Comprehensive Basis-Set Testing of Extended Symmetry-Adapted Perturbation Theory and Assessment of Mixed-Basis Combinations to Reduce Cost

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 highest occupied molecular orbital-lowest unoccupied molecular orbital gaps) are expected to decay exponentially with increasing real-space distance from the diagonal. 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 S-1 being significantly less sparse than its co-variant 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 singles correction in combination with compact, low l-quantum-number basis sets, showing promising results for non-covalent interactions.

Computational analysis of lupenone derivatives as potential inhibitor of human papillomavirus oncoprotein E6 associated cervical cancer

Cervical cancer remains a major global health challenge, largely driven by persistent infections with high-risk human papillomavirus (HPV). Although preventive vaccines have reduced cervical cancer incidence in some settings, effective therapeutic strategies for established HPV-associated malignancies remain limited. High-risk HPV types (particularly 16 and 18) utilize their E6 oncoprotein to promote ubiquitin-mediated degradation of the tumor suppressor p53, thereby facilitating uncontrolled cell proliferation and immune evasion. Targeting E6 has thus emerged as a key strategy to counteract HPV-driven carcinogenesis. In this work, we employed a comprehensive in silico framework-encompassing density functional theory (DFT), ADMET (absorption, distribution, metabolism, excretion, and toxicity) profiling, molecular docking (including refinement and validation), and molecular dynamics (MD) simulations-to evaluate a series of chemically modified lupenone derivatives as potential HPV oncoprotein inhibitors. Initially, lupenone was modified with different functional groups, and each derivative was screened for drug-likeness via ADMET analysis to confirm pharmacological viability. Concurrently, pharmacophore mapping highlighted key alignments between ligand functional groups and pharmacophoric sites, while DFT calculations elucidated each compound's electronic structure, conformational stability, and chemical reactivity. Subsequent docking assessments against E6 oncoprotein and molecular dynamics simulations further confirmed structural robustness in several top-performing compounds, indicating minimal conformational fluctuations over time. These findings demonstrate the potential of lupenone derivatives as promising scaffolds for anti-HPV therapy. However, in vitro and in vivo investigations are necessary to confirm their efficacy, toxicity profiles, and clinical relevance in mitigating HPV-related cervical cancer.

Simplified Tuning of Long-Range Corrected Time-Dependent Density Functional Theory

Range-separated hybrid functionals have dramatically improved the description of charge-transfer excitations in time-dependent density functional theory (TD-DFT), especially when the range-separation parameter is adjusted in order to satisfy the ionization energy (IE) criterion, εHOMO = -IE. However, this "optimal tuning" procedure is molecule-specific, inconvenient, expensive for large systems, and problematic in extended or periodic systems. Here, we consider an alternative procedure known as global density-dependent (GDD) tuning, which sets the range-separation parameter in an automated way based on properties of the exchange hole. In small molecules, we find that long-range corrected functionals with either IE or GDD tuning afford remarkably similar TD-DFT excitation energies, for both valence and charge-transfer excitations. However, GDD tuning is more efficient and is well-behaved even for large systems. It provides a black-box solution to the optimal-tuning problem that can replace IE tuning for many applications of TD-DFT.

Substituent and Heteroatom Effects on π-π Interactions: Evidence That Parallel-Displaced π-Stacking is Not Driven by Quadrupolar Electrostatics

Stacking interactions are a recurring motif in supramolecular chemistry and biochemistry, where a persistent theme is a preference for parallel-displaced aromatic rings rather than face-to-face π-stacking. This is typically explained in terms of quadrupole-quadrupole interactions between the arene moieties but that interpretation is inconsistent with accurate calculations, which reveal that the quadrupolar picture is qualitatively wrong. At typical π-stacking distances, quadrupolar electrostatics may differ in sign from an exact calculation based on charge densities of the interacting arenes. We apply symmetry-adapted perturbation theory to dimers composed of substituted benzene and various aromatic heterocycles, which display a wide range of electrostatic interactions, and we investigate the interplay of Pauli repulsion, dispersion, and electrostatics as it pertains to parallel-displaced π-stacking. Profiles of energy components along cofacial slip-stacking coordinates support a prominent role for the "van der Waals model" (dispersion in competition with Pauli repulsion), even for polar monomers where electrostatic interactions are significant. While electrostatic interactions are necessary to explain the optimal face-to-face π-stacking distance and to account for the relative orientation of one polar arene with respect to another, we find no evidence to support continued invocation of quadrupolar electrostatics as a basis for π-stacking. Our results suggest that a driving force for offset-stacking exists even in the absence of electrostatic interactions. Consequently, tuning electrostatics via functionalization does not guarantee that slip-stacking can be avoided. This has implications for rational design of soft materials and other supramolecular architectures.

