arXiv subjects

Martin Head-Gordon

Publications and source records attributed to Martin Head-Gordon.

At least 37 records · Page 2Linked to original sources

arXiv2025

Coupled-cluster pairing models for radicals with strong correlations

The pairing hierarchy of perfect pairing (PP), perfect quadruples (PQ) and perfect hextuples (PH) are sparsified coupled cluster models that are exact in a pairing active space for 2, 4, and 6 electron clusters, respectively. We describe and implement three extensions for radicals. First is the trivial generalization that does not correlate radical orbitals. The second model (PQr, PHr) includes terms that entangle pair indices and radical indices such that their maximum total number is 2 for PQ and 3 for PH (like their closed-shell versions). The third family of extended radical models (PPxr, PQxr, and PHxr) include cluster amplitudes that entangle up to 1, 2, and 3 pair indices with up to 1, 2, and 3 radical indices. Notably, PPxr and PQxr are exact for (3e,3o) and (5e,5o), respectively, while still having only $O(N)$ and $O(N^{2}$) amplitudes like their parent models (for $N$ paired electrons). Orbital optimization is considered for PPxr. A series of large-scale numerical tests of these models are presented for spin gaps, and ionization energies of polyenes and polyenyl radicals, ranging in size from ethene and allyl radical up to C$_{22}$H$_{24}$ in full-valence active spaces up to (122e,122o). The xR models perform best.

physics.chem-ph↗

arXiv2025

The Conundrum of Diffuse Basis Sets: A Blessing for Accuracy yet a Curse for Sparsity

Diffuse atomic orbital basis sets have proven to be essential to obtain accurate interaction energies, especially in regard to non-covalent interactions. However, they also have a detrimental impact on the sparsity of the one-particle density matrix (1-PDM), to a degree stronger than the spatial extent of the basis functions alone could explain. This is despite the fact that the matrix elements of the 1-PDM of insulators (systems with significant HOMO-LUMO gaps) are expected to decay exponentially with increasing real-space distance from the diagonal and the asymptotic decay rate is expected to have a well-defined basis set limit. The observed low sparsity of the 1-PDM appears to be independent of representation and even persists after projecting the 1-PDM onto a real-space grid, leading to the conclusion that this "curse of sparsity" is solely a basis set artifact, which, counterintuitively, becomes worse for larger basis sets, seemingly contradicting the notion of a well-defined basis set limit. We show that this is a consequence of the low locality of the contra-variant basis functions as quantified by the inverse overlap matrix $\mathbf{S}^{-1}$ being significantly less sparse than its covariant dual. Introducing the model system of an infinite non-interacting chain of helium atoms, we are able to quantify the exponential decay rate to be proportional to the diffuseness as well as local incompleteness of the basis set, meaning small and diffuse basis sets are affected the most. Finally, we propose one solution to the conundrum in the form of the complementary auxiliary basis set (CABS) singles correction in combination with compact, low l-quantum-number basis sets, showing promising results for non-covalent interactions.

physics.chem-ph↗

arXiv2024

Real-time propagation of adaptive sampling selected configuration interaction wave function

We have developed a new time propagation method, time-dependent adaptive sampling configuration interaction (TD-ASCI), to describe the dynamics of a strongly correlated system. We employ the short iterative Lanczos (SIL) method as the time-integrator, which provides a unitary, norm-conserving, and stable long-time propagation scheme. We used the TD-ASCI method to evaluate the time-domain correlation functions of molecular systems. The accuracy of the correlation function was assessed by Fourier transforming (FT) into the frequency domain to compute the dipole-allowed absorption spectra. The FT has been carried out with a short-time signal of the correlation function to reduce the computation time, using an efficient alternative FT scheme based on the ESPRIT signal processing algorithm. We have applied the {TD-ASCI} method to prototypical strongly correlated molecular systems and compared the absorption spectra to spectra evaluated using the equation of motion coupled cluster (EOMCC) method with a truncation at single-doubles-triples (SDT) level.

