Basis Set Method Research Articles

BCG Artifact Removal for Reconstructing Full-scalp EEG inside the MR Scanner.

In simultaneous EEG/fMRI acquisition, the ballistocardiogram (BCG) artifact presents a major challenge for meaningful EEG signal interpretation and needs to be removed. This is very difficult, especially in continuous studies where BCG cannot be removed with averaging. In this study, we take advantage of a high-density EEG-cap and propose an integrated learning and inference approach to estimate the BCG contribution to the overall noisy recording. In particular, we present a special-designed experiment to enable a near-optimal subset selection scheme to identify a small set (20 out of 256 channels), and argue that in real-recording, BCG artifact signal from all channels can be estimated from this set. We call this new approach "Direct Recording Temporal Spatial Encoding" (DRTSE) to reflect these properties. In a preliminary evaluation, the DRTSE is combined with a direct subtraction and an optimization scheme to reconstruct the EEG signal. The performance was compared against the benchmark Optimal Basis Set (OBS) method. In the challenging nonevent-related EEG studies, the DRTSE method, with the optimization-based approach, yields an EEG reconstruction that reduces the normalized RMSE by approximately 13 folds, compared to OBS.

Density functional theory, restricted Hartree – Fock simulations and FTIR, FT-Raman and UV–Vis spectroscopic studies on lamotrigine

The Fourier Transform Infrared (FTIR) and FT Raman spectra of lamotrigine have been recorded in the region 4000–450cm−1 and 4000–50cm−1, respectively. The title compound is used as Antiepileptic drug. The optimized geometry, frequency, and intensities of the vibrational bands of the lamotrigine were obtained by Density Functional Theory (DFT) using B3LYP/631G** basis set and ab initio method at the restricted Hartree Fock/6-31** level. The harmonic vibrational frequencies, Natural population analysis, HOMO–LUMO energy gap, infra red intensities and Raman scattering activities, force constant were calculated by DFT and RHF methods. The quality of lamotrigine under different storage containers were analyzed using UV–Vis spectral technique.

Theoretical studies on [2 + 2 + 2] reaction mechanisms of three ethynes. More accurate estimation of activation energy

The mechanisms of the [2 + 2 + 2] cycloaddition reaction of three ethyne molecules were studied by ab initio molecular orbital and density functional methods. The transition states range from that of the concerted mechanism with D3h symmetry to that of the stepwise mechanism with C2 symmetry. The transition state structure and the activation energy depend on the basis set and computational method employed in the analysis. The activation energy barrier was determined to be in the range of 36–44 kcal/mol. The activation energy determined by various methods corresponds to the interaction energy, which is related to the electron correlation energy. The best estimation of the activation energy barrier is 41.6 kcal/mol, achieved from the relation between the interaction energy and the activation energy. Copyright © 2013 John Wiley & Sons, Ltd.

Conformational analysis and parallel QM/MM X-ray refinement of protein bound anti-Alzheimer drug donepezil.

The recognition and association of donepezil with acetylcholinesterase (AChE) has been extensively studied in the past several decades because of the former's use as a palliative treatment for mild Alzheimer disease. Herein we examine the conformational properties of donepezil and we re-examine the donepezil-AChE crystal structure using combined quantum mechanical/molecular mechanical (QM/MM) X-ray refinement tools. Donepezil's conformational energy surface was explored using the M06 suite of density functionals and with the MP2/complete basis set (CBS) method using the aug-cc-pVXZ (X = D and T) basis sets. The donepezil-AChE complex (PDB 1EVE) was also re-refined through a parallel QM/MM X-ray refinement approach based on an in-house ab initio code QUICK, which uses the message passing interface (MPI) in a distributed SCF algorithm to accelerate the calculation via parallelization. In the QM/MM re-refined donepezil structure, coordinate errors that previously existed in the PDB deposited geometry were improved leading to an improvement of the modeling of the interaction between donepezil and the aromatic side chains located in the AChE active site gorge. As a result of the re-refinement there was a 93% reduction in the donepezil conformational strain energy versus the original PDB structure. The results of the present effort offer further detailed structural and biochemical inhibitor-AChE information for the continued development of more effective and palliative treatments of Alzheimer disease.

