Increasing Basis Set Research Articles

Correlation consistent basis sets designed for density functional theory: Third-row atoms (Ga-Br).

The correlation consistent basis sets (cc-pVnZ with n = D, T, Q, 5) for the Ga-Br elements have been redesigned, tuning the sets for use for density functional approximations. Steps to redesign these basis sets for an improved correlation energy recovery and efficiency include truncation of higher angular momentum functions, recontraction of basis set coefficients, and reoptimization of basis set exponents. These redesigned basis sets are compared with conventional cc-pVnZ basis sets and other basis sets, which are, in principle, designed to achieve systematic improvement with respect to increasing basis set size. The convergence of atomic energies, bond lengths, bond dissociation energies, and enthalpies of formation to the Kohn-Sham limit is improved relative to other basis sets where convergence to the Kohn-Sham limit is typically not observed.

A failure of double hybrid density functional method: Out‐of‐plane bending vibrations for the carbon‐carbon double‐bonded molecules

AbstractIn this work, we report anomalous descriptions of bending modes of the carbon–carbon double bonded molecules with double hybrid density functional theories. The harmonic frequencies of the out‐of‐plane modes are found to be extremely low, and the anharmonicities are found to be very large. The unphysical large anharmonities of these modes increase significantly with a basis set having diffuse function. Increasing basis set size does not necessarily reduce or eliminate the problem. We observe that the problem with the double hybrid functional is in‐built due to the presence of the part of the second‐order perturbation terms in the functional.

Calculation of the local environment of a barium monofluoride molecule in a neon matrix

ABSTRACT The local environment of a barium monofluoride (BaF) molecule embedded in a neon matrix is studied theoretically. The energy of the BaF-Ne triatomic system is calculated with a scalar relativistic Hamiltonian, using coupled-cluster theory at the CCSD(T) level for 1625 positions of the Ne atom relative to the BaF molecule. The calculations are repeated with increasing basis sets (from double to quintuple zeta), and are extrapolated to estimate the complete-basis-set limit. Using the potential obtained from these calculations, it is determined that substituting a BaF molecule for ten Ne atoms is favoured compared to substitutions for other numbers of Ne atoms. The equilibrium position and orientation of the BaF molecule and the displacement of its nearby Ne neighbours are determined. The potential barriers that prevent the BaF molecule from migrating and rotating are calculated. These barriers are essential for the EDM 3 collaboration, which is using BaF molecules embedded in a noble-gas solid to perform a precision measurement of the electron electric dipole moment.

Accurate calculation of the interaction of a barium monofluoride molecule with an argon atom: A step towards using matrix isolation of BaF for determining the electron electric dipole moment

Calculations of the BaF–Ar triatomic system are performed with a relativistic Hamiltonian and coupled cluster theory at the CCSD(T) level for 1386 positions of the Ar atom relative to the BaF molecule. Calculations are repeated with increasing basis sets (double-, triple-, quadruple- and quintuple-zeta), and these are extrapolated to estimate the complete-basis-set limit. The resulting energies provide a potential energy for the interaction of an Ar atom with a BaF molecule. A fit is presented that parametrizes this potential. This work is needed for an understanding of the position, modes of motion and energy shifts of BaF isolated in an Ar matrix. This understanding will guide the EDM3 collaboration in its pursuit of a precision measurement of the electron electric dipole moment using BaF isolated in a cryogenic Ar matrix.

Non-iterative method for constructing valence antibonding molecular orbitals and a molecule-adapted minimum basis.

