Systematic Evaluation of Counterpoise Correction in Density Functional Theory

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.

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.

Delocalization error poisons the density-functional many-body expansion

The many-body expansion is a fragment-based approach to large-scale quantum chemistry that partitions a single monolithic calculation into manageable subsystems. This technique is increasingly being used as a basis for fitting classical force fields to electronic structure data, especially for water and aqueous ions, and for machine learning. Here, we show that the many-body expansion based on semilocal density functional theory affords wild oscillations and runaway error accumulation for ion-water interactions, typified by F-(H2O) N with N ≳ 15. We attribute these oscillations to self-interaction error in the density-functional approximation. The effect is minor or negligible in small water clusters, explaining why it has not been noticed previously, but grows to catastrophic proportion in clusters that are only moderately larger. This behavior can be counteracted with hybrid functionals but only if the fraction of exact exchange is ≳50%, whereas modern meta-generalized gradient approximations including ωB97X-V, SCAN, and SCAN0 are insufficient to eliminate divergent behavior. Other mitigation strategies including counterpoise correction, density correction (i.e., exchange-correlation functionals evaluated atop Hartree-Fock densities), and dielectric continuum boundary conditions do little to curtail the problematic oscillations. In contrast, energy-based screening to cull unimportant subsystems can successfully forestall divergent behavior. These results suggest that extreme caution is warranted when the many-body expansion is combined with density functional theory.

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.

Strategies to Obtain Reliable Energy Landscapes from Embedded Multireference Correlated Wavefunction Methods for Surface Reactions

Embedded correlated wavefunction (ECW) theory is a powerful tool for studying ground- and excited-state reaction mechanisms and associated energetics in heterogeneous catalysis. Several factors are important to obtaining reliable ECW energies, critically the construction of consistent active spaces (ASs) along reaction pathways when using a multireference correlated wavefunction (CW) method that relies on a subset of orbital spaces in the configuration interaction expansion to account for static electron correlation, e.g., complete AS self-consistent field theory, in addition to the adequate partitioning of the system into a cluster and environment, as well as the choice of a suitable basis set and number of states included in excited-state simulations. Here, we conducted a series of systematic studies to develop best-practice guidelines for ground- and excited-state ECW theory simulations, utilizing the decomposition of NH3 on Pd(111) as an example. We determine that ECW theory results are relatively insensitive to cluster size, the aug-cc-pVDZ basis set provides an adequate compromise between computational complexity and accuracy, and that a fixed-clean-surface approximation holds well for the derivation of the embedding potential. Additionally, we demonstrate that a merging approach, which involves generating ASs from the molecular fragments at each configuration, is preferable to a creeping approach, which utilizes ASs from adjacent structures as an initial guess, for the generation of consistent potential energy curves involving open-d-shell metal surfaces, and, finally, we show that it is essential to include bands of excited states in their entirety when simulating excited-state reaction pathways.

Evaluation of naked-eye sensing and anion binding studies in meso-fluorescein substituted one-walled calix[4]pyrrole (C4P)

In this paper, we have design, synthesized and fully characterized a new meso-fluorescein substituted one-walled calix[4]pyrrole (C4P7), obtained from simple and easily available starting materials such as fluorescein, 4-hydroxyacetophenone and pyrrole. The anion sensing studies reveal that the C4P7 system displays selective and sensitive naked-eye sensing towards fluoride, phosphate, and acetate anions with the limit of detection of 4.27 mg L-1, 6.4 mg L-1, and 5.94 mg L-1, respectively. Moreover, the C4P7 receptor displays good results of binding (host-guest, 1 : 1) towards a variety of anions. The 1 : 1 binding stoichiometry was further confirmed by means of Job's plots. TD-DFT calculations showed that the HOMO-LUMO gap decreases in all the complexes (C4P7@anions) in comparison to the free C4P7 system. The authors are of the opinion that this work may provide a good platform to explore calix[4]pyrrole chemistry in the arena of recognition/sensing of biologically significant analytes in future studies.

