Choice Of Basis Set Research Articles

Complex absorbing potentials within EOM-CC family of methods: theory, implementation, and benchmarks.

A production-level implementation of equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) for electron attachment and excitation energies augmented by a complex absorbing potential (CAP) is presented. The new method enables the treatment of metastable states within the EOM-CC formalism in a similar manner as bound states. The numeric performance of the method and the sensitivity of resonance positions and lifetimes to the CAP parameters and the choice of one-electron basis set are investigated. A protocol for studying molecular shape resonances based on the use of standard basis sets and a universal criterion for choosing the CAP parameters are presented. Our results for a variety of π(*) shape resonances of small to medium-size molecules demonstrate that CAP-augmented EOM-CCSD is competitive relative to other theoretical approaches for the treatment of resonances and is often able to reproduce experimental results.

Time-Dependent Density Functional Methods for Raman Spectra in Open-Shell Systems

We present an implementation of a time-dependent density functional theory (TD-DFT) linear response module in NWChem for unrestricted DFT calculations and apply it to the calculation of resonant Raman spectra in open-shell molecular systems using the short-time approximation. The new source code was validated and applied to simulate Raman spectra on several doublet organic radicals (e.g., benzyl, benzosemiquinone, TMPD, trans-stilbene anion and cation, and methyl viologen) and the metal complex copper phthalocyanine. We also introduce a divide-and-conquer approach for the evaluation of polarizabilities in relatively large systems (e.g., copper phthalocyanine). The implemented tool gives comparisons with experiment that are similar to what is commonly found for closed-shell systems, with good agreement for most features except for small frequency shifts, and occasionally large deviations for some modes that depend on the molecular system studied, experimental conditions not being accounted in the modeling such as solvation effects and extra solvent-based peaks, and approximations in the underlying theory. The approximations used in the quantum chemical modeling include (i) choice of exchange-correlation functional and basis set; (ii) harmonic approximation used in the frequency analysis to determine vibrational normal modes; and (iii) short-time approximation (omission of nuclear motion effects) used in calculating resonant Raman spectra.

Ab initio analytical Raman intensities for periodic systems through a coupled perturbed Hartree-Fock/Kohn-Sham method in an atomic orbital basis. II. Validation and comparison with experiments

In this work, we validate a new, fully analytical method for calculating Raman intensities of periodic systems, developed and presented in Paper I [L. Maschio, B. Kirtman, M. Rérat, R. Orlando, and R. Dovesi, J. Chem. Phys. 139, 164101 (2013)]. Our validation of this method and its implementation in the CRYSTAL code is done through several internal checks as well as comparison with experiment. The internal checks include consistency of results when increasing the number of periodic directions (from 0D to 1D, 2D, 3D), comparison with numerical differentiation, and a test of the sum rule for derivatives of the polarizability tensor. The choice of basis set as well as the Hamiltonian is also studied. Simulated Raman spectra of α-quartz and of the UiO-66 Metal-Organic Framework are compared with the experimental data.

Reply to “Comment on ‘Nonanalyticity of the optimized effective potential with finite basis sets’ ”

The Comment by Friedrich et al. does not dispute the central result of our paper [Phys. Rev. A 85, 052508 (2012)] that nonanalytic behavior is present in long-established mathematical pathologies arising in the solution of finite basis optimized effective potential (OEP) equations. In the Comment, the terms ``balancing of basis sets'' and ``basis-set convergence'' imply a particular order towards the limit of a large orbital basis sets where the large-orbital-base limit is always taken first, before the large-auxiliary-base limit, until overall convergence is achieved, at a high computational cost. The authors claim that, on physical grounds, this order of limits is not only sufficient, but also necessary in order to avoid the mathematical pathologies. In response to the Comment, we remark that it is already written in our paper that the nonanalyticity trivially disappears with large orbital basis sets. We point out that the authors of the Comment give an incorrect proof of this statement. We also show that the order of limits towards convergence of the potential is immaterial. A recent paper by the authors of the Comment proposes a partial correction for the incomplete orbital basis error in the full-potential linearized augmented-plane-wave method. Similar to the correction developed in our paper, this correction also benefits from an effectively complete orbital basis, even though only a finite orbital basis is employed in the calculation. This shows that it is unnecessary to take, in practice, the limit of an infinite orbital basis in order to avoid mathematical pathologies in the OEP. Our paper is a significant contribution in that direction with general applicability to any choice of basis sets. Finally, contrary to an allusion in the abstract and assertions in the main text of the Comment that unphysical oscillations of the OEP are supposedly attributed to the common energy denominator approximation, in fact, such anomalies arise with the full treatment of the small eigenvalues of the density response function. This characteristic of the finite basis OEP is well known in the literature but also is clearly demonstrated in our paper.