While bonding molecular orbitals exhibit constructive interference relative to atomic orbitals, antibonding orbitals show destructive interference. When full localization of occupied orbitals into bonds is possible, bonding and antibonding orbitals exist in 1:1 correspondence with each other. Antibonding orbitals play an important role in chemistry because they are frontier orbitals that determine orbital interactions, as well as much of the response of the bonding orbital to perturbations. In this work, we present an efficient method to construct antibonding orbitals by finding the orbital that yields the maximum opposite spin pair correlation amplitude in second order perturbation theory (AB2) and compare it with other techniques with increasing basis set size. We conclude the AB2 antibonding orbitals are a more robust alternative to the Sano orbitals as initial guesses for valence bond calculations due to having a useful basis set limit. The AB2 orbitals are also useful for efficiently constructing an active space, and they work as good initial guesses for valence excited states. In addition, when combined with the localized occupied orbitals, and relocalized, the result is a set of molecule-adapted minimal basis functions that is built without any reference to atomic orbitals of the free atom. As examples, they are applied to the population analysis of halogenated methane derivatives, H-Be-Cl, and SF6, where they show some advantages relative to good alternative methods.

Guest–Host Interactions in Clathrate Hydrates: Benchmark MP2 and CCSD(T)/CBS Binding Energies of CH4, CO2, and H2S in (H2O)20Cages

We present benchmark binding energies of naturally occurring gas molecules CH4, CO2, and H2S in the small cage, namely, the pentagonal dodecahedron (512) (H2O)20, which is one of the constituent cages of the 3 major lattices (structures I, II, and H) of clathrate hydrates. These weak interactions require higher levels of electron correlation and converge slowly with an increasing basis set to the complete basis set (CBS) limit, necessitating the use of large basis sets up to the aug-cc-pV5Z and subsequent correction for basis set superposition error (BSSE). For the host hollow (H2O)20 cages, we have identified a most stable isomer with binding energy of -200.8 ± 2.1 kcal/mol at the CCSD(T)/CBS limit (-199.2 ± 0.5 kcal/mol at the MP2/CBS limit). Additionally, we report converged second order Møller-Plesset (MP2) CBS binding energies for the encapsulation of guests in the (H2O)20 cage of -4.3 ± 0.1 for CH4@(H2O)20, -6.6 ± 0.1 for CO2@(H2O)20, and -8.5 ± 0.1 kcal/mol for H2S@(H2O)20, respectively. For CH4@(H2O)20, exhibiting the weakest encapsulation affinity among the three, we report CCSD(T)/aug-cc-pVTZ binding energies and, based on them, a CCSD(T)/CBS estimate of -4.75 ± 0.1 kcal/mol. To the best of our knowledge, the CCSD(T)/aug-cc-pVTZ calculation for CH4@(H2O)20 is the largest one reported to date (168 valence electrons, 1978 basis functions, and the correlation of 84 doubly occupied and 1873 virtual orbitals) and required a scalable implementation of the (T) module on 6144 nodes (350 208 cores) of the "Cori" supercomputer at the National Energy Research Supercomputing Center (NERSC) for a total execution time of 195 min (for the (T) part). These efficient scalable implementations of highly correlated methods offer the capability to obtain long-lasting benchmarks of intermolecular interactions in complex systems. They also provide a path toward parametrizing classical potentials needed to study the dynamical and transport properties in these complex systems as well as assess the accuracy of lower scaling electronic structure methods such as density functional theory (DFT) and MP2 including its spin-biased variants.

Highly Efficient Resolution-of-Identity Density Functional Theory Calculations on Central and Graphics Processing Units.

We present an efficient method to evaluate Coulomb potential matrices using the resolution of identity approximation and semilocal exchange-correlation potentials on central (CPU) and graphics processing units (GPU). The new GPU-based RI-algorithm shows a high performance and ensures the favorable scaling with increasing basis set size as the conventional CPU-based method. Furthermore, our method is based on the J-engine algorithm [White; , Head-Gordon, J. Chem. Phys. 1996, 7, 2620], which allows for further optimizations that also provide a significant improvement of the corresponding CPU-based algorithm. Due to the increased performance for the Coulomb evaluation, the calculation of the exchange-correlation potential of density functional theory on CPUs quickly becomes a bottleneck to the overall computational time. Hence, we also present a GPU-based algorithm to evaluate the exchange-correlation terms, which results in an overall high-performance method for density functional calculations. The algorithms to evaluate the potential and nuclear derivative terms are discussed, and their performance on CPUs and GPUs is demonstrated for illustrative calculations.