Capturing CO2 in Quadrupolar Binding Pockets: Broadband Microwave Spectroscopy of Pyrimidine-(CO2)n, n = 1,2

Pyrimidine has two in-plane CH(δ+)/N̈(δ-)/CH(δ+) binding sites that are complementary to the (δ-/2δ+/δ-) quadrupole moment of CO2. We recorded broadband microwave spectra over the 7.5-17.5 GHz range for pyrimidine-(CO2)n with n = 1 and 2 formed in a supersonic expansion. Based on fits of the rotational transitions, including nuclear hyperfine splitting due to the two 14N nuclei, we have assigned 313 hyperfine components across 105 rotational transitions for the n = 1 complex and 208 hyperfine components across 105 rotational transitions for the n = 2 complex. The pyrimidine-CO2 complex is planar, with CO2 occupying one of the quadrupolar binding sites, forming a structure in which the CO2 is stabilized in the plane by interactions with the C-H hydrogens adjacent to the nitrogen atom. This structure is closely analogous to that of the pyridine-CO2 complex studied previously by (Doran, J. L. J. Mol. Struct. 2012, 1019, 191-195). The fit to the n = 2 cluster gives rotational constants consistent with a planar cluster of C2v symmetry in which the second CO2 molecule binds in the second quadrupolar binding pocket on the opposite side of the ring. The calculated total binding energy in pyrimidine-CO2 is -13.7 kJ mol-1, including corrections for basis set superposition error and zero-point energy, at the CCSD(T)/ 6-311++G(3df,2p) level, while that in pyrimidine-(CO2)2 is almost exactly double that size, indicating little interaction between the two CO2 molecules in the two binding sites. The enthalpy, entropy, and free energy of binding are also calculated at 300 K within the harmonic oscillator/rigid-rotor model. This model is shown to lack quantitative accuracy when it is applied to the formation of weakly bound complexes.

Halide Complexes of 5,6-Dicyano-2,1,3-Benzoselenadiazole with 1 : 4 Stoichiometry: Cooperativity between Chalcogen and Hydrogen Bonding

The [M4 -Hal]- (M=the title compound; Hal=Cl, Br, and I) complexes were isolated in the form of salts of [Et4 N]+ cation and characterized by XRD, NMR, UV-Vis, DFT, QTAIM, EDD, and EDA. Their stoichiometry is caused by a cooperative interplay of σ-hole-driven chalcogen (ChB) and hydrogen (HB) bondings. In the crystal, [M4 -Hal]- are connected by the π-hole-driven ChB; overall, each [Hal]- is six-coordinated. In the ChB, the electrostatic interaction dominates over orbital and dispersion interactions. In UV-Vis spectra of the M+[Hal]- solutions, ChB-typical and [Hal]- -dependent charge-transfer bands are present; they reflect orbital interactions and allow identification of the individual [Hal]- . However, the structural situation in the solutions is not entirely clear. Particularly, the UV-Vis spectra of the solutions are different from the solid-state spectra of the [Et4 N]+ [M4 -Hal]- ; very tentatively, species in the solutions are assigned [M-Hal]- . It is supposed that the formation of the [M4 -Hal]- proceeds during the crystallization of the [Et4 N]+ [M4 -Hal]- . Overall, M can be considered as a chromogenic receptor and prototype sensor of [Hal]- . The findings are also useful for crystal engineering and supramolecular chemistry.

Boron-based octahedral dication experimentally detected: DFT surface confirms its availability

Borane and heteroborane clusters have been known as neutral or anionic species. In contrast to them, several ten-vertex monocationic nido and closo dicarbaborane-based systems have recently emerged from the reaction of the parent bicapped-square antiprismatic dicarbaboranes with N-heterocyclic carbenes followed by the protonization of the corresponding nido intermediates. The expansion of these efforts has afforded the very first closo-dicationic octahedral phosphahexaborane along with new closo-monocationic pnictogenahexaboranes of the same shapes. All are the products of the one-pot procedure that consists in the reaction of the same carbenes with the parent closo-1,2-Pn₂B₄Br₄ (Pn = As, P). Whereas in the case of phosphorus such a monocation appears to be a mixture of stable intermediates, and arsenahexaboranyl monocation has occurred as the final product, all of them without using any subsequent reaction. The well-established DFT/ZORA/NMR approach has unambiguously confirmed the existence of these species in solution, and computed electrostatic potentials have revealed the delocalization of the positive charge in these monocations and in the very first dication, namely within the octahedral shapes in both cases.