A procedure for bypassing metastable states in local basis set DFT+U calculations and its application to uranium dioxide surfaces

We present a study of the bulk and the (100), (110) and (111) surfaces of uranium dioxide (UO2) using DFT+U in combination with a mixed Gaussian and plane waves basis set method, as implemented in the CP2K program package. The compromise of accuracy against computational efficiency by which this method enables calculations of relatively large UO2 systems is found to be acceptable in light of the almost 50-fold improvement in calculation times. A novel scheme is presented which reliably allows the system to escape the lower-lying metastable states that arise from the improved treatment of the strongly correlated 5f electrons of uranium. Based on the electronic configurations obtained by an f-occupation smearing combined with U ramping, this method relaxes the local energy minima by averaging the f-occupation matrices used to calculate the corrections in DFT+U. Various surface terminations are investigated and their calculated formation energies are found to be consistent with the experimentally observed morphologies. The direction of the antiferromagmentic ordering in relation to the surfaces exerts little influence on the results of the calculations while surface reconstructions can induce significant structural changes extending well into the bulk.

Quantum chemical calculations of bond dissociation energies for COOH scission and electronic structure in some acids

Quantum chemical calculations are performed to investigate the equilibrium C—COOH bond distances and the bond dissociation energies (BDEs) for 15 acids. These compounds are studied by utilizing the hybrid density functional theory (DFT) (B3LYP, B3PW91, B3P86, PBE1PBE) and the complete basis set (CBS—Q) method in conjunction with the 6-311G** basis as DFT methods have been found to have low basis sets sensitivity for small and medium molecules in our previous work. Comparisons between the computational results and the experimental values reveal that CBS—Q method, which can produce reasonable BDEs for some systems in our previous work, seems unable to predict accurate BDEs here. However, the B3P86 calculated results accord very well with the experimental values, within an average absolute error of 2.3 kcal/mol. Thus, B3P86 method is suitable for computing the reliable BDEs of C—COOH bond for carboxylic acid compounds. In addition, the energy gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of studied compounds are estimated, based on which the relative thermal stabilities of the studied acids are also discussed.

Theoretical study on the molecular tautomerism of the 3-hydroxy-pyridin-4-one system

3-hydroxy-pyridin-4-one is a parent molecule for the family of hydroxypyridinones that are known in coordination chemistry as efficient metal ions chelators. In this work, relative stabilities of some possible tautomers were investigated using several quantum chemical methods: CBS (complete basis set methods), Gn, DFT (density functional theory), Hartree–Fock and MP2. Performed calculations show that the system under consideration exists as a mixture of two tautomers with comparable energies. Among them, the hydroxypyridinone structure of the studied molecular system seems to be a bit more stable than the o-dihydroxypyridine one, by a few kJ/mol only. Aromaticity and intra-molecular hydrogen bonding are the main effects influencing the stability of the studied tautomeric structures. Consequently, aromatic effects were calculated using several indices of aromaticity: HOMA (harmonic oscillator model of aromaticity), NICS (nucleus independent chemical shift), H, PDI (para delocalisation index), MCI (multi-centre index) and ASE (aromatic stabilisation energy). The strength of possible intra-molecular hydrogen bonds (H-bonds) was determined by means of the AIM (atoms-in-molecules) method and by calculating enthalpies for theoretical reactions that do or do not involve H-bonds. The AIM method was employed to understand how variations in atomic energies influence the stability of different tautomeric structures.

Exploring Relative Thermodynamic Stabilities of Formic Acid and Formamide Dimers - Role of Low-Frequency Hydrogen-Bond Vibrations.

The low-frequency fundamentals together with the high-frequency modes, responsible for hydrogen bonding (OH/NH stretching modes), were analyzed to correlate the intensities with the hydrogen-bond strengths/binding energies of the formic acid and formamide dimers using Møller-Plesset second-order perturbation (MP2) and coupled cluster computations with explicit anharmonicity corrections. Linear correlations were observed for both the formic acid and formamide dimers, and as consequence of such correlation an additive properties of binding energies with respect to the local hydrogen-bond energies of fragments involved (for these dimers) has been proposed. It has been further observed that (i) the nature of their six low-frequency fundamentals are very similar, and (ii) the in-plane bending and stretch-bend fundamentals of different dimers of these two species (depending on the dimer structure), in this low-frequency region, modulate their strength of hydrogen-bond/binding hence their relative stability order. These results were further verified against the results from Gaussian-G4-MP2 (G4MP2), Gaussian-G2-MP2 (G2MP2), and complete basis set (CBS-QB3) methods of high accuracy energy calculations.

