Choice Of Basis Set Research Articles

Implementation of a semiclassical light-matter interaction using the Gauss-Hermite quadrature: A simple alternative to the multipole expansion

We present an analytical and numerical solution of the calculation of the transition moments for the exact semi-classical light-matter interaction for wavefunctions expanded in a Gaussian basis. By a simple manipulation we show that the exact semi-classical light-matter interaction of a plane wave can be compared to a Fourier transformation of a Gaussian where analytical recursive formulas are well known and hence making the difficulty in the implementation of the exact semi-classical light-matter interaction comparable to the transition dipole. Since the evaluation of the analytical expression involves a new Gaussian we instead have chosen to evaluate the integrals using a standard Gau{\ss}-Hermite quadrature since this is faster. A brief discussion of the numerical advantages of the exact semi-classical light-matter interaction in comparison to the multipole expansion along with the unphysical interpretation of the multipole expansion is discussed. Numerical examples on [CuCl$_4$]$^{2-}$ to show that the usual features of the multipole expansion is immediately visible also for the exact semi-classical light-matter interaction and that this can be used to distinguish between symmetries. Calculation on [FeCl$_4$]$^{1-}$ is presented to demonstrate the better numerical stability with respect to the choice of basis set in comparison to the multipole expansion and finally Fe-O-Fe to show origin independence is a given for the exact operator. The implementation is freely available in OpenMolcas.

An Assessment of Computational Methods for Calculating Accurate Structures and Energies of Bio-Relevant Polysulfur/Selenium-Containing Compounds.

The heavier chalcogens sulfur and selenium are important in organic and inorganic chemistry, and the role of such chalcogens in biological systems has recently gained more attention. Sulfur and, to a lesser extent selenium, are involved in diverse reactions from redox signaling to antioxidant activity and are considered essential nutrients. We investigated the ability of the DFT functionals (B3LYP, B3PW91, ωB97XD, M06-2X, and M08-HX) relative to electron correlation methods MP2 and QCISD to produce reliable and accurate structures as well as thermochemical data for sulfur/selenium-containing systems. Bond lengths, proton affinities (PA), gas phase basicities (GPB), chalcogen–chalcogen bond dissociation enthalpies (BDE), and the hydrogen affinities (HA) of thiyl/selenyl radicals were evaluated for a range of small polysulfur/selenium compounds and cysteine per/polysulfide. The S–S bond length was found to be the most sensitive to basis set choice, while the geometry of selenium-containing compounds was less sensitive to basis set. In mixed chalcogens species of sulfur and selenium, the location of the sulfur atom affects the S–Se bond length as it can hold more negative charge. PA, GPB, BDE, and HA of selenium systems were all lower, indicating more acidity and more stability of radicals. Extending the sulfur chain in cysteine results in a decrease of BDE and HA, but these plateau at a certain point (199 kJ mol−1 and 295 kJ mol−1), and PA and GPB are also decreased relative to the thiol, indicating that the polysulfur species exist as thiolates in a biological system. In general, it was found that ωB97XD/6-311G(2d,p) gave the most reasonable structures and thermochemistry relative to benchmark calculations. However, nuances in performance are observed and discussed.

Invertibility of the dual energy x-ray data transform.

The Alvarez-Macovski method extracts the x-ray energy-dependent information by expanding the attenuation coefficient as a linear combination of functions of energy multiplied by basis set coefficients. Since the basis functions are known a priori, the coefficients represent all the energy-dependent information. The method then computes the line integrals of these coefficients, summarized as a vector A, from measurements with multiple x-ray spectra, summarized as a vector L. The purpose of this paper is to determine the factors that affect the invertibility of the L(A) transformation with a two function basis set and two spectral measurements, the dual energy transformation. A general invertibility theorem is applied that requires testing for zero values of the Jacobian of the transformation in its input domain. General conditions for invertibility are proved. It is shown that the generalized A vector noise variance is proportional to the generalized measurement noise variance divided by the square of the Jacobian. The relationship between the zero Jacobian values and ambiguous sets of A vector points with the same L values is determined. The effect of zero Jacobian values on an iterative algorithm that inverts L(A) is simulated. The choice of a particular valid basis set does not affect invertibility. Nonoverlapping measurement spectra such as those from photon counting detectors with perfect pulse height analysis are invertible. The widely used x-ray tube spectra with different voltages are shown to be invertible. Spectra with the same maximum energy, such as those from layered detectors, approach noninvertibility with small absolute value Jacobian for large object thicknesses. The zero Jacobian values fall on curves in A vector space that, except for a simple artificial case, are close to but not exactly straight lines. With noninvertible spectra, pairs of ambiguous points are located on opposite sides of the zero Jacobian curve. The iterative algorithm has large convergence errors near zero Jacobian curves and converges to the closest ambiguous point to the initial estimate for other points. The invertibility of dual energy systems is determined by the presence of zero values of the Jacobian of the dual x-ray energy data transformation L(A) in the input domain.