Quantum Chemical Approach of Hexaammine (NH3)6 complexant with alkali and alkaline earth metals for their potential use as NLO materials

In this study, nine new electron rich compounds are presented, and their electronic, geometrical, and nonlinear optical (NLO) characteristics have been investigated by using the Density functional theory. The basic design principle of these compounds is placing alkaline earth metal (AEM) inside and alkali metal (AM) outside the hexaammine complexant. The properties of nine newly designed compounds are contrasted with the reference molecule (Hexaammine). The effect of this doping on Hexaamine complexant is explored by different analyses such as electron density distribution map (EDDM), frontier molecular orbitals (FMOs), density of states (DOS) absorption maximum (λ_max), hyperpolarizabilities, dipole moment, transition density matrix (TDM). Non-covalent interaction (NCI) study assisted with isosurfaces has been accomplished to explore the vibrational frequencies and types of synergy. The doping of hexaammine complexant with AM and AEM significantly improved its characteristics by reducing values of HOMO-LUMO energy gaps from 10.7eV to 3.15eV compared to 10.7 eV of hexaammine. The polarizability and hyperpolarizability (α_o and β_o) values inquisitively increase from 72 to 919 au and 4.31 × 10^-31 to 2.00 × 10^-27esu respectively. The higher values of hyperpolarizability in comparison to hexaammine (taken as a reference molecule) are credited to the presence of additional electrons. The absorption profile of the newly designed molecules clearly illustrates that they are highly accompanied by higher λ_max showing maximum absorbance in red and far-red regions ranging from 654.07 nm to 783.94 nm. These newly designed compounds have superior outcomes having effectiveness for using them as proficient NLO materials and have a gateway for advanced investigation of more stable and highly progressive NLO materials.

Polymorphism of Butyl Ester of Oleanolic Acid—The Dominance of Dispersive Interactions over Electrostatic

Oleanolic (OA) and glycyrrhetinic acids (GE), as well as their derivatives, show a variety of pharmacological properties. Their crystal structures provide valuable information related to the assembly modes of these biologically active compounds. In the known-to-date crystals of OA esters, their 11-oxo derivatives, and GE ester crystals, triterpenes associate, forming different types of ribbons and layers whose construction is based mainly on van der Waals forces and weak C-H···O interactions. New crystal structures of 11-oxo OA methyl ester and the polymorph of OA butyl ester reveal an alternative aggregation mode. Supramolecular architectures consist of helical chains which are stabilized by hydrogen bonds of O-H···O type. It was found that two polymorphic forms of butyl OA ester (layered and helical) are related monotropically. In a structure of metastable form, O-H···O hydrogen bonds occur, while the thermodynamically preferred phase is governed mainly by van der Waals interactions. The intermolecular interaction energies calculated using CrystalExplorer, PIXEL, and Psi4 programs showed that even in motifs formed through O-H···O hydrogen bonds, the dispersive forces have a significant impact.

DFT and TD-DFT study of hydrogen bonded complexes of aspartic acid and n water (n = 1 and 2)

CONTEXT

Hydrogen bonds (HB) influence the conformational preferences of biomolecules and their optical and electronic properties. The directional interaction of molecules of water can be a prototype to understand the effects of HBs on biomolecules. Among the neurotransmitters (NT), L-aspartic acid (ASP) stands out due to its importance in health and as a precursor of several biomolecules. As it presents different functional groups and readily forms inter- and intramolecular HBs, ASP can be considered a prototype for understanding the behavior of NTs when interacting by HB with other substances. Although several theoretical studies have been performed in the past on isolated ASP and its formed complexes with water, both in gas and liquid phases, using DFT and TD-DFT formalisms, these works did not perform large basis set calculations or study electronic transitions of ASP-water complexes. We investigated the HB interactions in complexes of ASP and water molecules. The results show that the interactions between the carboxylic groups of ASP with water molecules, forming cyclic structures with two HBs, lead to more stable and less polar complexes than other conformers formed between water and the NH₂ group. It was observed that there is a relationship between the deviation in the UV-Vis absorption band of the ASP and the interactions of water with the HOMO and LUMO orbitals with the stabilization/destabilization of the S₁ state to the S₀ of the complexes. However, in some cases, such as 1:1 complex ASP-W2, this analysis may be inaccurate due to small changes in ΔE.

METHODS

We studied the landscapes of the ground state surface of different conformers of isolated L-ASP and the L-ASP-(H₂O)_n complexes (n = 1 and 2) using the DFT formalism, with the B3LYP functional, and six different basis sets: 6-31 +  + G(d,p), 6-311 +  + G(d,p), D95 +  + (d,p), D95V +  + (d,p), cc-pVDZ, and, cc-pVTZ basis sets. The cc-pVTZ basis set provides the minimum energy of all conformers, and therefore, we performed the analysis with this basis set. We evaluated the stabilization of the ASP and complexes using the minimum ground state energy, corrected by the zero point energy and the interaction energy between the ASP and the water molecules. We also calculated the vertical electronic transitions S₁ ← S₀, and their properties using the TD-DFT formalism at B3LYP/cc-pVTZ level with the optimized geometries for S₀ state with the same basis set. For the analysis of the vertical transitions of isolated ASP and the ASP-(H₂O)_n complexes, we calculated the electrostatic energy in the S₀ and S₁ states. We performed the calculations with the Gaussian 09 software package. We used the VMD software package to visualize the geometries and shapes of the molecule and complexes.