Effects of London dispersion correction in density functional theory on the structures of organic molecules in the gas phase

A benchmark set of 25 rotational constants measured in the gas phase for nine molecules (termed ROT25) was compiled from available experimental data. The medium-sized molecules with 18-35 atoms cover common (bio)organic structure motifs including hydrogen bonding and flexible side chains. They were each considered in a single conformation. The experimental B0 values were back-corrected to reference equilibrium rotational constants (Be) by computation of the vibrational corrections ΔBvib. Various density functional theory (DFT) methods and Hartree-Fock with and without dispersion corrections as well as MP2 type methods and semi-empirical quantum chemical approaches are investigated. The ROT25 benchmark tests their ability to describe covalent bond lengths, longer inter-atomic distances, and the relative orientation of functional groups (intramolecular non-covalent interactions). In general, dispersion corrections to DFT and HF increase Be values (shrink molecular size) significantly by about 0.5-1.5% thereby in general improving agreement with the reference data. Regarding DFT methods, the overall accuracy of the optimized structures roughly follows the 'Jacobs ladder' classification scheme, i.e., it decreases in the series double-hybrid > (meta)hybrid > (meta)GGA > LDA. With B2PLYP-D3, SCS-MP2, B3LYP-D3/NL, or PW6B95-D3 methods and extended QZVP (def2-TZVP) AO basis sets, Be values, accurate to about 0.3-0.6 (0.5-1)% on average, can be computed routinely. The accuracy of B2PLYP-D3/QZVP with a mean deviation of only 3 MHz and a standard deviation of 0.24% is exceptional and we recommend this method when highly accurate structures are required or for problematic conformer assignments. The correlation effects for three inter-atomic distance regimes (covalent, medium-range, long) and the performance of minimal basis set (semi-empirical) methods are discussed.

Simulating Constant Current STM Images of the Rutile TiO2 (110) Surface for Applications in Solar Water Splitting

ABSTRACTSolar water splitting has shown promise as a source of environmentally friendly hydrogen fuel. Understanding the interactions between semiconductor surfaces and water is essential to improve conversion efficiencies of water splitting systems. TiO2 has been widely adopted as a reference material and rutile surfaces have been studied experimentally and theoretically. Scanning Tunneling Microscopy (STM) is commonly used to study surfaces, as it probes the atomic and electronic structure of the surface layer. A systematic and transferable method to simulate constant current STM images using local atomic basis set methods is reported. This consists of adding more diffuse p and d functions to the basis sets of surface O and Ti atoms, in order to describe the long range tails of the conduction and valence bands (and, thus, the vacuum above the surface). The rutile TiO2 (110) surface is considered as a case study.

Experimental and Computational Studies on the Thermal Degradation of Nitroazidobenzenes

AbstractIn this combined experimental and theoretical study the thermal degradation of 2‐nitroazidobenzene (I), 2,4‐dinitroazidobenzene (II) and 2,4,6‐trinitroazidobenzene (III) to yield benzofuroxan (IV), 4‐nitrobenzofuroxan (V), and 4,6‐dinitrobenzofuroxan (VI) were investigated by thermoanalytical (TG, DSC) and computational methods. In contrast, furoxan formation was not observed for 4‐nitroazidobenzene (VII) under heating due to the para position of the nitro group in the benzene ring. All compounds were characterized by elemental analysis, vibrational (IR) spectroscopy and mass spectrometry. The crystal structure of compound III was determined by single‐crystal X‐ray diffraction. DFT‐based structure optimizations and frequency analyses were performed at the B3LYP/cc‐pVDZ level of theory. The structural parameters of the fully optimized compound III showed very good agreement with the single‐crystal X‐ray data. The enthalpies of formation for compounds I, II, III, IV, V, and VI were calculated using the complete basis set (CBS‐4M) method of Petersson and co‐workers in order to obtain accurate energies. The enthalpies of degradation for compounds I, II, and III were obtained from calculated enthalpies of formation according to the Hess Law and were compared with the experimental values, which were available from DSC analysis and were found to be in very good agreement.

Novel approach to theoretical investigation of heavy quasi-molecules

The new approach to the theoretical investigation of heavy quasi-molecules is created. The approach is based on the application of finite basis set method in Cassini coordinates. The method allows the generation of accurate quasi-complete spectrum of two-center Dirac Hamiltonian eigen-states.

