arXiv subjects

Martin Head-Gordon

Publications and source records attributed to Martin Head-Gordon.

At least 19 recordsLinked to original sources

arXiv2026

Efficient, precise DFT calculations of NMR shieldings: Revisiting the finite field approach

Absolute nuclear magnetic shielding constants and relative chemical shifts are second-derivative response properties that underpin the interpretation of Nuclear Magnetic Resonance (NMR) spectra and provide critical insights into the structural and electronic environments of diverse chemical systems. However, their accurate computation is often constrained by the need for method-specific, analytical response implementation, and therefore is particularly challenging for non-variational, correlated wavefunction methods where analytical second derivatives are frequently unavailable. Here we present a scalable framework that computes NMR shielding tensors through finite magnetic field differentiation of complex-valued, gauge-including atomic-orbital (GIAO) based self-consistent field (SCF) calculations. By combining hybrid MPI and OpenMP parallelization and resolution-of-identity (RI) approximation-based Coulomb (J) and Exchange (K) implementation and mixed numerical/analytical derivatives computational scheme, we achieve very good efficiency for hybrid density functional theory (DFT) NMR shielding, relative to existing state-of-the-art analytic implementations across realistic chemical systems of various sizes. Forward differentiation with optimal step sizes derived from rigorous error analysis retains favorable numerical errors much smaller than experimental uncertainty or intrinsic DFT errors. The results demonstrate that RI-accelerated finite magnetic field calculations can obtain DFT-level NMR shielding constants very precisely, providing a scalable foundation for extensions to more advanced quantum chemistry methods in future work.

physics.chem-ph↗

arXiv2026

An embedding method with constant potential boundary conditions

We present a self-consistent field framework for finite embedded quantum-chemical clusters with constant potential boundary conditions. The coupling is realized through an energy-independent self-energy commonly employed in quantum-transport calculations within the wide-band approximation. Starting from the corresponding non-equilibrium Green's function formalism, we derive an analytic expression for the one-particle density matrix update that can be incorporated into conventional Hartree--Fock and density functional theory. The resulting non-Hermitian self-consistent field equations are solved using adapted Pulay-type mixing schemes. Applications to a quasi-periodic hydrogen ring demonstrate that a finite fragment coupled through an optimized self-energy accurately reproduces the polarization response of the extended system, while calculations on a lithium cluster capture metallic charge transfer and fractional occupations under open-boundary conditions. The proposed framework establishes practical grand-canonical boundary conditions for finite quantum-chemical clusters and lays the methodological foundation for quantum embedding methods for electrochemical systems.

physics.chem-ph↗

arXiv2026

Reduction of finite-size effects for second-order M{\o}ller-Plesset perturbation theory with singularity subtraction

Second-order Moller-Plesset perturbation theory (MP2) provides accurate correlation energies for periodic systems but suffers from finite-size errors (FSEs) that have inverse volume scaling due to the Coulomb kernel singularity in reciprocal space. This error scaling limits the routine applicability of MP2 to real materials, requiring prohibitively dense k-point meshes for convergence toward the thermodynamic limit (TDL). We introduce MP2 singularity subtraction (MP2SS), a systematic approach that applies the singularity subtraction strategy to reduce MP2 FSEs. The method employs auxiliary functions and fitting procedures that consider both the singularities present at the origin in reciprocal space and also the discontinuities in the MP2 structure factor that arise from finite k-point sampling. We present three possible MP2SS configurations (Gaussian, exponential, and tuned) which use different combinations of decay functions and demonstrate their performance for gapped systems. All MP2SS configurations consistently achieve millihartree accuracy for correlation energies at coarser k-point meshes than with no correction. Our results establish singularity subtraction as a powerful and flexible approach for mitigating finite-size errors in periodic correlation methods and provide a foundation for extending the technique to higher-order perturbation theories and other post-SCF methods.