CO2 cycloaddition with propylene oxide to form propylene carbonate on a copper metal-organic framework: A density functional theory study

Metal-organic frameworks (MOFs) have emerged as unique catalysts for CO2 conversion, but the catalytic mechanism remains elusive. In this study, a density functional theory (DFT) study is reported on CO2 cycloaddition with propylene oxide (PO) to produce propylene carbonate (PC), catalyzed by a Cu-MOF (NTU-180) in the presence of tetrabutylammonium bromide (TBAB). This reaction was experimentally observed to have a remarkably high efficiency. We compute the electronic and Gibbs energies of the reactants, intermediates, transition states and products for two alternative reaction pathways. On NTU-180/TBAB, the three-member ring opening of PO is revealed to possess a higher activation barrier than the five-member ring closure of PC, and thus it is the rate-determining step. Pathway I is kinetically more favorable as its ring opening has a lower barrier than in Pathway II. Moreover, the activation barriers of ring opening and ring closure steps on NTU-180/TBAB are substantially lower than those in the gas phase, and also lower than those on TBAB alone and on a Cu2 paddle-wheel/TBAB complex. At a molecular level, these results unambiguously highlight the important roles of the Cu sites and the confinement effect of NTU-180 in enhancing the stabilities of reaction intermediates and transition states, and promoting the catalytic cycloaddition of CO2 with PO. In addition, the sensitivities of the DFT calculation results to the choice of functional and basis set are critically analyzed. While the electronic and Gibbs energies vary substantially with functional, the activation barriers in the rate-determining step are affected only slightly by the functional and marginally by the basis set. This theoretical study provides microscopic and quantitative insights into the high catalytic activity observed experimentally for CO2 cycloaddition on NTU-180/TBAB, and might facilitate the development of new catalysts for efficient CO2 conversion.

Simulating X-ray Emission Spectroscopy with Algebraic Diagrammatic Construction Schemes for the Polarization Propagator.

The calculation of X-ray emission spectra has been addressed with the algebraic diagrammatic construction (ADC) scheme, using a core-ionized wave function as the reference state. With this, the valence-to-core transitions are found as the first eigenstates with negative eigenvalues. The performance of the ADC hierarchical methods ADC(2), ADC(2)-x, and ADC(3/2) has been investigated on 17 transition of second-row elements (C, N, O, F, and Ne), and 5 transitions of third-row elements (S and Cl). We report ADC(2) results within 0.20 ± 0.36 eV of experimental values with an appropriate choice of basis set and when accounting for relativistic effects, with a slight tendency toward underestimating emission energies. By comparison, ADC(2)-x yields a similar spread in relative energies, but a consistent overestimation of approximately 1.5 eV. Going to ADC(3/2), we now observe an underestimation of emission energies and a larger error spread. By comparison, calculations of X-ray absorption spectra have been reported to favor the ADC(2)-x method, with ADC(2) showing the largest error when comparing to experimental values. The difference in ADC performance trends between these core spectroscopies are attributed to the different electron rearrangement effects in X-ray absorption and emission processes.

