RHF Levels Research Articles

Single-Point Extrapolation to the Complete Basis Set Limit through Deep Learning.

Machine learning (ML) offers an attractive method for making predictions about molecular systems while circumventing the need to run expensive electronic structure calculations. Once trained on ab initio data, the promise of ML is to deliver accurate predictions of molecular properties that were previously computationally infeasible. In this work, we develop and train a graph neural network model to correct the basis set incompleteness error (BSIE) between a small and large basis set at the RHF and B3LYP levels of theory. Our results show that, when compared to fitting to the total potential, an ML model fitted to correct the BSIE is better at generalizing to systems not seen during training. We test this ability by training on single molecules while evaluating on molecular complexes. We also show that ensemble models yield better behaved potentials in situations where the training data is insufficient. However, even when only fitting to the BSIE, acceptable performance is only achieved when the training data sufficiently resemble the systems one wants to make predictions on. The test error of the final model trained to predict the difference between the cc-pVDZ and cc-pV5Z potential is 0.184 kcal/mol for the B3LYP density functional, and the ensemble model accurately reproduces the large basis set interaction energy curves on the S66x8 dataset.

Study of electronic structure, optoelectronics, linear and nonlinear optical properties and chemical descriptors of dibromodinitrofluorescein isomers in gasphase and solvent media using abinitio and DFT methods

In this work, we have studied the electronic structure, optoelectronics, linear and nonlinear optical properties of dibromodinitrofluorescein isomers in the gas phase and some solvents media using RHF and B3LYP levels of theory with a cc-pVDZ basis set. Our results suggest that solvent media have an effect on certain properties while some are unaffected. We have also determined the energy band gap and some other parameters like ionization potential, electron affinity, and molar refractivity. Finally, we have calculated the reactivity descriptors through some parameters including chemical hardness (η), chemical potential(μ), electrophilicity index(ω), softness (ϑ), electronegativity (EN), Fermi energy (EF), Electro accepting power (ω+), electron-donating power (ω−) and net electrophilicity Δω±, the reflectivity (R), optical frequencyωop, Max of Electron charge (ΔEMAX), Energy change (ΔE) and total Energy minimum(ΔEMIN) of the compounds. Due to the large ⟨α⟩, β, γ, E, P, χ, Ɛ, n, and D of these molecules, we think that these molecules have potential applications in the field of optoelectronics, such as optical communication, optical computing, optical switching, and dynamic image processing.

Detection and Identification of Reaction Intermediates in the Photorearrangement of Pyridazine N-Oxide: Discrepancies between Experiment and Theory.

Photolysis of pyridazine N-oxide (PNO) results in the detection of a complex series of transient phenomena. On the ultrafast (fs) timescale, we could detect the decay of the first singlet excited state of PNO and the formation of a short-lived transient species, which, based on its time-resolved resonance Raman (TR3) spectrum, we assign to oxaziridine 1,2-diaza-7-oxa-bicyclo[4.1.0]hepta-2,4-diene. On a longer (hundreds of ns) timescale, this species rearranges to a ring-opened diazo compound, which we have also detected by time-resolved infrared and TR3 spectroscopy. In addition, we identify 1-oxa-3,4-diazepine as a long-lived species formed in the photochemistry of PNO. This species is formed via its oxirane isomer, which in turn is likely formed directly from the S1 state of PNO via a conical intersection. The barrier determined experimentally for the decay of 1,2-diaza-7-oxa-bicyclo[4.1.0]hepta-2,4-diene (Ea = (7.1 ± 0.5) kcal mol-1) is far larger than any barrier calculated by any method that includes dynamic electron correlation but very close to the barriers calculated at the RHF or CASSCF levels of theory. Many methods (B3LYP, MP2, and MP4) fail to give a minimum structure for 1,2-diaza-7-oxa-bicyclo[4.1.0]hepta-2,4-diene, while M06, M06-2X, MP3, CCSD, or CCSD(T) yield activation energies for its electrocyclic ring opening that are far too small. In addition, we note that several important geometric parameters, both of 1,2-diaza-7-oxa-bicyclo[4.1.0]hepta-2,4-diene and of the transition state of its ring opening reaction, clearly have reached no convergence, even at the fully optimized CCSD(T)/cc-pVTZ level of theory. We therefore suggest that the transient species described in this contribution might be excellent test molecules for further development of highly correlated and density functional theory methods.