physics.chem-ph↗

arXiv2024

A static quantum embedding scheme based on coupled cluster theory

We develop a static quantum embedding scheme that utilizes different levels of approximations to coupled cluster (CC) theory for an active fragment region and its environment. To reduce the computational cost, we solve the local fragment problem using a high-level CC method and address the environment problem with a lower-level Møller-Plesset (MP) perturbative method. This embedding approach inherits many conceptual developments from the hybrid MP2 and CC works by Nooijen and Sherrill (J. Chem. Phys. 111, 10815 (1999), J. Chem. Phys. 122, 234110 (2005)). We go beyond those works here by primarily targeting a specific localized fragment of a molecule and also introducing an alternative mechanism to relax the environment within this framework. We will call this approach MP-CC. We demonstrate the effectiveness of MP-CC on several potential energy curves, and a set of thermochemical reaction energies, using CC with singles and doubles as the fragment solver, and MP2-like treatments of the environment. The results are substantially improved by the inclusion of orbital relaxation in the environment. Using localized bonds as the active fragment, we also report results for \ce{N=N} bond breaking in azomethane and for the central \ce{C-C} bond torsion in butadiene. We find that when the fragment Hilbert space size remains fixed (e.g., when determined by an intrinsic atomic orbital approach), the method achieves comparable accuracy with both a small and a large basis set. Additionally, our results indicate that increasing the fragment Hilbert space size systematically enhances the accuracy of observables, approaching the precision of the full CC solver.

physics.chem-ph↗

arXiv2024

The Role of Spin-Orbit Coupling on the Linear Absorption Spectrum and Intersystem Crossing Rate Coefficients of Ruthenium Polypyridyl Dyes

The successful use of molecular dyes for solar energy conversion requires efficient charge injection, which in turn requires the formation of states with sufficiently long lifetimes (e.g. triplets). The molecular structure elements that confer this property can be found empirically, however computational predictions using $\textit{ab initio}$ electronic structure methods are invaluable to identify structure-property relations for dye sensitizers. The primary challenge for simulations to elucidate the electronic and nuclear origins of these properties is a spin-orbit interaction which drives transitions between electronic states. In this work, we present a computational analysis of the spin-orbit corrected linear absorption cross sections and intersystem crossing rate coefficients for a derivative set of phosphonated tris(2,2'-bipyridine)ruthenium(2+) dye molecules. After sampling the ground state vibrational distributions, the predicted linear absorption cross sections indicate that the mixture between singlet and triplet states plays a crucial role in defining the line shape of the metal-to-ligand charge transfer bands in these derivatives. Additionally, an analysis of the intersystem crossing rate coefficients suggests that transitions from the singlet into the triplet manifolds are ultrafast with rate coefficients on the order of $10^{13}$ s$^{-1}$ for each dye molecule.

physics.chem-ph↗

arXiv2024

Spin parameter optimization for spin-polarized extended tight-binding methods

We present an optimization strategy for atom-specific spin-polarization constants within the spin-polarized GFN2-xTB framework, aiming to enhance the accuracy of molecular simulations. We compare a sequential and global optimization of spin parameters for hydrogen, carbon, nitrogen, oxygen, and fluorine. Sensitivity analysis using Sobol indices guides the identification of the most influential parameters for a given reference dataset, allowing for a nuanced understanding of their impact on diverse molecular properties. In the case of the W4-11 dataset, substantial error reduction was achieved, demonstrating the potential of the optimization. Transferability of the optimized spin-polarization constants over different properties, however, is limited, as we demonstrate by applying the optimized parameters on a set of singlet-triplet gaps in carbenes. Further studies on ionization potentials and electron affinities highlight some inherent limitations of current extended tight-binding methods that can not be resolved by simple parameter optimization. We conclude that the significantly improved accuracy strongly encourages the present re-optimization of the spin-polarization constants, whereas the limited transferability motivates a property-specific optimization strategy.

physics.chem-ph↗

arXiv2024

Measurement of Coherent Vibrational Dynamics with X-ray Transient Absorption Spectroscopy Simultaneously at the Carbon K- and Chlorine L$_{2,3}$- Edges