A combined experimental/theoretical approach to accelerated fuel cell development by quantitative prediction of redox potentials

This article presents a combined experimental/theoretical approach to accurately predict electrochemical redox potentials based on potential energy calculations. The approach works for experimental setups using different solvents and different reference electrodes and compensates for shortcomings in the prediction of redox potentials originating from the choice of DFT functional, basis set, and solvation model. The methodology is applied to two different sets of iron containing complexes which are used as redox catalysts in Chemically Regenerative Redox Fuel Cells (CRRFCs). For both sets of iron complexes with different 5 N donor ligands, an average deviation to the experimental values of <0.02V is obtained. Expectedly, the deviation is slightly larger with changes being made in the first coordination shell, but is still within the predictive limit. The scheme is then applied to obtain ligands with both improved properties and lowest production cost.

SCI: a robust and reliable density-based descriptor to determine multiple covalent bond orders

Very recently [J. Phys. Chem. A 2018, 122 (11), 3087-3095], we proposed to employ the Pauli energy to identify and determine strong covalent interactions (SCI), whose bond order are equal to or larger than two. This is done through the signature isosurface shape between the two bonding atoms. We discovered that the signature shape for a double, triple, and quadruple covalent bond is like a dumbbell, donut (torus), and four-beats, respectively. Systems with even higher bond orders were examined and confirmed. This work is a follow-up study of our previous work. The dependence of thesignature isosurface shape on the choice of methodologies and basis sets is systematically investigated. Its effectiveness and robustness in determining bond orders are highlighted again with more examples. In addition, using the molybdenum dimer in different environments, e.g., in vacuum, sandwiched between molecules, and encapsulated in the C80 cage, as illustrative examples, we show that, generally speaking, bond strength and bond order are two different chemical concepts. For systems containing transition metals, it is not always true that a short metal-metal bond length corresponds to a larger bond order. Put together, these results should provide additional pieces of convincing evidence showing that the SCI index is a robust and reliable density-based descriptor to accurately determine multiple covalent bond orders.

On the Choice of a Distributed Basis Set in Calculations of Transition-Dipole Moments in the One-Determinant Approximation

The so-called “asymptotic projection technique” developed in previous papers of the authors is applied to the calculation of electronic transition-dipole moments (TDMs) in the one-determinant approximation between states of the same spin and spatial symmetry. The basic equations of the method and specific features of their application to a TDM calculation are briefly discussed. The attention focusses on the choice of a finite one-particle basis set. For this purpose, two possible algorithms for constructing distributed basis sets are proposed. In the first of them, the construction is based on minimization of the Hartree–Fock energy (EHF) with respect to nonlinear basis set parameters. In the second case, the parameters are determined by minimizing the functional E = EHF + EMP2, which includes the electron correlation through the second order of Moller–Plesset perturbation theory (ЕМР2). On the whole, the results of calculations in both basis sets are in agreement with high-accuracy calculations performed by configuration interaction methods. The basis set adapted for E = EHF + EMP2 significantly improves the accuracy as compared to the basis set of the first type.

ABSORPTION OF SOME SMALL SILVER CLUSTERS: DFT AND CASPT2 CALCULATIONS

Two quantum chemical methods which are the time-dependent density functional theory (TD-DFT) and the complete active space CASPT2/CASSCF have been used in modeling absorption spectra of silver clusters Agn (n = 2, 3, 4, 6, 8). There is an overall good agreement between TD-DFT and CASPT2 results for transition energies. The absorption spectra of the Agn clusters examined can reasonably be simulated using the excitation energies obtained by either TD-DFT or CASPT2 method. The main result emerged from this calculation is that the TD-DFT method is suitable for treatment of excited states of Ag clusters. The choice of specific functionals and basis sets to be used in some cases induces important effects on the calculated spectra. It is also noteworthy to mention that for some clusters, the neutral Ag6 for instance, the effect of noble gas environment is significant, while for some others such as the neutral Ag8, it is not. Therefore, carrying out TD-DFT calculations to reproduce and to assign a given structure to an experimental absorption spectrum of a silver cluster, it is not only to select suitable functionals but also to take enough effects of environments into account.