Adsorption of alanine with heteroatom substituted fullerene for solar cell application: A DFT study

C20 is the most important fullerene cage and alanine is the simplest representation of a backbone unit of the protein. The absorption feasibility of alanine molecule in the Si-doped C20 and B-doped C20 fullerenes has been studied based on calculated electronic properties of fullerenes using density functional theory (DFT). In this work, we explore the ability of Si-doped C20, B-doped C20 fullerene to interact with alanine at the DFT-B3LYP/6-31G, RHF level of theory. We find that noticeable structural change takes place in C20 when one of its carbon is substituted with Si or B. The molecular geometry, electronic properties and vibrational analysis have also been performed on the title compounds. The NMR study reveals the aromaticity of the pure and doped fullerene compounds. Stability of the doped fullerene – alanine compound arises from hyper conjugative interactions. It leads to one of the major property of bioactivity, charge transfer and delocalization of charge and this properties has been analyzed using Natural Bond Orbital (NBO) analysis. The energy gap of the doped fullerene reveals that there is a decrease in the size of energy gap significantly, making them more reactive as compared to C20 fullerene. Theoretical studies of the electronic spectra by using time – dependent density functional theory (TD-DFT) method were helpful to interpret the observed electronic transition state. We aim to optimize the performance of the solar cells by altering the frontier orbital energy gaps. Considering all studied properties, it may be inferred that the applicability of C20 fullerene as the non-linear optical (NLO) material and its NLO property would increase on doping fullerene with Si and B atom. Specifically C19Si would be better among them.

Computational determination of the Electronic and Nonlinear Optical properties of the molecules 2-(4-aminophenyl) Quinoline, 4-(4-aminophenyl) Quinoline, Anthracene, Anthraquinone and Phenanthrene

The Electronic and Nonlinear Optical properties of the donor-acceptor molecules 2-(4-aminophenyl) Quinoline, 4-(4-aminophenyl) Quinoline, Anthraquinone; and the molecules Anthracene and Phenanthrene have been determined and some of these properties compared with literature values. The theoretical calculations were performed at the RHF level of theory and with two different hybrid density functional theories (DFT) (B3LYP and B3PW91), using the 6-31+G** basis set. The results show that these molecular systems have large average polarizability, anisotropy and first molecular hyperpolarizabilities. The small values of ε, and LUMO-HOMO energy band gap (Egap) and the high values χ, η,<α>, and (βmol) show that the molecules have very good electronic, nonlinear optical, optoelectronic and photonic applications. Furthermore, the (Egap) of Phenanthrene shows that Phenanthrene is a good promising organic superconductor material.

A strong N[sbnd]H…Br vibrational behaviour studied through X-ray, vibrational spectra and quantum chemical studies in an isomorphous crystal: 2-Nitroanilinium bromide

A needle shaped transparent light brown crystals of 2-nitroanilinium bromide were successfully synthesized and crystallized from an aqueous mixture by slow evaporation technique. Single crystal XRD studies confirm the crystalline phase of this isomorphous compound which contains a positively charge 2-nitroanilinium cation and a negatively charged bromide anion. The solid phase FT-IR and FT-Raman spectra of the compound have been recorded in the range of 4000–400cm−1. The observed modes are correlated by the factor group theory analysis and different IR and Raman active species were identified. Geometrical optimisations were carried out and harmonic vibrational wave numbers were computed for the minimum energy molecular structure at RHF level invoking 6-311++G(d,p) and SDD basis sets. Optimised molecular geometry was compared with the crystallographic data. The calculated wavenumbers were compared with the experimental values. The NH vibrational bands are shifted from its normal range and the shifting is associated with the influence of the intermolecular hydrogen bonds in the crystal. A strong intensity peak in theoretical and corresponding band in experimental confirms the presence of NH…Br interaction as predicted in crystalline state.