physics.comp-ph↗

arXiv2026

DFT-assisted natural abundance 13C zero-field NMR via optical magnetometry

Zero-field (ZF) nuclear magnetic resonance (NMR) spectroscopy probes scalar J-couplings between nuclei while dispensing with large homogeneous magnetic fields, enabling low-cost and geometrically flexible detection, including through conductive enclosures. Despite these advantages, its broader use for chemical analysis has been limited by sensitivity and by the difficulty of predicting the dense spectral multiplets that arise at zero field. Here we demonstrate natural-abundance (1.1%) 13C ZF spectroscopy on off-the-shelf liquids using a compact commercial 87Rb magnetometer for the first time, without hyperpolarization or special sample preparation. Instrumental advances yield improved sensitivity, <250-mHz linewidths and >week-long stability, enabling isotopomer-resolved fingerprint spectra across a 13-molecule library, including the ability to discern rare (0.0121%) doubly 13C-labelled species. In parallel, we demonstrate vibrationally corrected density-functional theory (DFT) based prediction of ZF NMR spectra for chemically diverse molecules with few-hertz accuracy. Comparing experiment with these calculations renders residual deviations as chemically informative, reporting on hydrogen bonding, hydration and ion pairing at high ionic strength. Together, these results contribute towards DFT-assisted ZF NMR as a general platform for field-constraint-free molecular identification and for extracting transient solution-state structure from responsive J-coupling observables.

physics.chem-ph↗

arXiv2026

Reaching for the performance limit of hybrid density functional theory for molecular chemistry

Density functional theory (DFT) offers an exceptional balance between accuracy and efficiency, but practical density functional approximations face an unavoidable trade-off among simplicity, accuracy, and transferability. A systematic protocol is therefore needed to develop functionals that are reliably most accurate within a chosen application domain. Here we present such a protocol by combining constraint enforcement, flexible functional forms, and modern optimization. Applying this strategy to the range-separated hybrid (RSH) meta-GGA framework, we obtain the carefully optimized and appropriately constrained hybrid (COACH) functional. Across broad molecular benchmarks, COACH improves both accuracy and transferability relative to leading RSH meta-GGAs, including \omegaB97M-V, while retaining the computational practicality of its rung. Finally, our analysis of the remaining trade-offs and saturation behavior suggests that further systematic progress will likely require the incorporation of genuinely nonlocal information.

physics.chem-ph↗

arXiv2026

Consistent inclusion of triple substitutions within a coupled cluster based static quantum embedding theory

We incorporate a solver for the fragment problem with accuracy beyond coupled cluster singles and doubles (CCSD) into the previously proposed static embedding framework, MPCC. To this end, we employ a CCSDT solver for the fragment subsystem. For the environment subsystem, we construct a perturbative estimate of the triples amplitudes, explicitly accounting for feedback from all fragment amplitudes. The resulting approach is denoted MPCCSDT(pt). We further introduce a more complete formulation in which feedback from the environment amplitudes to the fragment amplitudes is also included. This scheme involves an iterative treatment of the environment triples amplitudes and is denoted MPCCSDT(it). In addition, we assess the accuracy of the previously proposed low-level method by introducing a modified low-level approach that incorporates a lowest-order treatment of selected long-range effects, including spin fluctuations and charge polarization. All resulting approaches may be viewed as post-CCSD(T) methods. We therefore consider test cases for which CCSD(T) exhibits substantial deviations from CCSDT. Our results demonstrate that inclusion of triples amplitudes at the fragment level alone is insufficient; a perturbative treatment of the environment triples amplitudes is required. For many energy-difference applications, feedback from the environment triples amplitudes to the fragment amplitudes, is not essential, but it does play a role in the very challenging molecules. A very interesting finding from our study is that in some challenging cases, we need an improved (second-order) perturbative method for the SD amplitudes, going beyond the first-order one used in our earlier work.

physics.chem-ph↗

arXiv2025

An algorithm for atom-centered lossy compression of the atomic orbital basis in density functional theory calculations