Convergent Protocols for Computing Protein-Ligand Interaction Energies Using Fragment-Based Quantum Chemistry

Fragment-based quantum chemistry methods offer a means to sidestep the steep nonlinear scaling of electronic structure calculations so that large molecular systems can be investigated using high-level methods. Here, we use fragmentation to compute protein-ligand interaction energies in systems with several thousand atoms, using a new software platform for managing fragment-based calculations that implements a screened many-body expansion. Convergence tests using a minimal-basis semiempirical method (HF-3c) indicate that two-body calculations, with single-residue fragments and simple hydrogen caps, are sufficient to reproduce interaction energies obtained using conventional supramolecular electronic structure calculations, to within 1 kcal/mol at about 1% of the computational cost. We also demonstrate that the HF-3c results are illustrative of trends obtained with density functional theory in basis sets up to augmented quadruple-ζ quality. Strategic deployment of fragmentation facilitates the use of converged biomolecular model systems alongside high-quality electronic structure methods and basis sets, bringing ab initio quantum chemistry to systems of hitherto unimaginable size. This will be useful for generation of high-quality training data for machine learning applications.

Quick-and-Easy Validation of Protein-Ligand Binding Models Using Fragment-Based Semiempirical Quantum Chemistry

Electronic structure calculations in enzymes converge very slowly with respect to the size of the model region that is described using quantum mechanics (QM), requiring hundreds of atoms to obtain converged results and exhibiting substantial sensitivity (at least in smaller models) to which amino acids are included in the QM region. As such, there is considerable interest in developing automated procedures to construct a QM model region based on well-defined criteria. However, testing such procedures is burdensome due to the cost of large-scale electronic structure calculations. Here, we show that semiempirical methods can be used as alternatives to density functional theory (DFT) to assess convergence in sequences of models generated by various automated protocols. The cost of these convergence tests is reduced even further by means of a many-body expansion. We use this approach to examine convergence (with respect to model size) of protein-ligand binding energies. Fragment-based semiempirical calculations afford well-converged interaction energies in a tiny fraction of the cost required for DFT calculations. Two-body interactions between the ligand and single-residue amino acid fragments afford a low-cost way to construct a "QM-informed" enzyme model of reduced size, furnishing an automatable active-site model-building procedure. This provides a streamlined, user-friendly approach for constructing ligand binding-site models that requires neither a priori information nor manual adjustments. Extension to model-building for thermochemical calculations should be straightforward.

Probing the performance of DFT in the structural characterization of [FeFe] hydrogenase models

In this work, a series of DFT and DFT-D methods is combined with double-ζ basis sets to benchmark their performance in predicting the structures of five newly synthesized hexacarbonyl diiron complexes with a bridging ligand featuring a μ-S2C3 motif in a ring-containing unit functionalized with aromatic groups. Such complexes have been considered as [FeFe] hydrogenase catalytic site models with potential for eco-friendly energetic applications. According to this assessment, r2SCAN is identified as the density functional recommended for the reliable description of the molecular and crystal structures of the herein studied models. However, the butterfly (μ-S)2Fe2 core of the models demonstrates a minor deformation of its optimized geometry obtained from both molecular and periodic calculations. The FeFe bond length is slightly underestimated while the FeS bonds tend to be too long. Adding the D3(BJ) correction to r2SCAN does not lead to any improvement in the calculated structures.