X-ray Transient Absorption Spectroscopy near the carbon K-edge (1s, $\sim$ 285 eV) and chlorine L$_{2,3}$ edges (2p, $\sim$ 200 eV) is used to study the nuclear dynamics of CCl$_4$ vibrationally activated by impulsive stimulated Raman scattering with a few-cycle 800 nm pump pulse. The totally symmetric stretching mode leads to a strong response in the inner-shell spectra, with the concerted elongation (contraction) in bond lengths leading to a red (blue) shift in the X-ray absorption energies associated with core-to-antibonding excitations. The relative slopes of the potential energy surfaces associated with the relevant core-excited states along the symmetric stretching mode are experimentally measured and compared to results from restricted open-shell Kohn-Sham calculations. A combination of experiment and theory indicates that the slope of the core-excited potential energy surface vs totally symmetric bond elongation is $-11.1 \pm 0.8$ eV/Å for the Cl 2p$\to7a_1^*$ excitation, $-9.0\pm0.6$ eV/Å for the Cl 2p$\to8t_2^*$ excitation and $-5.2\pm 0.4$ eV/Å for the C 1s$\to8t_2^*$ excitation, to 95% confidence. The much larger slopes for the Cl 2p excitations compared to the C 1s state are attributed to greater contributions from Cl to the $7a_1^*$ or $8t_2^*$ antibonding orbitals to which the inner-shell electrons are being excited. No net displacement of the center of the vibrational wavefunction along the other vibrational modes is induced by the pump pulse, leading to absence of transient signal. The results highlight the ability of X-ray Transient Absorption Spectroscopy to reveal nuclear dynamics involving tiny ($<0.01$ Å) atomic displacements and also provide direct measurement of forces on core-excited potential energy surfaces.

physics.chem-ph↗

arXiv2024

The Staggered Mesh Method: Accurate Exact Exchange towards the Thermodynamic Limit for Solids

In periodic systems, the Hartree-Fock (HF) exchange energy exhibits the slowest convergence of all HF energy components as the system size approaches the thermodynamic limit. We demonstrate that the recently proposed staggered mesh method for Fock exchange energy [Xing, Li, and Lin, Math. Comp., 2024], which is specifically designed to sidestep certain singularities in exchange energy evaluation, can expedite the finite-size convergence rate for the exact exchange energy across a range of insulators and semiconductors when compared to the regular and truncated Coulomb methods. This remains true even for two computationally cheaper versions of this new method, which we call Non-SCF and Split-SCF staggered mesh. Additionally, a sequence of numerical tests on simple solids showcases the staggered mesh method's ability to improve convergence towards the thermodynamic limit for band gaps, bulk moduli, equilibrium lattice dimensions, energies, and phonon force constants.

physics.comp-ph↗

arXiv2023

Programmable Simulations of Molecules and Materials with Reconfigurable Quantum Processors

Simulations of quantum chemistry and quantum materials are believed to be among the most important potential applications of quantum information processors, but realizing practical quantum advantage for such problems is challenging. Here, we introduce a simulation framework for strongly correlated quantum systems that can be represented by model spin Hamiltonians. Our approach leverages reconfigurable qubit architectures to programmably simulate real-time dynamics and introduces an algorithm for extracting chemically relevant spectral properties via classical co-processing of quantum measurement results. We develop a digital-analog simulation toolbox for efficient Hamiltonian time evolution utilizing digital Floquet engineering and hardware-optimized multi-qubit operations to accurately realize complex spin-spin interactions, and as an example present an implementation proposal based on Rydberg atom arrays. Then, we show how detailed spectral information can be extracted from these dynamics through snapshot measurements and single-ancilla control, enabling the evaluation of excitation energies and finite-temperature susceptibilities from a single-dataset. To illustrate the approach, we show how this method can be used to compute key properties of a polynuclear transition-metal catalyst and 2D magnetic materials.

quant-ph↗

arXiv2023

Generalization of one-center non orthogonal configuration interaction singles to open shell singlet reference states: Theory and application to valence-core pump-probe states in acetylacetone