Theoretical studies on the anionic association of phenol and its derivatives in acetonitrile

The potentials of mean force (PMF) were determined for homoconjugated systems of anionic complexes composed of phenol and its derivatives with their conjugate anionic bases in acetonitrile (ACN). For each acid-base pair studied, a series of umbrella-sampling molecular dynamics simulations using the AMBER force field with explicit solvent was carried out; the respective PMF was calculated using the Weighted Histogram Analysis Method (WHAM). Subsequently, association equilibrium constants were calculated by numerical integration of the PMF profiles. The PMF curves had a typical shape, i.e., a very deep and narrow contact-minimum, a desolvation maximum, and a shallow solvent-separated minimum. All pairs formed complexes in solution, which was confirmed by the presence of contact minima corresponding to the existence of hydrogen bonds in the PMF curves. The calculated association constants in acetonitrile were subsequently compared with experimentally obtained values for the same solvent.Ab initio methods at the RHF level (utilizing the Gaussian 6-31++G** basis set) enabled the in vacuo calculation of energies and Gibbs free energies of interaction for each phenol derivative and anionic base pair along with a molecule of acetonitrile; this allowed the contribution of the solvent molecule to the PMF to be assessed. It was found that the interaction energies of anionic bases in acetonitrile are stronger than their related neutral phenol derivatives.

Hybrid RHF/MP2 Geometry Optimizations with the Effective Fragment Molecular Orbital Method

The frozen domain effective fragment molecular orbital method is extended to allow for the treatment of a single fragment at the MP2 level of theory. The approach is applied to the conversion of chorismate to prephenate by Chorismate Mutase, where the substrate is treated at the MP2 level of theory while the rest of the system is treated at the RHF level. MP2 geometry optimization is found to lower the barrier by up to 3.5 kcal/mol compared to RHF optimzations and ONIOM energy refinement and leads to a smoother convergence with respect to the basis set for the reaction profile. For double zeta basis sets the increase in CPU time relative to RHF is roughly a factor of two.

Steric and electronic structure of 2-alkoxyphenyltrichlorostannanes according to results of ab initio calculations

Steric and electronic structure of 2-methoxy- and 2-ethoxyphenyltrichlorostannanes, as well as of 2-methoxyphenyltrichlorostannanes substituted in the ring, was studied using the RHF and B3LYP levels with the 3–21G* basis set. The results of calculations were compared with experimental 35Cl NQR data. In all studied molecules the Sn atom is pentacoordinated. The structure of the coordination polyhedron is a highly distorted trigonal bipyramid. Replacing methyl group in the alkoxy substituent involved in the Sn←O coordinating interaction by a more electron-donor ethyl group increases the strength of the Sn←O coordination bond. The same occurs also at the introduction of an electron-releasing substituent in the aromatic ring.

The Structure and Chemical Bond of FOX-7: The AIM Analysis and Vibrational Normal Modes

FOX-7 (1,1-diamino-2,2-dinitroethylene) recently is expected as a relatively new energetic material with high-performance and low sensitivity. The RHF and MP2 levels and DFT method with B3LYP functional with aug-cc-pVDZ basis set have been used for obtaining equilibrium geometry and Rho function (electron density distribution). By the aid of fundamental physical theorems implemented in the Quantum Theory of Atoms In Molecules (QTAIM), the structure, the physical nature of chemical bonds and all Bond Critical Points (BCPs) properties have been determined for FOX-7 at the mentioned theoretical levels. Existence of resonance due to electron-withdrawing nitro groups and electron-donating amine groups in ethene backbone and intra-molecular hydrogen bonding are shown with AIM analysis and then the resonance structures of FOX-7 are found. Also the calculated IR spectrum of FOX-7 is compared with the experimental IR spectrum. It is demonstrated that the mathematical properties of molecular graph derived from charge density analysis are in good correlation with that of the vibrational normal modes derived from ab initio computations.