Optimization of damping function parameters for -D3 and -D4 dispersion models for Hartree-Fock based symmetry-adapted perturbation theory

Symmetry-adapted perturbation theory (SAPT) directly computes intermolecular interaction energy in terms of electrostatics, exchange-repulsion, induction/polarization, and London dispersion components. In SAPT based on Hartree-Fock ("SAPT0") or based on density functional theory, the most time-consuming step is the computation of the dispersion terms. Previous work has explored the replacement of these expensive dispersion terms with simple damped asymptotic models. We recently examined [Schriber et al. J. Chem. Phys. 154, 234107 (2021)] the accuracy of SAPT0 when replacing its dispersion term with Grimme's popular -D3 correction, reducing the computational cost scaling from O(N5) to O(N3). That work optimized damping function parameters for SAPT0-D3/jun-cc-pVDZ using estimates of the coupled-cluster complete basis set limit [CCSD(T)/CBS] on a 8299 dimer dataset. Here, we explore the accuracy of SAPT0-D3 with additional basis sets, along with an analogous model using -D4. Damping parameters are rather insensitive to basis sets, and the resulting SAPT0-D models are more accurate on average for total interaction energies than SAPT0. Our results are surprising in several respects: (1) improvement of -D4 over -D3 is negligible for these systems, even charged systems where -D4 should, in principle, be more accurate; (2) addition of Axilrod-Teller-Muto terms for three-body dispersion does not improve error statistics for this test set; and (3) SAPT0-D is even more accurate on average for total interaction energies than the much more computationally costly density functional theory based SAPT [SAPT(DFT)] in an aug-cc-pVDZ basis. However, SAPT0 and SAPT0-D3/D4 interaction energies benefit from significant error cancellation between exchange and dispersion terms.

An efficient method by combining different basis sets and SAPT levels

In symmetry-adapted perturbation theory (SAPT), accurate calculations on non-covalent interaction (NCI) for large complexes with more than 50 atoms are time-consuming using large basis sets. More efficient ones with smaller basis sets usually result in poor prediction in terms of dispersion and overall energies. In this study, we propose two composite methods with baseline calculated at SAPT2/aug-cc-pVDZ and SAPT2/aug-cc-pVTZ with dispersion term corrected at SAPT2+ level using bond functions and smaller basis set with δ MP2 corrections respectively. Benchmark results on representative NCI data sets, such as S22, S66, and so forth, show significant improvements on the accuracy compared to the original SAPT Silver standard and comparable to SAPT Gold standard in some cases with much less computational cost.

Assessing the domain-based local pair natural orbital (DLPNO) approximation for non-covalent interactions in sizable supramolecular complexes

The titular domain-based local pair natural orbital (DLPNO) approximation is the most widely used method for extending correlated wave function models to large molecular systems, yet its fidelity for intermolecular interaction energies in large supramolecular complexes has not been thoroughly vetted. Non-covalent interactions are sensitive to tails of the electron density and involve nonlocal dispersion that is discarded or approximated if the screening of pair natural orbitals (PNOs) is too aggressive. Meanwhile, the accuracy of the DLPNO approximation is known to deteriorate as molecular size increases. Here, we test the DLPNO approximation at the level of second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster theory with singles, doubles, and perturbative triples [CCSD(T)] for a variety of large supramolecular complexes. DLPNO-MP2 interaction energies are within 3% of canonical values for small dimers with ≲10 heavy atoms, but for larger systems, the DLPNO approximation is often quite poor unless the results are extrapolated to the canonical limit where the threshold for discarding PNOs is taken to zero. Counterpoise correction proves to be essential in reducing errors with respect to canonical results. For a sequence of nanoscale graphene dimers up to (C96H24)2, extrapolated DLPNO-MP2 interaction energies agree with canonical values to within 1%, independent of system size, provided that the basis set does not contain diffuse functions; these cause the DLPNO approximation to behave erratically, such that results cannot be extrapolated in a meaningful way. DLPNO-CCSD(T) calculations are typically performed using looser PNO thresholds as compared to DLPNO-MP2, but this significantly impacts accuracy for large supramolecular complexes. Standard DLPNO-CCSD(T) settings afford errors of 2-6 kcal/mol for dimers involving coronene (C24H12) and circumcoronene (C54H18), even at the DLPNO-CCSD(T1) level.