Large atomic-orbital (AO) basis sets of at least triple and preferably quadruple-zeta (QZ) size are required to adequately converge Kohn-Sham density functional theory (DFT) calculations towards the complete basis set limit. However, incrementing the cardinal number by one nearly doubles the AO basis dimension, and the computational cost scales as the cube of the AO dimension, so this is very computationally demanding. In this work, we develop and test a natural atomic orbital (NAO) scheme in which the NAOs are obtained as eigenfunctions of atomic blocks of the density matrix in a one-center orthogonalized representation. The NAO representation enables one-center compression of the AO basis in a manner that is optimal for a given threshold, by discarding NAOs with occupation numbers below that threshold. Extensive tests using the Hartree-Fock functional suggest that a threshold of $10^{-5}$ can yield a compression factor (ratio of AO to compressed NAO dimension) between 2.5 and 4.5 for the QZ pc-3 basis. The errors in relative energies are typically less than 0.1 kcal/mol when the compressed basis is used instead of the uncompressed basis. Between 10 and 100 times smaller errors (i.e., usually less than 0.01 kcal/mol) can be obtained with a threshold $10^{-7}$, while the compression factor is typically between 2 and 2.5.

physics.chem-ph↗

arXiv2025

Gold-Standard Chemical Database 137 (GSCDB137): A diverse set of accurate energy differences for assessing and developing density functionals

We present GSCDB137, a rigorously curated benchmark library of 137 data sets (8377 entries) covering main-group and transition-metal reaction energies and barrier heights, (intramolecular) non-covalent interactions, dipole moments, polarizabilities, electric-field response energies, and vibrational frequencies. Legacy data from GMTKN55 and MGCDB84 have been updated to today's best reference values; redundant, spin-contaminated, or low-quality points were removed, and many new, property-focused sets were added. Testing 29 popular density functional approximations (DFAs) confirms the expected Jacob's-ladder hierarchy overall but also reveals notable exceptions: functional performance for frequencies and electric-field properties correlates poorly with that for other ground-state energetics. {\omega}B97M-V and {\omega}B97X-V are the most balanced hybrid meta-GGA and hybrid GGA, respectively; B97M-V and revPBE-D4 lead the meta-GGA and GGA classes. Double hybrids lower mean errors by about 25 % versus the best hybrids but demand careful frozen-core, basis-set, and multi-reference treatment. GSCDB137 offers a comprehensive, openly documented platform for stringent DFA validation and for training the next generation of non-empirical and machine-learned functionals.

physics.chem-ph↗

arXiv2025

A Perspective on Quantum Computing Applications in Quantum Chemistry using 25--100 Logical Qubits

The intersection of quantum computing and quantum chemistry represents a promising frontier for achieving quantum utility in domains of both scientific and societal relevance. Owing to the exponential growth of classical resource requirements for simulating quantum systems, quantum chemistry has long been recognized as a natural candidate for quantum computation. This perspective focuses on identifying scientifically meaningful use cases where early fault-tolerant quantum computers, which are considered to be equipped with approximately 25--100 logical qubits, could deliver tangible impact. While recent advances in classical computing have pushed the boundaries of tractable simulations to unprecedented scales, this logical-qubit regime represents the first window where quantum devices can pursue qualitatively distinct strategies, such as polynomial-scaling phase estimation, direct simulation of quantum dynamics, and active-space embedding, that remain challenging for classical solvers, for instance, multireference charge-transfer and conical-intersection states central to photochemistry and materials design. We highlight near-term opportunities in algorithm and software design, discuss representative chemical problems suited for quantum acceleration, and propose strategic roadmaps and collaborative pathways for advancing practical quantum utility in quantum chemistry.

quant-ph↗

arXiv2025

Optimized auxiliary functions for robust mitigation of finite-size errors in periodic hybrid density functional theory