Mononuclear and polynuclear 5-coordinate zinc(II) model complexes: a quantum chemical calibration study of their structure and energy

To further our understanding of the properties of zinc-seamed pyrogallol[4]arene nanocapsules, we have investigated the energetic and geometric properties of the model complexes Zn(C2O2H3)2Y, Y = NH3, C5H5N, CH3OH, (CH3)2NCHO, or (CH3)2SO, with a zinc coordination sphere representative of that in the capsules. The effect of the choice of density functional, basis set, and zinc pseudopotential on the equilibrium structures and Y ligand bond dissociation enthalpies has been assessed. Among the ways in which the suitability of these models has been confirmed was the construction of polynuclear zinc complexes having 2, 4, 6, or 8 metal ions combined with C2O2H3 −, C4O3H4 2−, and NH3 ligands, which indeed show that a closed ring is formed. The natural curvature of these complexes suggests that pentacoordination of Zn may be a key factor in seaming the pre-existing cone-shaped pyrogallol[4]arenes to form dimer capsules.

Hydration Free Energies of Multifunctional Nitroaromatic Compounds.

Nitroaromatic compounds (NACs) are used as energetic materials, reagents, and pesticides; however, they are potentially hazardous for the environment and human health. To predict the environmental distribution of these compounds, the vapor pressure, aqueous solubility, and Henry's law constant are important properties, as is the solvation free energy in water from which the latter two can be computed. Here, we have calculated the hydration free energies for a set of nine nitroaromatic compounds containing one, two, and three nitro groups using the expanded ensemble molecular dynamics simulation method with TIP3P water and the GAFF, CGenFF, OPLS-AA, and TraPPE force field parameters and the RESP (gas phase), CHELPG (gas phase), and CM4 (aqueous phase) partial atomic charges calculated here. Also, we have computed hydration free energies using the reported default partial atomic charges of the OPLS-AA force field and using the semiempirical AM1-BCC charges with GAFF parameters. The effect of water model flexibility on the computation of hydration free energy is examined with CGenFF/(CHELPG+SPC-Fw) model. All the force fields studied generally led to less accurate predictions with increasing numbers of nitro groups. The average unsigned errors (AUE) show that 6 of 16 force-field/(charge+water) models used perform approximately equally well in predicting measured hydration free energies: these are CGenFF/(CHELPG+TIP3P), CGenFF/(CM4+TIP3P), OPLS-AA/(CHELPG+TIP3P), OPLS-AA/(CM4+TIP3P), TraPPE-UA/(CHELPG+TIP3P), and TraPPE-UA/(CM4+TIP3P). When using the default atomic charges, the OPLS-AA force field was the most accurate, though using CHELPG and CM4 charges led to better predictions. Our analyses indicate that not only the charges but also the van der Waals interaction parameters for the nitro-group nitrogen and oxygen atoms in the force fields are partly responsible for the performance variations in predicting solvation free energies. We also compared the force field-based simulation results with the predictions from the SM6 solvation model and Abraham linear solvation energy relationship (LSER) method. With an appropriate choice of theory and basis set both for geometry optimization and computation, which unfortunately is not known a priori, the SM6 model hydration free energy predictions for the NACs are comparable to the simulation results here. The Abraham LSER predictions with descriptors obtained from the Platts method are of reasonable accuracy. A useful addition to this paper is the Supporting Information that contains a compiled and evaluated list of the hydration free energies of the NACs studied here assembled from the literature.

Systematic Study of the Basis Set Superposition Error in Core–Electron Correlation Effects

In a recent paper, Xu et al. [J. Phys. Chem. A 2012, 116, 11668] emphasized the importance of core-electron correlation effects to describe the Si2H6BH3 complex and related systems properly. Unexpected large energy differences between a frozen core and all electron treatment were observed. In the present study, it will be shown that these energy differences are an artifact of an insufficient choice of basis set and can be attributed to an intramolecular basis set superposition error (BSSE). Although the general problem is known, systematic studies on the effect are scarce. Therefore, the BSSE in related systems is investigated. This study shows that the problem of BSSE for core-electron correlation is quite common if inadequate basis sets are applied and that it amounts to 2 kcal mol(-1) on average in binding energies for the given test set (with a maximum of 5.8 kcal mol(-1)).