Ab initio prediction of electronic, transport and bulk properties of Li2S

In this paper, we present results from ab initio, self-consistent, local density approximation (LDA) calculations of electronic and related properties of cubic antifluorite (anti-[Formula: see text]) lithium sulfide [Formula: see text]. Our nonrelativistic computations implemented the linear combination of atomic orbital (LCAO) formalism following the Bagayoko, Zhao and Williams method, as enhanced by Ekuma and Franklin (BZW–EF). Consequently, using several self-consistent calculations with increasing basis sets, we searched for the smallest basis set that yields the absolute minima of the occupied energies. The outcomes of the calculation with this basis set, called the optimal basis set, have the full physical content of density functional theory (DFT). Our calculated indirect band gap, from [Formula: see text] to [Formula: see text], is 3.723 eV, for the low temperature experimental lattice constant of 5.689 Å. The predicted indirect band gap of 3.702 eV is obtained for the computationally determined equilibrium lattice constant of 5.651 Å. We have also calculated the total density of states (DOS) and partial densities of states (pDOS), electron and hole effective masses and the bulk modulus of [Formula: see text]. Due to a lack of experimental results, most of the calculated ones reported here are predictions for this material suspected of exhibiting a high temperature superconductivity similar to that of [Formula: see text].

On the validity of the basis set superposition error and complete basis set limit extrapolations for the binding energy of the formic acid dimer.

We report the variation of the binding energy of the Formic Acid Dimer with the size of the basis set at the Coupled Cluster with iterative Singles, Doubles and perturbatively connected Triple replacements [CCSD(T)] level of theory, estimate the Complete Basis Set (CBS) limit, and examine the validity of the Basis Set Superposition Error (BSSE)-correction for this quantity that was previously challenged by Kalescky, Kraka, and Cremer (KKC) [J. Chem. Phys. 140, 084315 (2014)]. Our results indicate that the BSSE correction, including terms that account for the substantial geometry change of the monomers due to the formation of two strong hydrogen bonds in the dimer, is indeed valid for obtaining accurate estimates for the binding energy of this system as it exhibits the expected decrease with increasing basis set size. We attribute the discrepancy between our current results and those of KKC to their use of a valence basis set in conjunction with the correlation of all electrons (i.e., including the 1s of C and O). We further show that the use of a core-valence set in conjunction with all electron correlation converges faster to the CBS limit as the BSSE correction is less than half than the valence electron/valence basis set case. The uncorrected and BSSE-corrected binding energies were found to produce the same (within 0.1 kcal/mol) CBS limits. We obtain CCSD(T)/CBS best estimates for De = - 16.1 ± 0.1 kcal/mol and for D0 = - 14.3 ± 0.1 kcal/mol, the later in excellent agreement with the experimental value of -14.22 ± 0.12 kcal/mol.

Correlation consistent basis sets for the atoms In-Xe.

In this work, the correlation consistent family of Gaussian basis sets has been expanded to include all-electron basis sets for In-Xe. The methodology for developing these basis sets is described, and several examples of the performance and utility of the new sets have been provided. Dissociation energies and bond lengths for both homonuclear and heteronuclear diatomics demonstrate the systematic convergence behavior with respect to increasing basis set quality expected by the family of correlation consistent basis sets in describing molecular properties. Comparison with recently developed correlation consistent sets designed for use with the Douglas-Kroll Hamiltonian is provided.

Molecular Orbitals of NO, NO+, and NO–: A Computational Quantum Chemistry Experiment

This computational experiment presents qualitative molecular orbital (QMO) and computational quantum chemistry exercises of NO, NO+, and NO–. Initially students explore several properties of the target molecules by Lewis diagrams and the QMO theory. Then, they compare qualitative conclusions with EHT and DFT calculations and explore discrepancies from the experimental results, obtained from Internet databases. Next, they investigate how several properties change with increasing basis set and obtain reliable electronic energies by extrapolation to an infinite basis set. This experiment explores not only quantum chemistry calculations, but also the power of qualitative reasoning. Additionally, it also investigates the behavior of some properties with increasing basis set and the accurate energy calculations by the extrapolation to an infinite basis set.