Enhanced selectivity towards melanoma cells with zinc(II)-Schiff bases containing imidazole derivatives

Zinc(II)-complexes with the general formula [Zn(L)2] containing 8-hydroxyquinoline Schiff bases functionalized with 1-(3-aminopropyl)imidazole or 1-(3-aminopropyl)-2-methyl-1H-imidazole on 2-position and their respective ligands (HL1 or HL2) were synthesized and characterized by NMR, UV-Vis, FTIR and CD spectroscopies as well as ESI-MS spectrometry. Single crystals of HL2 and [Zn(L1)2]n were analysed by SC-XRD. [Zn(L1)2]n shows a 1D polymeric chain structure of alternating Zn(II) cations and bridging Schiff base ligands, in contrast to previously reported monomeric structures of analogous complexes. DFT calculations were performed to rationalize the polymeric X-ray structure of Zn(L1)2. Results showed that the ligands can bind as bi- or tridentate to Zn(II) and there is the possibility of a dynamic behavior for the complexes in solution. Both ligands and complexes present limited stability in aqueous media, however, in the presence of bovine serum albumin the complexes are stable. Molecular docking simulations and circular dichroism spectroscopic studies suggest binding to this protein in close proximity to the Trp213 residue. Biological studies on a panel of cancer cells revealed that the Zn(II)-complexes have a lower impact on cell viability than cisplatin, except for triple-negative breast cancer cells in which they were comparable. Notwithstanding, they display much higher selectivity towards cancer cells vs. normal cells, than cisplatin. They induce the generation of ROS and DNA double-strand breaks, primarily through apoptosis as the mode of cell death. Overall, the novel Zn(II)-complexes demonstrate improved induction of apoptosis and higher selectivity, particularly for melanoma cells, compared to previously reported analogues, making them promising candidates for clinical application.

Unraveling environmental effects in the absorption and fluorescence spectra of p-methoxyphenylpiperazine derivatives

The p-methoxyphenylpiperazine motif can be found in many biologically active molecules, including approved drugs. It is characterized by a relatively weak fluorescence, which can be employed in different types of studies involving molecules with this motif. In this work, a thorough analysis of the absorption, excitation and emission spectra of the diphenyl(aminomethyl)phosphine and tris(aminomethyl)phosphine derivatives of p-methoxyphenylpiperazine, supported by the DFT calculations (ωB97XD/6-311++G(d,p)) with NBO and QTAIM analysis also for different model molecules (e.g. 1-(4-methoxyphenyl)-4-methylpiperazine) enabled determination of the mechanisms underlying beneath the electronic transitions and allowed to rationalize mixed solvent effects observed in electronic spectra of the studied compounds. Electronic transition from the ground state to the first excited state can be regarded as the n,π → π* transition with no solvatochromic effects, however the hydrogen bonds between the HBD solvent molecules and the nitrogen atom bound directly to the aromatic ring (N(4)) are shifting strongly the 1st absorption or excitation band maxima to the higher energies. Fluorescence band, as a result of the electron transition from the equilibrated 1st excited state to the ground state, can be described as the π*→π with positive solvatochromism. N(4) in the excited states adopts a sp2 hybridization and is no longer able to form HBs. On the other hand, increased electron density on the aromatic ring makes the emission processes vulnerable to its direct environment.

Visualizing and characterizing excited states from time-dependent density functional theory

Time-dependent density functional theory (TD-DFT) is the most widely-used electronic structure method for excited states, due to a favorable combination of low cost and semi-quantitative accuracy in many contexts, even if there are well recognized limitations. This Perspective describes various ways in which excited states from TD-DFT calculations can be visualized and analyzed, both qualitatively and quantitatively. This includes not just orbitals and densities but also well-defined statistical measures of electron-hole separation and of Frenkel-type exciton delocalization. Emphasis is placed on mathematical connections between methods that have often been discussed separately. Particular attention is paid to charge-transfer diagnostics, which provide indicators of when TD-DFT may not be trustworthy due to its categorical failure to describe long-range electron transfer. Measures of exciton size and charge separation that are directly connected to the underlying transition density are recommended over more ad hoc metrics for quantifying charge-transfer character.