When calculating properties of periodic systems at the thermodynamic limit (TDL), the dominant source of finite size error (FSE) arises from the long-range Coulomb interaction, and can manifest as a slowly converging quadrature error when approximating an integral in the reciprocal space by a finite sum. The singularity subtraction (SS) method offers a systematic approach for reducing this quadrature error and thus the FSE. In this work, we first investigate the performance of the SS method in the simplest setting, aiming at reducing the FSE in exact exchange calculations by subtracting the Coulomb contribution with a single, adjustable Gaussian auxiliary function. We demonstrate that a simple fitting method can robustly estimate the optimal Gaussian width and leads to rapid convergence toward the TDL. Furthermore, we suggest new forms of the auxiliary function, whose optimal parameters could also be determined through least-squares fitting. For a range of semiconductors and insulators, the proposed auxiliary functions achieve robust, millihartree-level accuracy in hybrid density functional theory calculations, including cases with sparse k-meshes and large basis sets.

physics.comp-ph↗

arXiv2025

Extending orbital-optimized density functional theory to L-edge XPS and beyond: Spin-orbit coupling via non-orthogonal quasi-degenerate perturbation theory

Quantum mechanical calculations of core electron binding energies (CEBEs) leading to 2p hole states are relevant to interpreting L-edge x-ray photo-electron spectroscopy (XPS), as well as higher edges. Orbital-optimized density functional theory (OO-DFT) accurately predicts K-edge CEBEs but is challenged by the presence of significant spin-orbit coupling (SOC) at L- and higher edges. To extend OO-DFT to L-edges and higher, our method utilizes scalar-relativistic, spin-restricted OO-DFT to construct a minimal, quasi-degenerate basis of core-hole states corresponding to a chosen inner-shell (e.g. ionizing all six possible 2p spin orbitals). Non-orthogonal configuration interaction (NOCI) is then used to make the matrix elements of the full Hamiltonian including SOC in this quasi-degenerate model space of determinants. Using a screened 1-electron SOC operator parametrized with the Dirac-Coulomb-Breit (DCB) Hamiltonian results in doublet splitting (DS) values for 3rd row atoms that are nearly in quantitative agreement with experiment. The resulting NOCI eigenvalues are shifted by the average of the (scalar) OO-DFT CEBEs to yield CEBEs (split by SOC) corrected for dynamic correlation. Comparing calculations on gas phase molecules with experimental results establishes that NO-QDPT with the SCAN functional (NO-QDPT/SCAN), using the DCB screened 1-electron SOC operator is accurate to about 0.2 eV for L-edge CEBEs of molecules containing 3rd row atoms. However, this NO-QDPT approach becomes less accurate for 4th-row elements starting in the middle of the 3d transition metal series, especially as the atomic number increases.

physics.chem-ph↗

arXiv2025

An improved guess for the variational calculation of charge-transfer excitations in large systems

Charge-transfer excited states are highly relevant for applications in molecular electronics. However, the accurate calculation of these states in large systems is challenging since wave function methods are prohibitively expensive, time-dependent density functional theory with typical functionals is not precise, and the complicated topology of the electronic hypersurface makes the variational convergence to the targeted excited states a difficult task. We address the latter aspect by providing suitable initial guesses which we obtain by two separate constrained algorithms. Combined with subsequent squared-gradient minimization schemes, we demonstrate that OO-DFT calculations can reliably converge to the charge-transfer states of interest even for large molecular systems. We test this approach on two chemically very different supramolecular structures and also analyze the performance of two recently proposed methods for the tuning of the range-separation parameter in time-dependent DFT with range-separated hybrid functionals. Our results demonstrate that with the methods presented here, reliable convergence of charge-transfer excited states can be achieved with variational excited-state DFT methods, while time-dependent DFT calculations with an adequate tuning procedure for the range-separation parameter can provide a computationally efficient initial estimate of the corresponding energies.

physics.chem-ph↗

arXiv2025

Beyond real: Alternative unitary cluster Jastrow models for molecular electronic structure calculations on near-term quantum computers