Perturbative triples correction for explicitly correlated Mukherjee’s state-specific coupled cluster method

This paper reports incorporation of the perturbative triples correction within the explicitly correlated Mukherjee’s multireference coupled cluster method using the SP ansatz. In accord with the standard approximation, these corrections are not directly entered by the correlation factor amplitudes, but the explicitly correlated part of the effective Hamiltonian is included in full. The performance of the new method is tested on singlet methylene, potential curve of fluorine molecule and automerisation barrier of cyclobutadiene. It has been found that the convergence pattern of the MkCCSD(T)-F12 results with increasing basis set is improved by approximately one cardinal number, as compared to conventional MkCCSD(T). This improvement appears at the level of single and double excitations, whereas no significant impact of the explicit treatment of the electron correlation on the (T) correction has been observed, in analogy to a single-reference approach.

Highly accurate incremental CCSD(T) calculations on aqua- and amine-complexes

In this work, the accuracy of the second-order incremental expansion using the domain-specific basis set approach is tested for 20 cationic metal-aqua and 25 cationic metal-amine complexes. The accuracy of the approach is analysed by the statistical measures range, arithmetic mean, mean absolute deviation, root mean square deviation and standard deviation. Using these measures we find that the error due to the local approximations decreases with increasing basis set. Next we construct a local virtual space using projected atomic orbitals (PAOs). The accuracy of the incremental series in combination with a distance-based truncation of the PAO space is analysed and compared to the convergence of the incremental series within the domain-specific basis set approach. Furthermore, we establish the recently proposed incremental CCSD(T)|MP2 method as a benchmark method to obtain highly accurate CCSD(T) energies. In combination with a basis set of quintuple-ζ quality we establish benchmarks for the binding energies of the investigated complexes. Finally, we use the inc-CCSD(T)|MP2/aV5Z’ binding energies of 45 complexes and 34 dissociation reactions to compute the accuracy of several state of the art density functional theory (DFT) functionals like BP86, B3LYP, CAM-B3LYP, M06, PBE0 and TPSSh. With our implementation of the incremental scheme it was possible to compute the inc-CCSD(T)|MP2/aV5Z’ energy for Al(H2O)3+ 25 (6106 AOs).

The shape of Au8: gold leaf or gold nugget?

The size at which nonplanar isomers of neutral, pristine gold nanoclusters become energetically favored over planar ones is still debated amongst theoreticians and experimentalists. Spectroscopy confirms planarity is preferred at sizes up to Au7, however, starting with Au8, the uncertainty remains for larger nanoclusters. Au8 computational studies have had different outcomes: the planar D4h "cloverleaf" isomer competes with the nonplanar Td, C2v and D2d "nugget" isomers for greatest energetic stability. We here examine the 2D vs. 3D preference in Au8 by presenting our own B2PLYP, MP2 and CCSD(T) calculations on these isomers: these methods afford a better treatment of long-range correlation, which is at the root of gold's characteristic aurophilicity. We then use findings from these high-accuracy computations to evaluate two less expensive DFT approaches, applicable to much larger nanoclusters: alongside the standard functional PBE, we consider M06-L (highly parametrized to incorporate long-range dispersive interactions). We find that increasing basis set size within the B2PLYP framework has a greater destabilizing effect on the nuggets than it has on the Au8 cloverleaf. Our CCSD(T) and B2PLYP predictions, replicated by DFT-PBE, all identify the cloverleaf as the most stable isomer; MP2 and DFT-M06-L show overestimation of aurophilicity, and favor, respectively, the nonplanar D2d and Td nuggets in its stead. We conclude that PBE, which more closely reproduces CCSD(T) findings, may be a better candidate density functional for the simulation of gold nanoclusters in this context.