Comparison Chosen DFT Methods with Six Basis Sets on Harmine Molecule

The effect of the DFT methods and basis sets on harmine molecule has been investigated. 26 DFT methods with 6 basis sets were used. Two main comparison chosen DFT methods in this work has been investigated. It is concluded that this contribution is very important and cannot be neglected. In the following analysis, changes in energy levels were investigated by two different methods. Considering a specific basis set, changes in energy levels were obtained using different DFT methods. A specific DFT method is chosen and changes in energy levels have been investigated by means of various basis sets. Effect of the choice of basis sets on geometrical parameters on harmine molecule has also been investigated.

Empirical tight binding parameters for GaAs and MgO with explicit basis through DFT mapping

The Empirical Tight Binding (ETB) method is widely used in atomistic device simulations. The reliability of such simulations depends very strongly on the choice of basis sets and the ETB parameters. The traditional way of obtaining the ETB parameters is by fitting to experiment data, or critical theoretical bandedges and symmetries rather than a foundational mapping. A further shortcoming of traditional ETB is the lack of an explicit basis. In this work, a DFT mapping process which constructs TB parameters and explicit basis from DFT calculations is developed. The method is applied to two materials: GaAs and MgO. Compared with the existing TB parameters, the GaAs parameters by DFT mapping show better agreement with the DFT results in bulk band structure calculations and lead to different indirect valleys when applied to nanowire calculations. The MgO TB parameters and TB basis functions are also obtained through the DFT mapping process.

Gaussian basis sets for molecular applications

AbstractThe choice of basis set in quantum chemical calculations can have a huge impact on the quality of the results, especially for correlated ab initio methods. This article provides an overview of the development of Gaussian basis sets for molecular calculations, with a focus on four popular families of modern atom‐centered, energy‐optimized bases: atomic natural orbital, correlation consistent, polarization consistent, and def2. The terminology used for describing basis sets is briefly covered, along with an overview of the auxiliary basis sets used in a number of integral approximation techniques and an outlook on possible future directions of basis set design. © 2012 Wiley Periodicals, Inc.

The Ehrenfest force field: Topology and consequences for the definition of an atom in a molecule

The Ehrenfest force is the force acting on the electrons in a molecule due to the presence of the other electrons and the nuclei. There is an associated force field in three-dimensional space that is obtained by the integration of the corresponding Hermitian quantum force operator over the spin coordinates of all of the electrons and the space coordinates of all of the electrons but one. This paper analyzes the topology induced by this vector field and its consequences for the definition of molecular structure and of an atom in a molecule. Its phase portrait reveals: that the nuclei are attractors of the Ehrenfest force, the existence of separatrices yielding a dense partitioning of three-dimensional space into disjoint regions, and field lines connecting the attractors through these separatrices. From the numerical point of view, when the Ehrenfest force field is obtained as minus the divergence of the kinetic stress tensor, the induced topology was found to be highly sensitive to choice of gaussian basis sets at long range. Even the use of large split valence and highly uncontracted basis sets can yield spurious critical points that may alter the number of attraction basins. Nevertheless, at short distances from the nuclei, in general, the partitioning of three-dimensional space with the Ehrenfest force field coincides with that induced by the gradient field of the electron density. However, exceptions are found in molecules where the electron density yields results in conflict with chemical intuition. In these cases, the molecular graphs of the Ehrenfest force field reveal the expected atomic connectivities. This discrepancy between the definition of an atom in a molecule between the two vector fields casts some doubts on the physical meaning of the integration of Ehrenfest forces over the basins of the electron density.