Substitution effects on the polarizability (α) and first hyperpolarizability (β) of all-trans hexatriene

Polarizability (α) and first hyperpolarizability (β) have been calculated for a set of substituted all-trans hexatriene NO2-linker-D compounds at TDHF and CPHF/6-31+G∗ levels of theory. Effects due to the nature of D/A pair type on the geometrical structural and the electrical proprieties are investigated. It turns out that electronics polarizability and first hyperpolarizability are considerably intensified by the functionality of amino groups, as well the pair NO2/NEt2 associated the greatest α and β values. The relationships between βe and βv are investigated and for molecules with N heteroatom at the donor groups considered the βLv(0)/ βLe(0) ratio lies in the range 1.04–1.36. Although the level of theory employed herein gives significantly different results only for the vibrational, longitudinal hyperpolarizability counterpart than those obtained by Bishop et al. (1998) at the RHF level, the overall conclusions remain unchanged. For both static and dynamic polarizabilities values an excellent agreement between the CPHF, TDHF and PM6 results, they give a correlation coefficient of 0.96 and 0.95, respectively. The frequency and solvent effect were also considered.

Boron–nitrogen- and boron-substituted anthracenes and -phenanthrenes as models for doped carbon-based materials

The aim of this theoretical study is the investigation of hydrocarbon stability as a function of BN- and B-substitution degree. The targets are anthracene and phenanthrene because they resemble the zig-zag and armchair peripheries of graphene sheets. The computations are made at the RHF and MP2 level with various basis sets. The conclusions drawn are based on the results from calculations for more than 600 different structures created in a systematic way where pairs of carbon atoms are replaced by the respective number of B and N, or solely B-atoms. A common feature of all stable substituted molecules is the tendency for least fragmentation of the carbon skeleton, particularly, for preservation of maximum number of intact carbon aromatic cycles. The major dissimilarity between the BN- and B-substituted molecules are the preferred doping patterns and positions: the favorable structures feature alternation of B and N in the BN-derivatives and disjoint borons separated by C 2 fragments in the B-ones; the nitrogen atoms substitute predominantly secondary carbons, while borons prefer tertiary sites in the BN-substituted hydrocarbons and secondary positions in the B-modified structures. Overall, the anthracene isomers are more stable. The energy and AO contributions to the LUMOs of the studied species are rationalized in terms of electron-accepting properties of the latter, estimating their potential performance as oxidants. Energy depression of LUMOs is achieved mainly in B-substituted hydrocarbons due to large coefficients on the borons causing pronounced delocalization of the orbital. The findings can be used for directed synthesis of novel modified carbon-based materials for practical purposes.

A combined effective fragment potential–fragment molecular orbital method. I. The energy expression and initial applications

The effective fragment potential (EFP) method, a model potential for treating solvent effects and other intermolecular interactions, is interfaced with an electronic structure method, the fragment molecular orbital (FMO) method, that is able to retain high accuracy for ab initio calculations on large molecular systems. The accuracy of the total energies in this novel combined FMO/EFP method is assessed by comparisons with the conventional quantum mechanics (QM)/EFP method. The test cases are water clusters, a peptide, and a dianionic protein (treated with full QM and FMO) combined with water clusters (treated with EFP) at the RHF, B3LYP, and MP2 levels of theory. The basis sets employed range from minimal to augmented double zeta plus polarization. The energy differences between FMO/EFP and the conventional QM/EFP methods are within "chemical accuracy" (1 kcal/mol approximately = 4 kJ/mol).