We formulate a one-center non-orthogonal configuration interaction singles (1C-NOCIS) theory for the computation of core excited states of an initial singlet state with two unpaired electrons. This model, which we refer to as 1C-NOCIS two-electron open-shell (2eOS), is appropriate for computing the K-edge near-edge X-ray absorption spectra (NEXAS) of the valence excited states of closed-shell molecules relevant to pump-probe time-resolved (TR) NEXAS experiments. With inclusion of core hole relaxation effects and explicit spin adaptation, 1C-NOCIS 2eOS requires mild shifts to match experiment, is free of artifacts due to spin contamination, and can capture the high-energy region of the spectrum beyond the transitions into the singly occupied molecular orbitals (SOMO). Calculations on water and thymine illustrate the different key features of excited-state NEXAS, namely the core-to-SOMO transition as well as shifts and spin-splittings in the transitions analogous to those of the ground state. Finally, simulations of the TR-NEXAS of acetylacetone after excitation onto its pi to pi-star singlet excited state at the carbon K-edge - an experiment carried out recently - showcases the ability of 1C-NOCIS 2eOS to efficiently simulate NEXAS based on non-adiabatic molecular dynamics simulations.

physics.chem-ph↗

arXiv2023

Earth Mover's Distance as a metric to evaluate the extent of charge transfer in excitations using discretized real-space densities

This paper presents a novel theoretical measure, $μ^{\text{EMD}}$, based on the Earth Mover's Distance, for quantifying the density shift caused by electronic excitations in molecules. As input, the EMD metric uses only the discretized ground and excited state electron densities in real space, rendering it compatible with almost all electronic structure methods used to calculate excited states. The EMD metric is compared against other popular theoretical metrics for describing the extent of electron-hole separation in a wide range of excited states (valence, Rydberg, charge-transfer, etc). The results showcase the EMD metric's effectiveness across all excitation types and suggest that it is useful as an additional tool to characterize electronic excitations. The study also reveals that $μ^{\text{EMD}}$ can function as a promising diagnostic tool for predicting the failure of pure exchange-correlation functionals. Specifically, we show statistical relationships between the functional-driven errors, the exact exchange content within the functional, and the magnitude of $μ^{\text{EMD}}$ values.

physics.chem-ph↗

arXiv2023

Optimizing the Regularization in Size-Consistent Second-Order Brillouin-Wigner Perturbation Theory

Despite its simplicity and relatively low computational cost, second-order Møller-Plesset perturbation theory (MP2) is well-known to overbind noncovalent interactions between polarizable monomers and some organometallic bonds. In such situations, the pairwise-additive correlation energy expression in MP2 is inadequate. Although energy-gap dependent amplitude regularization can substantially improve the accuracy of conventional MP2 in these regimes, the same regularization parameter worsens the accuracy for small molecule thermochemistry and density-dependent properties. Recently, we proposed a repartitioning of Brillouin-Wigner perturbation theory that is size-consistent to second order (BW-s2), and a free parameter ($α$) was set to recover the exact dissociation limit of H2 in a minimal basis set. Alternatively $α$ can be viewed as a regularization parameter, where each value of $α$ represents a valid variant of BW-s2, which we denote as BW-s2($α$). In this work, we semi-empirically optimize $α$ for noncovalent interactions, thermochemistry, alkane conformational energies, electronic response properties, and transition metal datasets, leading to improvements in accuracy relative to the $\textit{ab initio}$ parameterization of BW-s2 and MP2. We demonstrate that the optimal $α$ parameter ($α = 4$) is more transferable across chemical problems than energy-gap-dependent regularization parameters. This is attributable to the fact that the BW-s2($α$) regularization strength depends on all of the information encoded in the t amplitudes rather than just orbital energy differences. While the computational scaling of BW-s2($α$) is iterative $O(N^5)$, this effective and transferable approach to amplitude regularization is a promising route to incorporate higher-order correlation effects at second-order cost.

physics.chem-ph↗

arXiv2023

The Doubles Connected Moments Expansion: A Tractable Approximate Horn-Weinstein Approach for Quantum Chemistry

