. Our approach is an exact generalization of the static-exchange approximation that ameliorates particle-hole interaction error associated with the adiabatic approximation and reduces errors in TDDFT XAS by orders of magnitude. With a statistical performance of just 0.5 eV root-mean-square error and the same computational scaling as TDDFT under the core-valence separation approximation, we anticipate that this approach will be of great utility in XAS calculations of large systems.

physics.chem-ph↗

arXiv2022

Accurate core excitation and ionization energies from a state-specific coupled-cluster singles and doubles approach

We investigate the use of orbital-optimized references in conjunction with single-reference coupled-cluster theory with single and double substitutions (CCSD) for the study of core excitations and ionizations of 18 small organic molecules, without any use of response theory or equation-of-motion formalisms. Three schemes are employed to successfully address the convergence difficulties associated with the coupled-cluster equations, and the spin contamination resulting from the use of a spin symmetry-broken reference, in the case of excitations. In order to gauge the inherent potential of the methods studied, an effort is made to provide reasonable basis set limit estimates for the transition energies. Overall, we find that the two best-performing schemes studied here for Delta-CCSD are capable of predicting excitation and ionization energies with errors comparable to experimental accuracies. The proposed Delta-CCSD schemes seem to fare better than the widely used equation-of-motion CCSD (EOM-CCSD) with core-valence separation protocol, with statistical errors being reduced by more than a factor of two when compared to FC-CVS-EOM-CCSD.

physics.chem-ph↗

arXiv2022

Jahn-Teller Distortion and Dissociation of CCl$_4^+$ by Transient X-ray Spectroscopy Simultaneously at the Carbon K- and Chlorine L-Edge

X-ray Transient Absorption Spectroscopy (XTAS) and theoretical calculations are used to study CCl$_4^+$ prepared by 800 nm strong-field ionization. XTAS simultaneously probes atoms at the carbon K-edge (280-300 eV) and chlorine L-edge (195-220 eV). Comparison of experiment to X-ray spectra computed by orbital-optimized density functional theory (OO-DFT) indicates that after ionization, CCl$_4^+$ undergoes symmetry breaking driven by Jahn-Teller distortion away from the initial tetrahedral structure (T$_d$) in 6$\pm$2 fs. The resultant symmetry-broken covalently bonded form subsequently separates to a noncovalently bound complex between CCl$_3^+$ and Cl over 90$\pm$10 fs, which is again predicted by theory. Finally, after more than 800 fs, L-edge signals for atomic Cl are observed, indicating dissociation to free CCl$_3^+$ and Cl. The results for Jahn-Teller distortion to the symmetry-broken form of CCl$_4^+$ and formation of the Cl -- CCl$_3^+$ complex characterize previously unobserved new species along the route to dissociation.

physics.chem-ph↗

arXiv2022

Say NO to Optimization: A Non-Orthogonal Quantum Eigensolver

A balanced description of both static and dynamic correlations in electronic systems with nearly degenerate low-lying states presents a challenge for multi-configurational methods on classical computers. We present here a quantum algorithm utilizing the action of correlating cluster operators to provide high-quality wavefunction ansätze employing a non-orthogonal multireference basis that captures a significant portion of the exact wavefunction in a highly compact manner, and that allows computation of the resulting energies and wavefunctions at polynomial cost with a quantum computer. This enables a significant improvement over the corresponding classical non-orthogonal solver, which incurs an exponential cost when evaluating off-diagonal matrix elements between the ansatz states, and is therefore intractable. We implement the non-orthogonal quantum eigensolver (NOQE) here with an efficient ansatz parameterization inspired by classical quantum chemistry methods that succeed in capturing significant amounts of electronic correlation accurately. By taking advantage of classical methods for chemistry, NOQE provides a flexible, compact, and rigorous description of both static and dynamic electronic correlation, making it an attractive method for the calculation of electronic states of a wide range of molecular systems.

quant-ph↗

arXiv2022

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

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 performance and accuracy. The functionals $ω$B97X-D and BMK are found to offer the best performance overall with a Root-Mean Square Error (RMSE) of 0.28 eV, better than the computationally more demanding CIS(D) wavefunction method with a RMSE of 0.36 eV. The results also suggest that Jacob's ladder still holds for TDDFT excitation energies, though hybrid 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.

physics.chem-ph↗

arXiv2022

Relativistic Orbital Optimized Density Functional Theory for Accurate Core-Level Spectroscopy