On the accuracy of retinal protonated Schiff base models

ABSTRACTWe investigate the molecular geometries of the ground state and the minimal energy conical intersections between the ground and first excited states of the models for the retinal protonated Schiff base in the gas phase using the extended multistate complete active space second-order perturbation theory (XMS-CASPT2). The biggest model in this work is the rhodopsin chromophore truncated between the ε and δ carbon atoms, which consists of 54 atoms and 12-orbital π conjugation. The results are compared with those obtained by the state-averaged complete active space self-consistent field (SA-CASSCF). The XMS-CASPT2 results suggest that the minimum energy conical intersection associated with the so-called 13–14 isomerisation is thermally inaccessible, which is in contrast to the SA-CASSCF results. The differences between the geometries of the conical intersections computed by SA-CASSCF and XMS-CASPT2 are ascribed to the fact that the charge transfer states are more stabilised by dynamical electron correlation than the diradicaloid states. The impact of the various choices of active spaces, basis sets and state-averaging schemes is also examined.

Application of the finite-field coupled-cluster method to calculate molecular properties relevant to electron electric-dipole-moment searches

Heavy polar diatomic molecules are currently among the most promising probes of fundamental physics. Constraining the electric dipole moment of the electron (eEDM), in order to explore physics beyond the Standard Model, requires a synergy of molecular experiment and theory. Recent advances in experiment in this field have motivated us to implement a finite field coupled cluster approach (FFCC). This work has distinct advantages over the theoretical methods that we had used earlier in the analysis of eEDM searches. We used the relativistic FFCC to calculate molecular properties of interest to eEDM experiments, that is, the effective electric field (Eeff), and the permanent electric dipole moment (PDM). We theoretically determine these quantities for the alkaline earth monofluorides (AEMs), the mercury monohalides (HgX), and PbF. The latter two systems, as well as BaF from the AEMs, are of interest to eEDM searches. We also report the calculations of the properties using a relativistic coupled cluster approach with single, double, and partial triples' excitations, which is considered to be the gold standard of electronic structure calculations. We also present a detailed error estimate, including errors that stem from the choice of basis sets, and higher order correlation effects.

Density Functional Theory and the Basis Set Truncation Problem with Correlation Consistent Basis Sets: Elephant in the Room or Mouse in the Closet?

Two recent papers in this journal called into question the suitability of the correlation consistent basis sets for density functional theory (DFT) calculations, because the sets were designed for correlated methods such as configuration interaction, perturbation theory, and coupled cluster theory. These papers focused on the ability of the correlation consistent and other basis sets to reproduce total energies, atomization energies, and dipole moments obtained from "quasi-exact" multiwavelet results. Undesirably large errors were observed for the correlation consistent basis sets. One of the papers argued that basis sets specifically optimized for DFT methods were "essential" for obtaining high accuracy. In this work we re-examined the performance of the correlation consistent basis sets by resolving problems with the previous calculations and by making more appropriate basis set choices for the alkali and alkaline-earth metals and second-row elements. When this is done, the statistical errors with respect to the benchmark values and with respect to DFT optimized basis sets are greatly reduced, especially in light of the relatively large intrinsic error of the underlying DFT method. When judged with respect to high-quality Feller-Peterson-Dixon coupled cluster theory atomization energies, the PBE0 DFT method used in the previous studies exhibits a mean absolute deviation more than a factor of 50 larger than the quintuple zeta basis set truncation error.

Effect of crystal packing and coordinated solvent molecules on metal-ligand bond distances in linear trinuclear nickel compounds with bridging acetato and Schiff base ligands

Abstract A combined experimental and theoretical study on the molecular structure of linear trinuclear nickel compounds of general formula [Ni3(μ-Zsaltn)2(μ-AcO)2(S)2] (Z = H, 1S, and Br, 2S, where S identifies coordinated solvent molecules) is here presented. In these complexes the three metal ions are linked together by bridging acetato ions and tetradentate Schiff base ligands, these last derived from the condensation of 1,3-diaminopropane with two equivalents of 5-Z-salicylaldehyde. Two solvent molecules S can also interact with the terminal nickel ions to complete an octahedral coordination environment. We report the synthesis of [Ni3(μ-Brsaltn)2(μ-AcO)2] (2), and its crystal structure with two coordinated dimethylformamide molecules, [Ni3(μ-Brsaltn)2(μ-AcO)2(DMF)2] (2DMF). Its comparison with the crystal structure of 2 without solvent, together with the series of compounds 1, 1DMF, 1MeOH, 1DMSO, 1Py and 1H2O (MeOH = methanol, DMSO = dimethylsulfoxide, Py = pyridine) available in the literature, allows recognising modification in Ni O and Ni N coordination bond lengths and peculiar intermolecular contacts between neighbour molecules. In order to discern among the contribution of solvent molecules, crystal packing and substituent Z (H or Br) on bond distances (and angles), we performed a systematic theoretical study on four representative derivatives, namely 1, 1DFM, 2 and 2DMF, with the M06 functional and a careful choice of the best basis set. The results indicate that, while the major modulating factor is the presence or absence of the sixth solvent molecule to the peripheral nickel(II) ion, even if less strongly coordinated with Ni O/N bond distances > 2.15 A, π-π stacking interactions and C H⋯π and/or C Br⋯π non-bonded interactions affect the coordination geometry in a significant way.