Ab initio methods based on the second-order and higher connected moments, or cumulants, of a reference function have seen limited use in the determination of correlation energies of chemical systems throughout the years. Moment-based methods have remained unattractive relative to more ubiquitous methods, such as perturbation theory and coupled cluster theory, due in part to the intractable cost of assembling moments of high-order and poor performance of low-order expansions. Many of the traditional quantum chemical methodologies can be recast as a selective summation of perturbative contributions to their energy; using this familiar structure as a guide in selecting terms, we develop a scheme to approximate connected moments limited to double excitations. The tractable Double Connected Moments (DCM(N)) approximation is developed and tested against a multitude of common single-reference methods to determine its efficacy in the determination of the correlation energy of model systems and small molecules. The DCM(N) sequence of energies exhibits smooth convergence, with compute costs that scale as a non-iterative O(N^6) with molecule size, M. Numerical tests on correlation energy recovery for 55 small molecules comprising the G1 test set in the cc-pVDZ basis show that DCM(N) strongly outperforms MP2 and even CCD with a Hartree-Fock reference. When using an approximate Brueckner reference from orbital-optimized (oo) MP2, the resulting oo:DCM(N) energies converge to values more accurate than CCSD for 49 of 55 molecules.

physics.chem-ph↗

arXiv2023

Fantastical Excited State Optimized Structures and Where to Find Them

The quantum chemistry community has developed analytic forces for approximate electronic excited states to enable walking on excited state potential energy surfaces (PES). One can thereby computationally characterize excited state minima and saddle points. Always implicit in using this machinery is the fact that an excited state PES only exists within the realm of the Born-Oppenheimer approximation, where the nuclear and electronic degrees of freedom separate. This work demonstrates through ab initio calculations and simple nonadiabatic dynamics that some excited state minimum structures are fantastical: they appear to exist as stable configurations only as a consequence of the PES construct, rather than being physically observable. One such case is the S2 excited state of phosphine and a second case are local minima of a number of states of tris(bipyridine)ruthenium(II). Each fantastical structure exhibits an unphysically high predicted harmonic frequency and associated force constant. This fact can serve as a valuable diagnostic of when an optimized excited state structure is non-observable. Their origin lies in the coupling between different electronic states, and the resulting avoided crossings. The upper state may exhibit a minimum very close to the crossing, where the force constant relates to the strength of the electronic coupling rather than to any characteristic excited state vibration. Nonadiabatic dynamics results using a Landau-Zener model illustrate that fantastical excited state structures have extremely short lifetimes on the order of a few femtoseconds. Their appearance in a calculation signals the presence of a nearby avoided crossing or conical intersection through which the system will rapidly cross to a lower surface.

physics.chem-ph↗

arXiv2023

Greater Transferability and Accuracy of Norm-conserving Pseudopotentials using Nonlinear Core Corrections

We present an investigation into the transferability of pseudopotentials (PPs) with a nonlinear core correction (NLCC) using the Goedecker, Teter, and Hutter (GTH) protocol across a range of pure GGA, meta-GGA and hybrid functionals, and their impact on thermochemical and non-thermochemical properties. The GTH-NLCC PP for the PBE density functional demonstrates remarkable transferability to the PBE0 and $ω$B97X-V exchange-correlation functionals, and relative to no NLCC, improves agreement significantly for thermochemical benchmarks compared to all-electron calculations. On the other hand, the B97M-rV meta-GGA functional performs poorly with the PBE-derived GTH-NLCC PP, which is mitigated by reoptimizing the NLCC parameters for this specific functional. The findings reveal that atomization energies exhibit the greatest improvements from use of the NLCC, which thus provides an important correction needed for covalent interactions relevant to applications involving chemical reactivity. Finally we test the NLCC-GTH PPs when combined with medium-size TZV2P molecularly optimized (MOLOPT) basis sets which are typically utilized in condensed phase simulations, and show that they lead to consistently good results when compared to all-electron calculations for atomization energies, ionization potentials, barrier heights, and non-covalent interactions, but lead to somewhat larger errors for electron affinities.

physics.chem-ph↗

arXiv2023

Probing C-I Bond Fission in the UV Photochemistry of 2-Iodothiophene with Core-to-Valence Transient Absorption Spectroscopy