Population Evolution of Rydberg Rubidium Atoms by Half-Cycle Pulses

Using the B-spline basis set method combined with model potential, the Stark energy level of rubidium atoms in the vicinity of n = 30 is presented. By using a using time-dependent multilevel approach, we calculate the population redistribution of high Rydberg rubidium atoms under the interaction of external time-dependent half-cycle pulses. Our numerical results show that the population of rubidium atoms can be driven to lower or higher n levels with a train of half cycle pulses, the final population distribution of all the l states for the same n is observed after these interactions.

Quantum Mechanical Study on the Structure and Vibrational Spectra of Cyclobutanone and 1,2-Cyclobutanedione

For 1,2-cyclobutanedione and cyclobutanone, we have carried out a comparative study of different methods like B3LYP, LSDA, and B3PW91 of DFT using 6-31G (d, p) basis set and MP2 method. On comparing these methods we find that B3PW91 method is closer to the experimental one. So by using B3PW91 method, we have made a comparative study of their structures, normal mode analysis, and other properties of the two derivatives of cyclobutane. The molecular HOMO, LUMO composition, their respective energy gaps, and MESP contours/surfaces have also been drawn to explain the activity of 1,2-cyclobutanedione and cyclobutanone.

Relativistic polarization analysis of Rayleigh scattering by atomic hydrogen

A relativistic analysis of the polarization properties of light elastically scattered by atomic hydrogen is performed, based on the Dirac equation and second order perturbation theory. The relativistic atomic states used for the calculations are obtained by making use of the finite basis set method and expressed in terms of $B$ splines and $B$ polynomials. We introduce two experimental scenarios in which the light is circularly and linearly polarized, respectively. For each of these scenarios, the polarization-dependent angular distribution and the degrees of circular and linear polarization of the scattered light are investigated as a function of scattering angle and photon energy. Analytical expressions are derived for the polarization-dependent angular distribution which can be used for scattering by both hydrogenic as well as many-electron systems. Detailed computations are performed for Rayleigh scattering by atomic hydrogen within the incident photon energy range 0.5 to 10 keV. Particular attention is paid to the effects that arise from higher (nondipole) terms in the expansion of the electron-photon interaction.

Some new energetic benzaldoximes

5-Nitro-2-hydroxy benzaldoxime (I), 3-nitro-4-hydroxy benzaldoxime (II), 3,5-dinitro-2-hydroxy benzaldoxime (III), and 3,5-dinitro-4-hydroxy benzaldoxime (IV) were prepared from their respective nitrated aldehydes. Prepared oximes were characterized by IR spectroscopy, elemental analysis, and mass spectrometry. Suitable crystals of compounds II and III were obtained and molecular structures were determined by means of the single crystal XRD method. All benzaldoximes were investigated by TG. At temperatures above 140 °C, it was observed that compounds II and IV lost one H2O and was converted to the respective benzonitriles. Only thermal analysis peaks of 3,5-dinitro-4-hydroxy benzonitrile (V) were found proper for both experimental and theoretic calculations; whereas, compounds I and III were converted to phenoxazines by Beckmann rearrangement along with dehydration. Beckmann product of compound III is referred as compound VI and its tautomer as compound VII. Similarly only 3,5-dinitro phenoxazine (VIII) was investigated experimentally and theoretically since its thermal analysis peaks were proper for the purpose. DFT-based structure optimizations and frequency analyses were performed at the B3LYP/cc-pVDZ level of theory. The enthalpies of formation for compounds III–VIII were calculated by means of the complete basis set (CBS-4M) method of Petersson and coworkers to obtain accurate energies. The enthalpies of decomposition for compounds III and IV were obtained from calculated enthalpies of formation according to Hess’ law and were compared with the experimental values which were available from DSC analyses and were found to be in good agreement with the theoretic values.

Ab Initio and Density Functional Theory Study of Keto–Enol Equilibria of Deltic Acid in Gas and Aqueous Solution Phase: A Bimolecular Proton Transfer Mechanism