Atomic charge and atomic dipole fluxes during stretching displacements in small molecules

First, the convergence in values of dynamic quantities such as atomic charge flux and atomic dipole flux that take place in stretching displacements is investigated in this work by means of calculations with three basis sets (cc-pVDZ, cc-pVTZ and cc-pVQZ) and different theoretical methods (HF, MP2, MP4(SDQ) and CCSD). The charges were obtained from QTAIM, Mulliken and NPA formalisms while atomic dipoles are only calculated from QTAIM. We studied a group of simple diatomic and triatomic molecules with diverse chemical bonding character: HF, HCl, LiH, NaH, NaCl, LiF, NaF, BF, AlF, BeO, MgO, CO, ClF, HCN, HNC, OCS, CO2 and CS2. The data obtained indicate that these dynamic quantities show well-behaved convergence patterns except by those from Mulliken for some triatomic systems with increasing basis set size. Some relevant dependence of QTAIM fluxes was observed in HF and HNC when small basis sets are used but the results still converge when larger basis sets are employed. Moreover, charge fluxes from QTAIM are in nice accordance with chemical arguments while the other formalisms exhibit results that are not plausible in some cases. The most remarkable ones are noticed in highly ionic diatomic systems, which should present negligible charge flux values during bond stretching displacements around equilibrium geometries.

Ab Initio Quantum Chemistry for Protein Structures

Structural properties of over 55 small proteins have been determined using both density-based and wave-function-based electronic structure methods in order to assess the ability of ab initio "force fields" to retain the properties described by experimental structures measured with crystallography or nuclear magnetic resonance. The efficiency of the GPU-based quantum chemistry algorithms implemented in our TeraChem program enables us to carry out systematic optimization of ab initio protein structures, which we compare against experimental and molecular mechanics force field references. We show that the quality of the ab initio optimized structures, as judged by conventional protein health metrics, increases with increasing basis set size. On the other hand, there is little evidence for a significant improvement of predicted structures using density functional theory as compared to Hartree-Fock methods. Although occasional pathologies of minimal basis sets are observed, these are easily alleviated with even the smallest double-ζ basis sets.

Effects of adiabatic, relativistic, and quantum electrodynamics interactions on the pair potential and thermophysical properties of helium

The adiabatic, relativistic, and quantum electrodynamics (QED) contributions to the pair potential of helium were computed, fitted separately, and applied, together with the nonrelativistic Born-Oppenheimer (BO) potential, in calculations of thermophysical properties of helium and of the properties of the helium dimer. An analysis of the convergence patterns of the calculations with increasing basis set sizes allowed us to estimate the uncertainties of the total interaction energy to be below 50 ppm for interatomic separations R smaller than 4 bohrs and for the distance R = 5.6 bohrs. For other separations, the relative uncertainties are up to an order of magnitude larger (and obviously still larger near R = 4.8 bohrs where the potential crosses zero) and are dominated by the uncertainties of the nonrelativistic BO component. These estimates also include the contributions from the neglected relativistic and QED terms proportional to the fourth and higher powers of the fine-structure constant α. To obtain such high accuracy, it was necessary to employ explicitly correlated Gaussian expansions containing up to 2400 terms for smaller R (all R in the case of a QED component) and optimized orbital bases up to the cardinal number X = 7 for larger R. Near-exact asymptotic constants were used to describe the large-R behavior of all components. The fitted potential, exhibiting the minimum of -10.996 ± 0.004 K at R = 5.608 0 ± 0.000 1 bohr, was used to determine properties of the very weakly bound (4)He(2) dimer and thermophysical properties of gaseous helium. It is shown that the Casimir-Polder retardation effect, increasing the dimer size by about 2 Å relative to the nonrelativistic BO value, is almost completely accounted for by the inclusion of the Breit-interaction and the Araki-Sucher contributions to the potential, of the order α(2) and α(3), respectively. The remaining retardation effect, of the order of α(4) and higher, is practically negligible for the bound state, but is important for the thermophysical properties of helium. Such properties computed from our potential have uncertainties that are generally significantly smaller (sometimes by nearly two orders of magnitude) than those of the most accurate measurements and can be used to establish new metrology standards based on properties of low-density helium.