Applying Large Graph Neural Networks to Predict Transition Metal Complex Energies Using the tmQM_wB97MV Data Set

Machine learning (ML) methods have shown promise for discovering novel catalysts but are often restricted to specific chemical domains. Generalizable ML models require large and diverse training data sets, which exist for heterogeneous catalysis but not for homogeneous catalysis. The tmQM data set, which contains properties of 86,665 transition metal complexes calculated at the TPSSh/def2-SVP level of density functional theory (DFT), provided a promising training data set for homogeneous catalyst systems. However, we find that ML models trained on tmQM consistently underpredict the energies of a chemically distinct subset of the data. To address this, we present the tmQM_wB97MV data set, which filters out several structures in tmQM found to be missing hydrogens and recomputes the energies of all other structures at the ωB97M-V/def2-SVPD level of DFT. ML models trained on tmQM_wB97MV show no pattern of consistently incorrect predictions and much lower errors than those trained on tmQM. The ML models tested on tmQM_wB97MV were, from best to worst, GemNet-T > PaiNN ≈ SpinConv > SchNet. Performance consistently improves when using only neutral structures instead of the entire data set. However, while models saturate with only neutral structures, more data continue to improve the models when including charged species, indicating the importance of accurately capturing a range of oxidation states in future data generation and model development. Furthermore, a fine-tuning approach in which weights were initialized from models trained on OC20 led to drastic improvements in model performance, indicating transferability between ML strategies of heterogeneous and homogeneous systems.

Accurate three-body noncovalent interactions: the insights from energy decomposition

An impressive collection of accurate two-body interaction energies for small complexes has been assembled into benchmark databases and used to improve the performance of multiple density functional, semiempirical, and machine learning methods. Similar benchmark data on nonadditive three-body energies in molecular trimers are comparatively scarce, and the existing ones are practically limited to homotrimers. In this work, we present a benchmark dataset of 20 equilibrium noncovalent interaction energies for a small but diverse selection of 10 heteromolecular trimers. The new 3BHET dataset presents complexes that combine different interactions including π-π, anion-π, cation-π, and various motifs of hydrogen and halogen bonding in each trimer. A detailed symmetry-adapted perturbation theory (SAPT)-based energy decomposition of the two- and three-body interaction energies shows that 3BHET consists of electrostatics- and dispersion-dominated complexes. The nonadditive three-body contribution is dominated by induction, but its influence on the overall bonding type in the complex (as exemplified by its position on the ternary diagram) is quite small. We also tested the extended SAPT (XSAPT) approach which is capable of including some nonadditive interactions in clusters of any size. The resulting three-body dispersion term (obtained from the many-body dispersion formalism) is mostly in good agreement with the supermolecular CCSD(T)-MP2 values and the nonadditive induction term is similar to the three-body SAPT(DFT) data, but the overall three-body XSAPT energies are not very accurate as they are missing the first-order exchange terms.

Anticandidal Cu(I) complexes with neocuproine and 1-(4-methoxyphenyl)piperazine based diphenylaminomethylphosphine: Is Cu-diimine moiety a pharmacophore?