The UV photochemistry of small heteroaromatic molecules serves as a testbed for understanding fundamental photoinduced transformations in moderately complex compounds, including isomerization, ring-opening, and molecular dissociation. Here, a combined experimental-theoretical study of 268 nm UV light-induced dynamics in 2-iodothiophene (C$_4$H$_3$IS) is performed. The dynamics are experimentally monitored with a femtosecond XUV probe pulse that measures iodine N-edge 4d core-to-valence transitions. Experiments are complemented by density functional theory calculations of both the pump-pulse induced valence excitations as well as the XUV probe-induced core-to-valence transitions. Possible intramolecular relaxation dynamics are investigated by ab initio molecular dynamics simulations. Gradual absorption changes up to ~0.5-1 ps after excitation are observed for both the parent molecular species and emerging iodine fragments, with the latter appearing with a characteristic rise time of 160$\pm$30 fs. Comparison of spectral intensities and energies with the calculations identify an iodine dissociation pathway initiated by a predominant $π\toπ^*$ excitation. In contrast, initial excitation to a nearby n$_\perp\toσ^*$ excited state appears unlikely based on a significantly smaller oscillator strength and the absence of any corresponding XUV absorption signatures. Excitation to the $π\toπ^*$ state is followed by contraction of the C-I bond, enabling a nonadiabatic transition to a dissociative $π\toσ_\textrm{C-I}^*$ state. For the subsequent fragmentation, a narrow bond-length region along the C-I stretch coordinate between 230 and 280 pm is identified, where the transition between the parent molecule and the thienyl radical + iodine atom products becomes prominent in the XUV spectrum due to rapid localization of two singly-occupied molecular orbitals on the two fragments.

physics.chem-ph↗

arXiv2023

A New View on Density Corrected DFT: Can One Get a Better Answer for a Good Reason?

Despite its widespread use, density functional theory (DFT) has several notable areas of failure; perhaps the most well-studied of these failures is self-interaction error (SIE). Density corrected DFT (DC-DFT) was proposed as a potential solution to systems where SIE causes traditional DFT to fail. The Hartree-Fock (HF) density is then used for cases where the DFT energy is suitable but the self-consistent density is erroneous. In this study, we investigate the utility of the higher quality orbital optimized MP2 densities in DC-DFT for barrier heights and halogen bonded complexes. For functionals such as PBE and r$^2$SCAN, find that these densities yield worse results than the HF density due to favorable cancellation between the density-driven and functional-driven errors, confirming a recent study. Error decomposition reveals functional driven error, not density driven error, to be the primary cause of inaccuracy in DFT calculations where SIE is prominent. We therefore advise caution when using HF-DFT, because the only rigorous way to remove large functional-driven errors in lower rungs of Jacob's ladder is by climbing to higher rungs that include exact exchange. We recommend that better functionals be improved by using a better density in SIE-sensitive cases. Examples support the value of this variant of DC-DFT. We also emphasize that DC-DFT potential energy surfaces have first derivative discontinuities at Coulson-Fischer points, in contrast to the second derivative discontinuities in SCF solutions.

physics.chem-ph↗

arXiv2023

Highly Accurate Prediction of NMR Chemical Shifts from Low-Level Quantum Mechanics Calculations Using Machine Learning

Theoretical predictions of NMR chemical shifts from first-principles can greatly facilitate experimental interpretation and structure identification. However, accurate prediction of chemical shifts using the best coupled cluster methods can be prohibitively expensive for systems larger than ten to twenty non-hydrogen atoms on today's computers. By contrast machine learning methods offer inexpensive alternatives but are hampered by generalization to molecules outside the original training set. Here we propose a novel machine learning feature representation informed by intermediate calculations of atomic chemical shielding tensors within a molecular environment using an inexpensive quantum mechanics method, and training it to predict NMR chemical shieldings of a high-level composite theory that is comparable to CCSD(T) in the complete basis set limit. The inexpensive shift machine learning (iShiftML) algorithm is trained through a new progressive active learning workflow that reduces the total number of expensive calculations required when constructing the dataset, while allowing the model to continuously improve on data it has never seen. Furthermore, we show that the error estimations from our model correlate quite well with actual errors to provide confidence values on new predictions. We illustrate the predictive capacity of iShiftML across gas phase experimental chemical shifts for small organic molecules and much larger and more complex natural products in which we can accurately differentiate between subtle diastereomers based on chemical shift assignments.

physics.chem-ph↗