A joint experimental and theoretical study of kinetic and mechanism of rearrangement of allyl p-tolyl ether

A joint theoretical and experimental study of the kinetic and mechanism of the rearrangement of allyl p-tolyl ether was performed in order to study the kinetic and mechanism of the reaction. Experimental studies were performed in gas phase over a temperature range of 493.15–533.15 K. The experimental Arrhenius parameters of this reaction were measured to be E a = 36.08 kcal mol −1, Δ S # = −7.88 cal mol −1 K −1, and Log A = 11.74, experimentally. Using GC for the mixture of the reaction with and without cyclohexene demonstrated that the reaction is clean without any radical intermediates. The experimental results show that the studied reaction is unimolecular and proceeds through a concerted pathway. Theoretical calculation were performed at RHF and B3LYP levels of theory using 6-31G ∗, 6-31++G ∗∗ and 6-311G ∗ basis sets. These calculations showed that the reaction proceeds through an asynchronous concerted mechanism. The calculated kinetics parameters especially at B3LYP/6-31G ∗ level of theory are in good agreement with the experimental data. Also polarizable continuum model was used to study solvent effect on the reaction rate. These calculations indicated that the rate enhancement of the reaction in polar and protic solvents arise from specific solute–solvent interactions such as hydrogen bonding and the hydrophobic effects of solvent.

Steric and hyperconjugative contributions to rotation barriers in diboron analogs B2L4 (L=F, OH, NH2, CH3, and H)

The rotational barriers of B(2)L(4) (where L = F, OH, NH(2), CH(3), and H) were investigated with respect to the hyperconjugation and steric effects at the levels of RHF, MP2, and B3LYP using a basis set of 6-311G(d,p). At all levels of theory, the LBBL dihedral angle of the minimum energy conformation was found to increase with decreasing electronegativity of the atom bonded to boron. The L substituents that possess no lone pairs have greater steric exchange energy, destabilizing the planar conformation relative to the perpendicular. However, the planar conformation of compounds with L substituents having lone pairs on the heavy atom is counterstabilized by conjugative delocalization into the "empty" p-orbitals associated with boron. For B(2)(NH(2))(4), neither factor dominates and the optimal geometry is skewed at a dihedral angle of 37.62 degrees (MP2).

Theoretical study on molecular structures, intramolecular proton transfer reaction, and solvent effects of 1-phenyl-3-methyl-4-(6-hydro-4-amino-5-sulfo-2,3-pyrazine)-pyrazole-5-one

The molecular structures and intramolecular proton transfer reaction of 1-phenyl-3-methyl-4-(6-hydro-4-amino-5-sulfo-2,3-pyrazine)-pyrazole-5-one have been investigated with both ab initio method and the density functional theory. The solvent effects are simulated using the self-consistent reaction field (SCRF) method within the framework of the polarizable continuum model (PCM). The results show that the computed geometrical parameters at the B3LYP levels are in better agreement with experimental values than those at the RHF levels, and the choice of functional in DFT plays an important role in describing the title compound. It is found that strong hydrogen bonds (O–H···N and O···H–N) exist in the title compound, and in the proton transfer process, the O–H bond is broken while the N–H bond is formed. In addition, the order of stability of the isomers remains the same in different solvents, while the barrier height of the proton transfer reaction and dipole moments for the title compound grow with the increase of the solvent polarity. Eventually, the NBO analysis shows that the strength of the hydrogen bond reduces with the increase of the solvent polarity.

Electronic structure calculations toward new potentially AChE inhibitors

The main purpose of this study was the use of natural non-isoprenoid phenolic lipid of cashew nut shell liquid from Anacardium occidentale as lead material for generating new potentially candidates of acetylcholinesterase inhibitors. Therefore, we studied the electronic structure of 15 molecules derivatives from the cardanol using the following groups: methyl, acetyl, N, N-dimethylcarbamoyl, N, N-dimethylamine, N, N-diethylamine, piperidine, pyrrolidine, and N-benzylamine. The calculations were performed at RHF level using 6-31G, 6-31G(d), 6-31+G(d) and 6-311G(d,p) basis functions. Among the proposed compounds we found that the structures with substitution by acetyl, N, N-dimethylcarbamoyl, N, N-dimethylamine, and pyrrolidine groups were better correlated to rivastigmine indicating possible activity.