The studies on metal complexes as potential antifungals are of growing interest because they may be the answer to increasingly effective defense mechanisms. Herein we present two new copper(I) iodide or thiocyanide complexes with 2,9-dimethyl-1,10-phenanthroline (dmp) and diphenylphosphine derivative of 1-(4-methoxyphenyl)piperazine (4MP): [CuI(dmp)4MP] (1-4MP) and [CuNCS(dmp)4MP] (2-4MP) - their synthesis, as well as structural and spectroscopic characteristics. Interestingly, while 4MP and its oxide derivative (4MOP) show a very low or no activity against all tested Candida albicans strains (MIC50 ≥ 200 μM against CAF2-1 - laboratory control strain, DSY1050 - mutant without transporters Cdr1, Cdr2, Mdr1; isogenic for CAF2-1, and fluconazole resistant clinical isolates), for 1-4MP and 2-4MP MIC50 values were 0.4 μM, independently on the complex and strain tested. Determination of the viability of NHDF-Ad (Normal Adult Human Dermal Fibroblasts) cell line treated with 1-4MP and 2-4MP showed that for both complexes there was only a 20% reduction in the concentration range ¼ to 2 × MIC50 and the 70% at 4 × MIC50. Subsequently, the MLCT based luminescence of the complexes in aqueous media allowed to record the confocal micrographs of 1-4MP in the cells. The results show that it is situated most likely in the vacuoles (C. albicans) or lysosomes (NHDF-Ad).

Fragment-Based Calculations of Enzymatic Thermochemistry Require Dielectric Boundary Conditions

Electronic structure calculations on enzymes require hundreds of atoms to obtain converged results, but fragment-based approximations offer a cost-effective solution. We present calculations on enzyme models containing 500-600 atoms using the many-body expansion, comparing to benchmarks in which the entire enzyme-substrate complex is described at the same level of density functional theory. When the amino acid fragments contain ionic side chains, the many-body expansion oscillates under vacuum boundary conditions but rapid convergence is restored using low-dielectric boundary conditions. This implies that full-system calculations in the gas phase are inappropriate benchmarks for assessing errors in fragment-based approximations. A three-body protocol retains sub-kilocalorie per mole fidelity with respect to a supersystem calculation, as does a two-body calculation combined with a full-system correction at a low-cost level of theory. These protocols pave the way for application of high-level quantum chemistry to large systems via rigorous, ab initio treatment of many-body polarization.

Birth of the Hydrated Electron via Charge-Transfer-to-Solvent Excitation of Aqueous Iodide

A primary means to generate hydrated electrons in laboratory experiments is excitation to the charge-transfer-to-solvent (CTTS) state of a solute such as I^-(aq), but this initial step in the genesis of e^-(aq) has never been simulated directly using ab initio molecular dynamics. We report the first such simulations, combining ground- and excited-state simulations of I^-(aq) with a detailed analysis of fluctuations in the Coulomb potential experienced by the nascent solvated electron. What emerges is a two-step picture of the evolution of e^-(aq) starting from the CTTS state: I^-(aq) + hν → I^-*(aq) → I^•(aq) + e^-(aq). Notably, the equilibrated ground state of e^-(aq) evolves from I^-*(aq) without any nonadiabatic transitions, simply as a result of solvent reorganization. The methodology used here should be applicable to other photochemical electron transfer processes in solution, an important class of problems directly relevant to photocatalysis and energy transfer.

Systematic Evaluation of Counterpoise Correction in Density Functional Theory

A widespread belief persists that the Boys-Bernardi function counterpoise (CP) procedure "overcorrects" supramolecular interaction energies for the effects of basis-set superposition error. To the extent that this is true for correlated wave function methods, it is usually an artifact of low-quality basis sets. The question has not been considered systematically in the context of density functional theory, however, where basis-set convergence is generally less problematic. We present a systematic assessment of the CP procedure for a representative set of functionals and basis sets, considering both benchmark data sets of small dimers and larger supramolecular complexes. The latter include layered composite polymers with ∼150 atoms and ligand-protein models with ∼300 atoms. Provided that CP correction is used, we find that intermolecular interaction energies of nearly complete-basis quality can be obtained using only double-ζ basis sets. This is less expensive as compared to triple-ζ basis sets without CP correction. CP-corrected interaction energies are less sensitive to the presence of diffuse basis functions as compared to uncorrected energies, which is important because diffuse functions are expensive and often numerically problematic for large systems. Our results upend the conventional wisdom that CP "overcorrects" for basis-set incompleteness. In small basis sets, CP correction is mandatory in order to demonstrate that the results do not rest on error cancellation.