Proton affinities of deoxyribonucleosides via the ONIOM‐ccCA methodology

Utilizing the recently developed ONIOM-ccCA methodology, the proton affinities (PAs) of small biomolecules (∼15 nonhydrogen atoms) were determined. The ONIOM-ccCA method was used to predict the PAs of eight amine-containing molecules and these predictions were then compared with experiment. In these comparisons, a protocol for the determination of the model system size was established, and the low level method and basis set for the real system component of ONIOM-ccCA were considered. Several possible density functionals were investigated for description of the real system (low layer), including B3LYP, B97-1, B97-2, B98, BMK, M06, and M06-2X. The resulting proton affinities were compared both to experiment and to theoretical values that were calculated using the correlation consistent Composite Approach (ccCA). The impact of the choice of augmented correlation consistent basis sets in the ONIOM-ccCA low level calculation was also examined, and PAs calculated with augmented and non-augmented basis sets were compared to those extrapolated to the complete basis set (CBS) limit. ONIOM(ccCA:B3LYP/aug-cc-pVDZ) was then applied to deoxyribonucleosides to determine the PAs at possible sites of protonation.

What are the most efficient basis set strategies for correlated wave function calculations of reaction energies and barrier heights?

As electronic structure methods are being used to obtain quantitatively accurate reaction energies and barrier heights for increasingly larger systems, the choice of an efficient basis set is becoming more critical. The optimum strategy for achieving basis set convergence can depend on the way that electron correlation is treated and can take advantage of flexibility in the order in which basis functions are added. Here we study several approaches for estimating accurate reaction energies and barrier heights from post-Hartree-Fock electronic structure calculations. First and second, we evaluate methods of estimating the basis set limit of second order Møller-Plesset perturbation theory and of coupled cluster theory with single and double excitations and a quasiperturbative treatment of connected triple excitations by using explicitly correlated basis functions (in the F12a implementation) along with valence, polarization, and diffuse one-electron basis functions. Third, we test the scheme of adding a higher-order correction to MP2 results (sometimes called MP2∕CBS + ΔCCSD(T)). Finally, we evaluate the basis set requirements of these methods in light of comparisons to Weizmann-3.2, Weizmann-4, and CCSDT(2)(Q)∕CBS+CV+R results.

Inner shells do not cause grave difficulties in resonance studies for atoms with the direct complex-coordinate method

Many papers in the 1970s and 1980s state that inner shells cause considerable difficulties in resonance studies with the direct complex-coordinate method, especially for high-$Z$ systems. However, our studies show that after rotating the Hamiltonian into complex space, inner-shell orbitals for atoms are not highly oscillatory. Because of an overall exponential decay, they do not cause grave difficulties in resonance studies. The results depend greatly on the choice of basis set. To demonstrate this, the doubly excited 2${s}^{2}$ ${}^{1}S$ states of He and He-like Ne (Ne${}^{8+}$) are examined with a complex-scaled multireference configuration-interaction method.

Reply to the ‘Comment on “Dynamic factors in the reactions between the magic cluster Al13− and HCl/HI”: A wavefunction instability problem.’ by Young-Kyu Han, Phys. Chem. Chem. Phys. 2012, DOI: 10.1039/C2CP23908F

The reaction between a metal cluster Al13− and an inorganic molecule HI involves charge transfer and density functional calculations has deficiency to estimate the activation barrier due to the self-interaction error. Coupled-cluster calculation with single and double excitation (CCSD) based on spin-unrestricted Hartree-Fock wavefunction can improve the calculated barrier and the choice of basis set is important for the calculation. Energy difference can be as large as 4.9 kcal mol−1 for the reaction by using aug-cc-pvdz and 6-31++G** basis sets respectively.

On the discrepancy between theory and experiment for the F–F spin–spin coupling constant of difluoroethyne

The vicinal indirect nuclear spin-spin coupling constant (SSCC) between the two fluorine atoms in difluoroethyne has been reinvestigated. This coupling has previously proved to be difficult to calculate accurately. In this study we have therefore systematically investigated the dependence of this coupling on the choice of one-electron basis set, the choice of correlated wave function method and the inclusion of zero-point vibrational and temperature corrections. All terms of the SSCC have been evaluated at the second-order polarization propagator, SOPPA and SOPPA(CCSD), and coupled cluster singles and doubles (CCSD) levels of theory and for the most correlation dependent term, the paramagnetic spin-orbit contribution (PSO), also at the very accurate CC3 level. We find that in order to get results that are well converged with respect to the basis set, one needs to use special SSCC optimized basis sets of at least quadruple zeta quality and with added diffuse functions. Furthermore, the PSO term is not yet converged at the CCSD level as shown by the CC3 calculations. Finally, it is shown that vibrational effects are very important, as they are in this case of the same order of magnitude as the equilibrium geometry value of the coupling constant. Only by using a converged basis set and including both vibrational and higher order correlation effects can we obtain agreement with the experimental value for this coupling.