Exact Formulation of the Transverse Dynamic Spin Susceptibility as an Initial-Value Problem

The transverse dynamic spin susceptibility is a correlation function that yields exact information about spin excitations in systems with a collinear magnetic ground state, including collective spin-wave modes. In an ab initio context, it may be calculated within many-body perturbation theory or time-dependent density-functional theory, but the quantitative accuracy is currently limited by the available functionals for exchange and correlation in dynamically evolving systems. To circumvent this limitation, the spin susceptibility is here alternatively formulated as the solution of an initial-value problem. In this way, the challenge of accurately describing exchange and correlation in many-electron systems is shifted to the stationary initial state, which is much better understood. The proposed scheme further requires the choice of an auxiliary basis set, which determines the speed of convergence but always allows systematic convergence in practical implementations.

How Well Can the M06 Suite of Functionals Describe the Electron Densities of Ne, Ne6+, and Ne8+?

The development of better approximations to the exact exchange-correlation functional is essential to the accuracy of density functionals. A recent study suggested that functionals with few parameters provide more accurate electron densities than recently developed many-parameter functionals for light closed-shell atomic systems. In this study, we calculated electron densities, their gradients, and Laplacians of Ne, Ne6+, and Ne8+ using 19 electronic structure methods, and we compared them to the CCSD reference results. Two basis sets, namely, aug-cc-pωCV5Z and aug-cc-pV5Z, are utilized in the calculations. We found that the choice of basis set has a significant impact on the errors and rankings of some of the selected methods. The errors of electron densities, their gradients, and Laplacians calculated with the aug-cc-pV5Z basis set are substantially reduced, especially for Minnesota density functionals, as compared to the results using the aug-cc-pωCV5Z basis set (a larger basis set utilized in earlier work (Medvedev et al. Science 2017, 355, 49-52)). The rankings of the M06 suite of functionals among the 19 methods are greatly improved with the aug-cc-pV5Z basis set. In addition, the performances of the HSE06, BMK, MN12-L, and MN12-SX functionals are also improved with the aug-cc-pV5Z basis set. The M06 suite of functionals is capable of providing accurate electron densities, gradients, and Laplacians using the aug-cc-pV5Z basis set, and thus it is suitable for a wide range of applications in chemistry and physics.

Importance of the ligand basis set in ab initio thermochemical calculations of transition metal species

The impact of basis set choice has been considered for a series of transition metal (TM) species. The need for higher level correlation consistent basis sets on both the metal and ligand has been investigated, and permutations in the pairings of basis set used for TM’s and basis set used for ligands can lead to effective routes to complete basis set (CBS) limit extrapolations of thermochemical energetics with little change in thermochemical predictions as compared to those resulting from the use of traditional basis set pairings, while enabling computational cost savings. Basis set superposition errors (BSSE) that can arise have also been considered.

How Large is the Elephant in the Density Functional Theory Room?

A recent paper reported highly accurate density functional theory results for atomization energies and dipole moments using a multiwavelet-based method and compared the results with those obtained by standard Gaussian basis sets of the aug-cc-pVXZ type. Typical errors with the large aug-cc-pV5Z basis set were in the 0.2 kcal/mol range with outliers displaying errors of ∼2 kcal/mol, and these results could be taken as an indication that Gaussian basis sets in general are unsuitable for achieving high accuracy. We show that by choosing Gaussian basis sets optimized for density functional theory, basis set methods are capable of achieving accuracy comparable to that from the multiwavelet approach.