Gas phase isomerization enthalpies of organic compounds: A semiempirical, density functional theory, and ab initio post-Hartree–Fock theoretical study

A database of gas phase standard state isomerization enthalpies was constructed for 562 pure and nitrogen-, oxygen-, sulfur-, and halogen-containing hydrocarbon reactions. The PM6 and PDDG semiempirical methods, B3LYP and M062X hybrid density functionals with the 6-311++G(d,p) and 6-311+G(3df,3p) basis sets, and the CBS-Q//B3 and G4MP2 ab initio post-Hartree–Fock composite methods were examined for prediction accuracy within each class of isomerization reactions. At much lower computational cost, the PM6 and PDDG semiempirical methods offer modest isomerization enthalpy prediction performance approximately comparable to the B3LYP density functional. The M062X density functional provides nearly equivalent accuracy to the higher level CBS-Q//B3 and G4MP2 methods across all hydrocarbon classes. Increasing basis set size from 6-311++G(d,p) to 6-311+G(3df,3p) with the B3LYP and M062X density functionals does not influence their respective isomerization enthalpy prediction accuracies. Using the 6-311+G(3df,3p) basis set, the M062X functional also achieves near CBS-Q//B3 quality accuracy for enthalpies of formation using the atomization approach.

The accuracy of local MP2 methods for conformational energies

The relative energies of 95 conformers of four peptide models are studied using MP2 and LMP2 methods and correlation consistent basis sets ranging from double-zeta to augmented quintuple-zeta quality. It is found that both methods yield quite similar results, and the differences between MP2 and LMP2 decrease systematically with increasing basis set. Due to reduced intramolecular basis set superposition effects (BSSE), the LMP2 results converge more slowly to the basis set limit for most of these rather small systems. However, for larger peptides, the BSSE has a very large effect on the energy difference between extended and helical structures, leading to a very strong basis set dependence of the canonical MP2 results. It is demonstrated for alanine octapeptides that the basis set error exceeds 30 and 20kJ mol−1, respectively, if augmented double-zeta and triple-zeta basis sets are used. On the other hand, the LMP2 results are only slightly affected by the basis set size, and, even with augmented double-zeta basis sets, reasonably accurate results are obtained. Furthermore, for the larger systems, the computation times for the LMP2 calculations are shown to be up to one order or magnitude shorter than for canonical MP2 calculations with the same basis set.

Importance of the quality of metal and ligand basis sets in transition metal species

Recent development of pseudopotential-based correlation consistent basis sets (cc-pVnZ-PP) by Peterson and Puzzarini [Theor. Chem. Acc. 114, 283 (2005)] has enabled the relative importance of metal versus ligand basis set size to be examined systematically. The impact of basis set choice on geometries and dissociation energies for a series of group 11 transition metal species has been assessed via three series of calculations: (1) systematically increasing the size of the cc-pVnZ-PP basis set on the metal while holding the basis set on the ligand constant, (2) systematically increasing the size of the cc-pVnZ basis set on the ligand while holding the basis set on the metal constant, and (3) systematically increasing the size of the basis set on both the metal and the ligand. Holding the ligand basis set static while systematically increasing the metal basis set results in changes in the equilibrium bond length that are an order of magnitude smaller than for calculations where the metal basis set is held constant and the quality of the ligand basis set is systematically increased. Interestingly, holding the metal basis set static while systematically increasing the basis set size on the ligand results in monotonic convergence of dissociation energies with respect to increasing basis set size, while maintaining the basis set size on the ligand and increasing the size of the basis set on the metal do not result in monotonic convergence. Also, variance of the ligand basis set size has a greater impact on the energetics than variance of the metal basis set size. This suggests that the choice of basis set for the ligands is much more important for accurate chemical description than the choice of the transition metal basis set for these species and properties. In fact, complete basis set limit dissociation energies obtained from increasing the size of the basis set on the ligand while maintaining a constant level basis set on the metal at any level basis set result in similar energies to those obtained utilizing large basis sets on both the metal and the ligand at significant computational cost savings.