Rapid computation of intermolecular interactions in molecular and ionic clusters: self-consistent polarization plus symmetry-adapted perturbation theory

A method that we have recently introduced for rapid computation of intermolecular interaction energies is reformulated and subjected to further tests. The method employs monomer-based self-consistent field calculations with an electrostatic embedding designed to capture many-body polarization (the "XPol" procedure), augmented by pairwise symmetry-adapted perturbation theory (SAPT) to capture dispersion and exchange interactions along with any remaining induction effects. A rigorous derivation of the XPol+SAPT methodology is presented here, which demonstrates that the method is systematically improvable, and moreover introduces some additional intermolecular interactions as compared to the more heuristic derivation that was presented previously. Applications to various non-covalent complexes and clusters are presented, including geometry optimizations and one-dimensional potential energy scans. The performance of the XPol+SAPT methodology in its present form (based on second-order intermolecular perturbation theory and neglecting intramolecular electron correlation) is qualitatively acceptable across a wide variety of systems-and quantitatively quite good in certain cases-but the quality of the results is rather sensitive to the choice of one-particle basis set. Basis sets that work well for dispersion-bound systems offer less-than-optimal performance for clusters dominated by induction and electrostatic interactions, and vice versa. A compromise basis set is identified that affords good results for both induction and dispersion interactions, although this favorable performance ultimately relies on error cancellation, as in traditional low-order SAPT. Suggestions for future improvements to the methodology are discussed.

Mean Gradient Charge: A new definition of atomic charge using induced atomic gradient

A new definition of atomic charge, Mean Gradient Charge (MGC) is proposed on the basis of ‘induced atomic gradient’. Conceptually the connection between electric response to external point charge and Coulomb’s law made exact, providing a unique way of extracting atomic charges from quantum mechanical calculations without any numerical ambiguities. Furthermore MGC is relatively invariant with respect to molecular rotation, choices of basis set and even correlation treatments. Preliminary test calculations show that MGC values are in between Mulliken and NPA charges.

Assessment of Weak Intermolecular Interactions Across QM/MM Noncovalent Boundaries

An assessment of a number of quantum mechanical/molecular mechanical (QM/MM) combinations was performed for weak intermolecular interactions across noncovalent QM/MM 'boundaries'. The popular S22 data set, comprising of a number of weak hydrogen-bonded, dispersion-bound and complexes with mixed interactions was used for the assessment. A range of QM methods was combined with a number of popular MM force fields. The single-point interaction energies, at reference geometries, are presented as deviations to accurate CCSD(T)/CBS reference values. This investigation employed both additive and subtractive QM/MM schemes. The density functional has only a negligible effect; the choice of basis set was also negligible in terms of accuracy. The importance of selecting the most appropriate MM force field for accurately describing interactions at the noncovalent 'boundary' region has a dramatic effect on the accuracy.

Electrostatic interactions in finite systems treated with periodic boundary conditions: Application to linear-scaling density functional theory

We present a comparison of methods for treating the electrostatic interactions of finite, isolated systems within periodic boundary conditions (PBCs), within density functional theory (DFT), with particular emphasis on linear-scaling (LS) DFT. Often, PBCs are not physically realistic but are an unavoidable consequence of the choice of basis set and the efficacy of using Fourier transforms to compute the Hartree potential. In such cases the effects of PBCs on the calculations need to be avoided, so that the results obtained represent the open rather than the periodic boundary. The very large systems encountered in LS-DFT make the demands of the supercell approximation for isolated systems more difficult to manage, and we show cases where the open boundary (infinite cell) result cannot be obtained from extrapolation of calculations from periodic cells of increasing size. We discuss, implement, and test three very different approaches for overcoming or circumventing the effects of PBCs: truncation of the Coulomb interaction combined with padding of the simulation cell, approaches based on the minimum image convention, and the explicit use of open boundary conditions (OBCs). We have implemented these approaches in the ONETEP LS-DFT program and applied them to a range of systems, including a polar nanorod and a protein. We compare their accuracy, complexity, and rate of convergence with simulation cell size. We demonstrate that corrective approaches within PBCs can achieve the OBC result more efficiently and accurately than pure OBC approaches.