Isomeric xylene molecules in the Terahertz-far infrared regime: Computational chemistry and spectral modeling view

The theoretical assignments of spectral peaks of liquid phase ortho-, meta-, and para-xylene recorded with far-infrared (FIR) and THz spectroscopy in the spectral range between 550 and 50cm−1 is done with density functional theory (DFT) calculations. As THz spectroscopic techniques drastically evolved in recent years, the critical focus of this paper lies on the applicability of theoretical concepts, used as computational standard in near- and mid-IR spectra, to the FIR-THz region. An evaluation of the choice of functionals, basis sets, and appropriate scaling factors as well as the tractability of the liquid phase in a polarizable continuum model is performed. Alongside a new analysis procedure based on spectral Hard Modeling has been developed. DFT line spectra are fitted to experimental FIR spectra where a quantitative track record allows for meaningful comparisons. With all these tools we are able to reproduce experimental spectra in an optically appealing way and we can explain trends for each spectrum as well as across the row of the isomers.

Study on molecular structure, spectroscopic properties (FTIR and UV–Vis), NBO, QTAIM, HOMO-LUMO energies and docking studies of 5-fluorouracil, a substance used to treat cancer

Cancer cells can expand to other parts of body through blood system and nodes from a mechanism known as metastasis. Due to the large annual growth of cancer cases, various biological targets have been studied and related to this disorder. A very interesting target related to cancer is human epidermal growth factor receptor 2 (HER2). In this study, we analyzed the main intermolecular interactions between a drug used in the cancer treatment (5-fluorouracil) and HER2. Molecular modeling methods were also employed to assess the molecular structure, spectroscopic properties (FTIR and UV–Vis), NBO, QTAIM and HOMO-LUMO energies of 5-FU. From the docking simulations it was possible to analyze the interactions that occur between some residues in the binding site of HER2 and 5-FU. To validate the choice of basis set that was used in the NBO and QTAIM analyses, theoretical calculations were performed to obtain FT-IR and UV/Vis spectra, and the theoretical results are consistent with the experimental data, showing that the basis set chosen is suitable. For the maximum λ from the theoretical calculation (254.89nm) of UV/Vis, the electronic transition from HOMO to LUMO occurs at 4.89eV. From NBO analyses, we observed interactions between Asp863 and 5-FU, i.e. the orbitals with high transfer of electrons are LP O15 (donor NBO) and BD* (π) N1-H10 (acceptor NBO), being that the value of this interaction is 7.72kcal/mol. Results from QTAIM indicate one main intermolecular H bond, which is necessary to stabilize the complex formed between the ligands and the biological target. Therefore, this study allowed a careful evaluation on the main structural, spectroscopic and electronic properties involved in the interaction between 5-FU and HER2, an important biological complex related to the cancer treatment.

Estimation of ΔR/R values by benchmark study of the Mössbauer Isomer shifts for Ru, Os complexes using relativistic DFT calculations

The present study applies all-electron relativistic DFT calculation with Douglas-Kroll-Hess (DKH) Hamiltonian to each ten sets of Ru and Os compounds. We perform the benchmark investigation of three density functionals (BP86, B3LYP and B2PLYP) using segmented all-electron relativistically contracted (SARC) basis set with the experimental Mössbauer isomer shifts for 99Ru and 189Os nuclides. Geometry optimizations at BP86 theory of level locate the structure in a local minimum. We calculate the contact density to the wavefunction obtained by a single point calculation. All functionals show the good linear correlation with experimental isomer shifts for both 99Ru and 189Os. Especially, B3LYP functional gives a stronger correlation compared to BP86 and B2PLYP functionals. The comparison of contact density between SARC and well-tempered basis set (WTBS) indicated that the numerical convergence of contact density cannot be obtained, but the reproducibility is less sensitive to the choice of basis set. We also estimate the values of ΔR/R, which is an important nuclear constant, for 99Ru and 189Os nuclides by using the benchmark results. The sign of the calculated ΔR/R values is consistent with the predicted data for 99Ru and 189Os. We obtain computationally the ΔR/R values of 99Ru and 189Os (36.2 keV) as 2.35×10−4 and −0.20×10−4, respectively, at B3LYP level for SARC basis set.