Near-term quantum devices require wavefunction ans\"atze that are expressive while also of shallow circuit depth in order to both accurately and efficiently simulate molecular electronic structure. While unitary coupled cluster (e.g., UCCSD) has become a standard, the high gate count associated with the implementation of this limits its feasibility on noisy intermediate-scale quantum (NISQ) hardware. K-fold unitary cluster Jastrow (uCJ) ans\"atze mitigate this challenge by providing $O(kN^2)$ circuit scaling and favorable linear depth circuit implementation. Previous work has focused on the real orbital-rotation (Re-uCJ) variant of uCJ, which allows an exact (Trotter-free) implementation. Here we extend and generalize the $k$-fold uCJ framework by introducing two new variants, Im-uCJ and g-uCJ, which incorporate imaginary and fully complex orbital rotation operators, respectively. Similar to Re-uCJ, both of the new variants achieve quadratic gate-count scaling. Our results focus on the simplest $k=1$ model, and show that the uCJ models frequently maintain energy errors within chemical accuracy. Both g-uCJ and Im-uCJ are more expressive in terms of capturing electron correlation and are also more accurate than the earlier Re-uCJ ansatz. We further show that Im-uCJ and g-uCJ circuits can also be implemented exactly, without any Trotter decomposition. Numerical tests using $k=1$ on $H_2$, $H_3^+$, $Be_2$, $C_2H_4$, $C_2H_6$ and $C_6H_6$ in various basis sets confirm the practical feasibility of these shallow Jastrow-based ans\"atze for applications on near-term quantum hardware.

quant-ph↗

arXiv2025

An Error Mitigated Non-Orthogonal Quantum Eigensolver via Shadow Tomography

We present a shadow-tomography-enhanced Non-Orthogonal Quantum Eigensolver (NOQE) for more efficient and accurate electronic structure calculations on near-term quantum devices. By integrating shadow tomography into the NOQE, the measurement cost scales linearly rather than quadratically with the number of reference states, while also reducing the required qubits and circuit depth by half. This approach enables extraction of all matrix elements via randomized measurements and classical postprocessing. We analyze its sample complexity and show that, for small systems, it remains constant in the high-precision regime, while for larger systems, it scales linearly with the system size. We further apply shadow-based error mitigation to suppress noise-induced bias without increasing quantum resources. Demonstrations on the hydrogen molecule in the strongly correlated regime achieve chemical accuracy under realistic noise, showing that our method is both resource-efficient and noise-resilient for practical quantum chemistry simulations in the near term.

quant-ph↗

arXiv2025

Can Charge Transfer Across C-H...O Hydrogen Bonds Stabilize Oil Droplets in Water?

Oil-water emulsions resist aggregation due to the presence of negative charges at their surface that leads to mutual repulsion between droplets, but the molecular origin of oil charge is currently under debate. While much evidence has suggested that ionic species must accumulate at the interface, an alternative perspective attributes the negative charge on the oil droplet to charge transfer of electron density from water to oil molecules. While the charge transfer mechanism is consistent with the correct sign of oil charge, it is just as important to provide good estimates of the charge magnitude to explain emulsion stability and electrophoresis experiments. Here we show using energy decomposition analysis that the amount of net flow of charge from water to oil is negligibly small due to nearly equal forward and backward charge transfer through weak oil-water interactions, such that oil droplets would be unstable and coalesce, contrary to experiment. The lack of charge transfer also explains why vibrational sum frequency scattering reports a blue shift in the oil C-H frequency when forming emulsions with water, which arises from Pauli repulsion due to localized confinement at the interface. Finally, unlike ions, neither charge transfer nor dynamic polarization can produce a finite conductivity needed to couple to electric fields that would explain electrophoretic mobility.

physics.chem-ph↗

arXiv2025

Foundation Models for Atomistic Simulation of Chemistry and Materials

Given the power of large language and large vision models, it is of profound and fundamental interest to ask if a foundational model based on data and parameter scaling laws and pre-training strategies is possible for learned simulations of chemistry and materials. The scaling of large and diverse datasets and highly expressive architectures for chemical and materials sciences should result in a foundation model that is more efficient and broadly transferable, robust to out-of-distribution challenges, and easily fine-tuned to a variety of downstream observables, when compared to specific training from scratch on targeted applications in atomistic simulation. In this Perspective we aim to cover the rapidly advancing field of machine learned interatomic potentials (MLIP), and to illustrate a path to create chemistry and materials MLIP foundation models at larger scale.

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↗

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↗