Note on the choice of basis set in density functional theory calculations for electronic structures of molecules (test on the atoms from the first three rows of the periodic table (2 ⩽ N ⩽ Z ⩽ 18), water, ammonia and pyrrole) (original) (raw)
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Newly developed basis sets for density functional calculations
Journal of Computational Chemistry, 2005
Optimized contracted Gaussian basis sets of double-zeta valence polarized (DZVP) quality for first-row transition metals are presented. The DZVP functions were optimized using the PWP86 generalized gradient approximation (GGA) functional and the B3LYP hybrid functional. For a careful analysis of the basis sets performance the transition metal atoms and cations excitation energies were calculated and compared with the experimental ones. The calculated values were also compared with those obtained using the previously available DZVP basis sets developed at the local-density functional level. Because the new basis sets work better than the previous ones, possible reasons of this behavior are analyzed. The newly developed basis sets also provide a good estimation of other atomic properties such as ionization energies.
A new density functional method for electronic structure calculation of atoms and molecules
arXiv: Chemical Physics, 2019
This chapter concerns with the recent development of a new DFT methodology for accurate, reliable prediction of many-electron systems. Background, need for such a scheme, major difficulties encountered, as well as their potential remedies are discussed at some length. Within the realm of non relativistic Hohenberg-Kohn-Sham (HKS) DFT and making use of the familiar LCAO-MO principle, relevant KS eigenvalue problem is solved numerically. Unlike the commonly used atom-centered grid (ACG), here we employ a 3D cartesian coordinate grid (CCG) to build atom-centered localized basis set, electron density, as well as all the two-body potentials directly on grid. The Hartree potential is computed through a Fourier convolution technique via a decomposition in terms of short- and long-range interactions. Feasibility and viability of our proposed scheme is demonstrated for a series of chemical systems; first with homogeneous, local-density-approximated XC functionals followed by non-local, gradi...
Computer Physics Communications, 2001
The sensitivity of computed DFT (Density Functional Theory) molecular properties (including energetics, geometries, vibrational frequencies, and infrared intensities) to the radial and angular numerical integration grid meshes, as well as to the partitioning scheme, is discussed for a number of molecules using the Gaussian 98 program system. Problems with typical production grid sizes are particularly acute for third-row transition metal systems, but may still result in qualitatively incorrect results for a molecule as simple as CCH. Practical recommendations are made with respect to grid choices for the energy(+gradient) steps, as well as for the solution of the CPKS (Coupled Perturbed Kohn-Sham) equations.
Journal of Molecular Structure: THEOCHEM, 1997
Although Hartree-Fock wave functions can provide a semi-quantitative description of the electronic structure of molecules, accurate predictions cannot be made without explicit inclusion of the effects of electron correlation. In correlated calculations, the accuracy of the wave function is determined by two expansions: the many-electron expansion in terms of molecular orbitals that defines the form of the wave function and the basis set used to expand the one-electron molecular orbitals. Thus, to assess the accuracy of a given wave function (correlation method), it is necessary to examine the dependence of a given property on the basis set. In this work, systematic sequences of correlation consistent basis sets ranging in size from double-to sextuple-zeta (cc-pVnZ) have been employed together with several commonly used electron correlation methods, e.g., MPn (n = 2-4) CCSD, CCSD(T), and MRCI, to calculate the spectroscopic constants and selected molecular properties of the carbon monoxide molecule. The computed spectroscopic constants show excellent convergence toward the complete basis set (CBS) limit, and the inrrinsic errors of each correlation method have been assessed and compared. The effects of correlating the 1 s-like core electrons have also been determined using a sequence of core-valence cc-pCVnZ basis sets with the CCSD(T) and ACPF methods. A number of other properties have also been calculated for each correlation method as a function of the correlation consistent basis set: the dipole moment, quadrupole moment, dipole polarizability, and the first and second hyperpolarizabilities. For these calculations, results using the aug-cc-pVnZ basis sets are compared with those obtained using basis sets incorporating another complete shell of diffuse functions, d-aug-cc-pVnZ.