Core-level spectra of 1s electrons of elements heavier than Ne show significant relativistic effects. We combine advances in orbital optimized DFT (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 $\sim 0.5$ eV RMS error vs 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.

physics.chem-ph↗

arXiv2022

Computing X-ray absorption spectra from linear-response particles atop optimized holes

State specific orbital optimized density functional theory (OO-DFT) methods like 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 work, we present an approach to generate an approximate core-excited state density for use with the ROKS energy ansatz, that 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 use of electron-addition configuration interaction singles (EA-CIS) to obtain the particle level. This hybrid approach can be viewed as a DFT generalization of the static-exchange (STEX) method, and can attain $\sim 0.6$ eV RMS error for the K-edges of C-F through the use of local functionals like 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 for obtaining OO-DFT quality spectra. ROKS(STEX) therefore appears to be a useful technique for efficient prediction of X-ray absorption spectra.

physics.chem-ph↗

arXiv2021

Changes in polarization dictate necessary approximations for modeling electronic de-excitation intensity: an application to X-ray emission

We systematically investigate the underlying relations among different levels of approximation for simulating electronic de-excitations, with a focus on modeling X-ray emission spectroscopy (XES). Using Fermi's golden rule and explicit modeling of the initial, core-excited state and the final, valence-hole state, we show that XES can be accurately modeled by using orbital optimization for the various final states within a Slater-determinant framework. However, in this paper, we introduce a much cheaper approach reliant only on a single self-consistent field for all the final states, and show that it is typically sufficient. Further approximations reveal that these fundamentally many-body transitions can be reasonably approximated by projections of ground state orbitals, but that the ground state alone is insufficient. Furthermore, except in cases where the core-ionization induces negligible changes in polarization, linear-response approaches within the adiabatic approximation will have difficulty in accurately modeling de-excitation to the core level. Therefore, change in the net dipole moment of the valence electrons can serve as a metric for the validity of the linear-response approximation.

cond-mat.mtrl-sci↗

arXiv2021

Approaching the Basis Set Limit in Gaussian-Orbital-Based Periodic Calculations with Transferability: Performance of Pure Density Functionals for Simple Semiconductors

Simulating solids with quantum chemistry methods and Gaussian-type orbitals (GTOs) has been gaining popularity. Nonetheless, there are few systematic studies that assess the basis set incompleteness error (BSIE) in these GTO-based simulations over a variety of solids. In this work, we report a GTO-based implementation for solids, and apply it to address the basis set convergence issue. We employ a simple strategy to generate large uncontracted (unc) GTO basis sets, that we call the unc-def2-GTH sets. These basis sets exhibit systematic improvement towards the basis set limit as well as good transferability based on application to a total of 43 simple semiconductors. Most notably, we found the BSIE of unc-def2-QZVP-GTH to be smaller than 0.7 m$E_h$ per atom in total energies and 20 meV in band gaps for all systems considered here. Using unc-def2-QZVP-GTH, we report band gap benchmarks of a combinatorially designed meta generalized gradient functional (mGGA), B97M-rV, and show that B97M-rV performs similarly (a root-mean-square-deviation (RMSD) of 1.18 eV) to other modern mGGA functionals, M06-L (1.26 eV), MN15-L (1.29 eV), and SCAN (1.20 eV). This represents a clear improvement over older pure functionals such as LDA (1.71 eV) and PBE (1.49 eV) though all these mGGAs are still far from being quantitatively accurate. We also provide several cautionary notes on the use of our uncontracted bases and on future research on GTO basis set development for solids.

physics.chem-ph↗

arXiv2021

NewtonNet: A Newtonian message passing network for deep learning of interatomic potentials and forces

We report a new deep learning message passing network that takes inspiration from Newton's equations of motion to learn interatomic potentials and forces. With the advantage of directional information from trainable latent force vectors, and physics-infused operators that are inspired by the Newtonian physics, the entire model remains rotationally equivariant, and many-body interactions are inferred by more interpretable physical features. We test NewtonNet on the prediction of several reactive and non-reactive high quality ab initio data sets including single small molecule dynamics, a large set of chemically diverse molecules, and methane and hydrogen combustion reactions, achieving state-of-the-art test performance on energies and forces with far greater data and computational efficiency than other deep learning models.

physics.chem-ph↗