Keto-enol tautomerism in deltic acid (2,3-dihydroxycycloprop-2-en-1-one) has been studied using ab initio methods and the B3LYP functional of density functional theory, as well as complete basis set (CBS-QB3 and CBS-APNO) and G4 methods. Relative and absolute energies were calculated with each of the methods, whereas computations of geometries and harmonic frequencies for dihydroxycyclopropenone and hydroxycyclopropanedione were computed in the gas phase but were limited to HF, MP2, and the B3LYP functional, in combination with the 6-31++G(3df,3pd) basis set. Using the MP2/6-31++G(3df,3pd) gas phase optimized structure, each species was then optimized fully in aqueous solution by using the polarizable continuum model (PCM) self-consistent reaction field approach, in which HF, MP2, and B3LYP levels of theory were utilized, with the same 6-31++G(3df,3pd) basis set. In both gas and aqueous solution phases, the keto form is higher in energy for all of the model chemistries considered. From the B3LYP/6-31++G(3df,3pd) Gibbs free energy, the keto-enol tautomeric equilibrium constant for 2,3-dihydroxycycloprop-2-en-1-one/3-hydroxy-1,2-cyclopropanedione is computed to be K(T)(gas) = 2.768 × 10(-12) and K(T)(aq) = 5.469 × 10(-14). It is concluded that the enol form is overwhelmingly predominant in both environments.

MESMER: An Open-Source Master Equation Solver for Multi-Energy Well Reactions

The most commonly used theoretical models for describing chemical kinetics are accurate in two limits. When relaxation is fast with respect to reaction time scales, thermal transition state theory (TST) is the theoretical tool of choice. In the limit of slow relaxation, an energy resolved description like RRKM theory is more appropriate. For intermediate relaxation regimes, where much of the chemistry in nature occurs, theoretical approaches are somewhat less well established. However, in recent years master equation approaches have been successfully used to analyze and predict nonequilibrium chemical kinetics across a range of intermediate relaxation regimes spanning atmospheric, combustion, and (very recently) solution phase organic chemistry. In this article, we describe a Master Equation Solver for Multi-Energy Well Reactions (MESMER), a user-friendly, object-oriented, open-source code designed to facilitate kinetic simulations over multi-well molecular energy topologies where energy transfer with an external bath impacts phenomenological kinetics. MESMER offers users a range of user options specified via keywords and also includes some unique statistical mechanics approaches like contracted basis set methods and nonadiabatic RRKM theory for modeling spin-hopping. It is our hope that the design principles implemented in MESMER will facilitate its development and usage by workers across a range of fields concerned with chemical kinetics. As accurate thermodynamics data become more widely available, electronic structure theory is increasingly reliable, and as our fundamental understanding of energy transfer improves, we envision that tools like MESMER will eventually enable routine and reliable prediction of nonequilibrium kinetics in arbitrary systems.

Real-space imaginary-time propagators for non-local nucleon-nucleon potentials

Nuclear structure quantum Monte Carlo methods such as Green's function or auxiliary field diffusion Monte Carlo have used phenomenological local real-space potentials containing as few derivatives as possible, such as the Argonne-Urbana family of interactions, to make sampling simple and efficient. Basis set methods such as no-core shell model and coupled-cluster techniques typically use softer non-local potentials because of their more rapid convergence with basis set size. These non-local potentials are usually defined in momentum space and are often based on effective field theory. Comparisons of the results of the two types of methods can be difficult when different potentials are used. We show methods for evaluating the real-space imaginary-time propagators needed to perform quantum Monte Carlo calculations using such non-local potentials. We explore the universality of the large imaginary time propagators for different potentials and discuss how non-local potentials can be used in quantum Monte Carlo calculations.

Theoretical studies on the rotamers and dynamic behaviors of ethyl-5-acetyl-4-(3′,4′-dimethoxyphenyl)-2,6-dimethyl-1,4-dihydropyridine-3-carboxylate

The potential energy surfaces of ethyl-5-acetyl-4-(3′,4′-dimethoxyphenyl)-2,6-dimethyl-1,4-dihydropyridine-3-carboxylate have been explored by density functional theory B3LYP with 6-31G* basis set method. All minima and maxima points have a flat boat conformation and the aryl ring lies above the 1,4-dihydropyridine ring. Therefore, the rotation of aryl, acetyl, and carboethoxy groups do not cause a major conformational change in this compound. However, the orientations of carbonyl groups and the distortion from planarity of dihydropyridine ring have been changed. Intramolecular H-contacts involving CH-groups as proton donors have also been investigated. Comparative analysis of the results indicates that the barrier to rotation for aryl group is smaller than that of the carbonyl groups. In addition, the barriers to rotation for the carbonyl and aryl groups of the corresponding pyridine, i.e., ethyl-5-acetyl-4-(3′,4′-dimethoxyphenyl)-2,6-dimethyl-pyridine-3-carboxylate, have also been computed by a similar basis set to investigate the effect of aromaticity of the dihydropyridine ring on the these parameters.