Computational insight into relations between electronic and vibrational polarizabilities within the two-state valence-bond charge-transfer model

In this paper, the relationship between static vibrational and electronic hyperpolarizabilities of a series of push–pull molecules within the two-state valence-bond charge-transfer model are reinvestigated computationally at the Møller–Plesset level of theory. Although the level of theory employed here gives significantly different results for electronic and vibrational counterparts than those obtained by Bishop et al. [D. Bishop, B. Champagne, B. Kirtman, J. Chem. Phys. 109 (1998) 9987] at the RHF level, the overall conclusions remain unchanged: The comparison of ab initio computations with the predictions of the VB–CT model gives a little confidence in the latter.

Restricted Geometry Optimization: A Different Way To Estimate Stabilization Energies for Aromatic Molecules of Various Types

At RHF, MPn, and DFT levels, a procedure of geometry optimization under the restrictions of pi-orbital interactions (GOR) was developed, thus providing a conjugated molecule with the following two types of localized reference geometries: a "GL" geometry where all double bonds are localized, and n different "GE-n" geometries, in each of which only two double bonds were permitted to conjugate. Interestingly, the molecular energy differences between the corresponding pairs of GE-n and GL geometries were found to be additive in each of the acyclic polyenes, and these were not additive for benzene. As a result, an extra stabilization energy (ESE) value of -39.0 kcal/mol was found in benzene. Afterward, GOR was applied to benzene- and furan-like species, strained aromatic molecules, and substituted benzenes, and the calculated ESEs for these molecules were found to be in reasonable ranges. The GOR can isolate a specific group from other groups, and it has several special functions. First, with regard to the substituent effect, the ESE difference between substituted benzene and benzene can be partitioned into conjugative and inductive parts. Second, the behavior of strained aromatic molecules can be ascertained from the roles of their resonance interactions, strained-induced bond localization (SIBL), and inductive effects, indicating that it is resonance interactions, rather than SIBL, which are responsible for localizing double bonds. Emphatically, it is the GL and GE-n geometries of aromatic molecules, rather than nonaromatic compounds, which can be used as the reference structures for calculating ESE. Particularly, these localized geometries are no longer arbitrary.

Polarization-Consistent versus Correlation-Consistent Basis Sets in Predicting Molecular and Spectroscopic Properties

Compared to the correlation-consistent basis sets, it is not known if polarization-consistent pc-n basis sets, which were initially developed for HF and DFT calculations, can provide a monotonic and faster convergence toward the basis-set limit for results at correlated levels as well as better accuracy for a similar number of basis functions. It is also not known whether the pc-n basis sets can compute second derivatives of energy, such as nuclear magnetic shielding tensors, efficiently. To address these questions, the pc-n (n = 1-4), cc-pVxZ, and/or aug-cc-pVxZ (x = D, T, Q, 5, and 6) basis sets were used to compute the molecular and/or spectroscopic parameters of H2, H2O, and NH3 at the RHF, B3-LYP, MP2, and/or CCSD(T) levels of theory. The results show that compared to the cc-pVxZ and/or aug-cc-pVxZ basis sets the pc-n basis sets yield faster convergence toward the basis-set limit but equivalent molecular and/or spectroscopic parameters in the basis-set limit at the RHF, DFT, MP2, and CCSD(T) levels. Because the pc-n basis sets show faster convergence, fewer basis-set functions are needed to reach the accuracy obtained with the aug-cc-pVxZ basis sets, enabling faster calculations and less computer storage space. The results also show that the pc-n basis sets, in conjunction with the "locally dense" basis-set approach, could be applied to predict accurate parameters; thus, they could be used to estimate accurate molecular or spectroscopic properties (e.g., NMR parameters) for larger systems such as the active site of enzymes.