The effect of different density functional methods on basis set parameters
Chemical Physics Letters, 2005
It is shown that for density functional calculations, the use of basis sets optimized by density functional methods gives a small, but significant, improvement over basis sets optimized at the Hartree-Fock (HF) level. The difference between different exchangecorrelation functionals, however, is very marginal, and significantly less than the inherent error relative to the basis set limit. The difference between methods diminishes as the basis set becomes larger, and the main variation is due to the contraction coefficients, and not the exponent values. The uncontracted forms of the previously proposed polarization consistent basis sets should thus be useful for establishing the basis set limit for any density functional method, as well as estimating the HF limit for molecular systems.
Journal of Chemical Theory and Computation, 2007
The reliable prediction of molecular properties is a vital task of computational chemistry. In recent years, density functional theory (DFT) has become a popular method for calculating molecular properties for a vast array of systems varying in size from small organic molecules to large biological compounds such as proteins. In this work we assess the ability of many DFT methods to accurately determine atomic and molecular properties for small molecules containing elements commonly found in proteins, DNA, and RNA. These properties include bond lengths, bond angles, ground state vibrational frequencies, electron affinities, ionization potentials, heats of formation, hydrogen bond interaction energies, conformational energies, and reaction barrier heights. Calculations are carried out with the 3-21G*, 6-31G*, 3-21+G*, 6-31+G*, 6-31++G*, cc-pVxZ, and aug-cc-pVxZ (x=D,T) basis sets, while bond distance and bond angle calculations are also done using the cc-pVQZ and aug-cc-pVQZ basis sets. Members of the popular functional classes, namely, LSDA, GGA, meta-GGA, hybrid-GGA, and hybrid-meta-GGA, are considered in this work. For the purpose of comparison, Hartree-Fock (HF) and second order many-body perturbation (MP2) methods are also assessed in terms of their ability to determine these physical properties. Ultimately, it is observed that the split valence bases of the 6-31G variety provide accuracies similar to those of the more computationally expensive Dunning type basis sets. Another conclusion from this survey is that the hybrid-meta-GGA functionals are typically among the most accurate functionals for all of the properties examined in this work.
The Journal of Chemical Physics, 2002
Correlation consistent basis sets for accurately describing core-core and core-valence correlation effects in atoms and molecules have been developed for the second row atoms Al-Ar. Two different optimization strategies were investigated, which led to two families of core-valence basis sets when the optimized functions were added to the standard correlation consistent basis sets (cc-pVnZ). In the first case, the exponents of the augmenting primitive Gaussian functions were optimized with respect to the difference between all-electron and valence-electron correlated calculations, i.e., for the core-core plus core-valence correlation energy. This yielded the cc-pCVnZ family of basis sets, which are analogous to the sets developed previously for the first row atoms ͓D. E. Woon and T. H. Dunning, Jr., J. Chem. Phys. 103, 4572 ͑1995͔͒. Although the cc-pCVnZ sets exhibit systematic convergence to the all-electron correlation energy at the complete basis set limit, the intershell ͑core-valence͒ correlation energy converges more slowly than the intrashell ͑core-core͒ correlation energy. Since the effect of including the core electrons on the calculation of molecular properties tends to be dominated by core-valence correlation effects, a second scheme for determining the augmenting functions was investigated. In this approach, the exponents of the functions to be added to the cc-pVnZ sets were optimized with respect to just the core-valence ͑intershell͒ correlation energy, except that a small amount of core-core correlation energy was included in order to ensure systematic convergence to the complete basis set limit. These new sets, denoted weighted corevalence basis sets (cc-pwCVnZ), significantly improve the convergence of many molecular properties with n. Optimum cc-pwCVnZ sets for the first-row atoms were also developed and show similar advantages. Both the cc-pCVnZ and cc-pwCVnZ basis sets were benchmarked in coupled cluster ͓CCSD͑T͔͒ calculations on a series of second row homonuclear diatomic molecules (Al 2 , Si 2 , P 2 , S 2 , and Cl 2 ), as well as on selected diatomic molecules involving first row atoms ͑CO, SiO, PN, and BCl͒. For the calculation of core correlation effects on energetic and spectroscopic properties, the cc-pwCVnZ basis sets are recommended over the cc-pCVnZ ones.