Competition Between the Two σ-Holes in the Formation of a Chalcogen Bond

A chalcogen atom Y contains two separate σ-holes when in a R₁ YR₂ molecular bonding pattern. Quantum chemical calculations consider competition between these two σ-holes to engage in a chalcogen bond (ChB) with a NH₃ base. R groups considered include F, Br, I, and tert-butyl (tBu). Also examined is the situation where the Y lies within a chalcogenazole ring, where its neighbors are C and N. Both electron-withdrawing substituents R₁ and R₂ act cooperatively to deepen the two σ-holes, but the deeper of the two holes consistently lies opposite to the more electron-withdrawing group, and is also favored to form a stronger ChB. The formation of two simultaneous ChBs in a triad requires the Y atom to act as double electron acceptor, and so anti-cooperativity weakens each bond relative to the simple dyad. This effect is such that some of the shallower σ-holes are unable to form a ChB at all when a base occupies the other site.

Adjusting the balance between hydrogen and chalcogen bonds

A complex is assembled which pairs a carboxyl group of X₁COOH with a 1,2,5-chalcogenadiazole ring containing substituents on its C atoms. The OH of the carboxyl group donates a proton to a N atom of the ring to form a OH⋯N H-bond (HB), while its carbonyl O engages in a Y⋯O chalcogen bond (ChB) with the ring in which Y = S, Se, Te. The ChB is strengthened by enlarging the size of the Y atom from S to Se to Te. Placement of an electron-withdrawing group (EWG) X₁ on the acid strengthens the HB while weakening the ChB; the reverse occurs when EWGs are placed on the ring. By selection of the proper substituents on the two units, it is possible to achieve a near perfect balance between the strengths of these two bonds. These bond strengths are also reflected in the NMR spectroscopic properties of the chemical shielding of the various atoms and the coupling between the nuclei directly involved in each bond.

Supramolecular Diversity, Theoretical Investigation and Antibacterial Activity of Cu, Co and Cd Complexes Based on the Tridentate N,N,O-Schiff Base Ligand Formed In Situ

The four new complexes, [Cu(HL¹)(L²)Cl] (1), [Cu(HL¹)(L¹)]∙Cl∙2H₂O (2), [Co(L¹)₂]∙Cl (3) and [Cd(HL¹)I₂]∙dmso (4), have been prepared by one-pot reactions of the respective chloride or iodide metal salt with a non-aqueous solution of the polydentate Schiff base, HL¹, resulted from in situ condensation of benzhydrazide and 2-pyridinecarboxaldehyde, while a ligand HL², in case of 1, has been formed due to the oxidation of 2-pyridinecarboxaldehyde under reaction conditions. The crystallographic analysis revealed that the molecular building units in 1-4 are linked together into complex structures by hydrogen bonding, resulting in 1D, 2D and 3D supramolecular architectures for 1, 2 and 4, respectively, and the supramolecular trimer for 3. The electronic structures of 1-4 were investigated by the DFT theoretical calculations. The non-covalent interactions in the crystal structures of 1-4 were studied by means of the Hirshfeld surface analysis and the QTAIM theory with a special focus on the C-H⋯Cl bonding. From the DFT/DLPNO-CCSD(T) calculations, using a series of charged model {R₃C-H}⁰⋯Cl^- assemblies, we propose linear regressions for assessment of the interaction enthalpy (ΔH, kcal mol^-1) and the binding energy (BE, kcal mol^-1) between {R₃C-H}⁰ and Cl^- sites starting from the electron density at the bond critical point (ρ(r_BCP), a.u.): ΔH = -678 × ρ(r) + 3 and BE = -726 × ρ(r) + 4. It was also has been found that compounds 1, 3 and 4 during in vitro screening showed an antibacterial activity toward the nine bacteria species, comprising both Gram-positive and Gram-negative, with MIC values ranging from 156.2 to 625 mg/L. The best results have been obtained against Acinetobacter baumannii MβL.