Journal of Chemical Physics, 2021
Recently, a new type of orbital-dependent functional for the Kohn-Sham (KS) correlation energy, σ-functionals, was introduced. Technically, σ-functionals are closely related to the well-known direct random phase approximation (dRPA). Within the dRPA, a function of the eigenvalues σ of the frequency-dependent KS response function is integrated over purely imaginary frequencies. In σfunctionals, this function is replaced by one that is optimized with respect to reference sets of atomization, reaction, transition state, and non-covalent interaction energies. The previously introduced σ-functional uses input orbitals and eigenvalues from KS calculations with the generalized gradient approximation (GGA) exchange-correlation functional of Perdew, Burke, and Ernzerhof (PBE). Here, σ-functionals using input orbitals and eigenvalues from the meta-GGA TPSS and the hybrid-functionals PBE0 and B3LYP are presented and tested. The number of reference sets taken into account in the optimization of the σ-functionals is larger than in the first PBE based σ-functional and includes sets with 3d-transition metal compounds. Therefore, also a reparameterized PBE based σ-functional is introduced. The σ-functionals based on PBE0 and B3LYP orbitals and eigenvalues reach chemical accuracy for main group chemistry. For the 10 966 reactions from the highly accurate W4-11RE reference set, the B3LYP based σ-functional exhibits a mean average deviation of 1.03 kcal/mol compared to 1.08 kcal/mol for the coupled cluster singles doubles perturbative triples method if the same valence quadruple zeta basis set is used. For 3d-transition metal chemistry, accuracies of about 2 kcal/mol are reached. The computational effort for the post-self-consistent evaluation of the σ-functional is lower than that of a preceding PBE0 or B3LYP calculation for typical systems.
Highly accurate calculations of molecular electronic structure
1999
The highly accurate calculation of molecular electronic structure requires the expansion of the molecular electronic wavefunction to be as nearly complete as possible both in one-and nelectron space. In this review, we consider the convergence behaviour of computed electronic energies, in particular electronic enthalpies of reaction, as a function of the one-electron space. Based on the convergence behaviour, extrapolations to the limit of a complete one-electron basis are possible and such extrapolations are compared with the direct computation of electronic energies near the basis-set limit by means of explicitly correlated methods. The most elaborate and accurate computations are put into perspective with respect to standard and-from a computational point of view-inexpensive density functional, complete basis set (CBS) and Gaussian-2 calculations. Using the explicitly correlated coupled-cluster method including singles, doubles and non-iterative triples replacements, it is possible to compute (the electronic part of) enthalpies of reaction accurate to within 1 kJ mol −1 . To achieve this level of accuracy with standard coupled-cluster methods, large basis sets or extrapolations to the basis-set limit are necessary to exploit fully the intrinsic accuracy of the coupled-cluster methods.
The role of the basis set: Assessing density functional theory
Journal of Chemical Physics, 2003
When developing and assessing density functional theory methods, a finite basis set is usually employed. In most cases, however, the issue of basis set dependency is neglected. Here, we assess several basis sets and functionals. In addition, the dependency of the semiempirical fits to a given basis set for a generalised gradient approximation and a hybrid functional is investigated. The resulting functionals are then tested for other basis sets, evaluating their errors and transferability. 1 I. INTRODUCTION In the past years, Density Functional Theory (DFT) has become a very important approach for computational quantum chemistry. The Kohn-Sham implementation of DFT critically depends on the quality of the exchange-correlation functional for its success.