Basis Set Calculations Research Articles

Performance of the Harris functional for extended basis sets at the Hartree-Fock and density functional levels.

The Harris functional is a noniterative variational procedure that uses an input charge density to produce an energy that is surprisingly accurate compared to the converged Kohn-Sham self-consistent result. We adapted and generalized this functional for the Hartree-Fock closed- and open-shell cases as well as examined its use for hybrid density functional methods such as B3LYP. Analysis of extended basis set calculations shows that at the B3LYP level an input density formed from a double zeta + polarization orbital basis is accurate enough to reproduce the energy of triple zeta + double polarization + diffuse orbital basis. For large molecules this translates into a computational speed that can be an order of magnitude faster. In the case of Hartree-Fock calculations a "bootstrapping technique" that employs successive applications of the Harris functional can further reduce computational times while retaining sufficient accuracy.

O–H Bond dissociation enthalpies in hydroxyphenols. A time-resolved photoacoustic calorimetry and quantum chemistry study

Time-resolved photoacoustic calorimetry (TR-PAC) was used to investigate the energetics of O–H bonds of phenol, catechol, pyrogallol, and phloroglucinol. Values of −27.1 ± 3.9, −44.1 ± 4.4 and −1.6 ± 3.8 kJ mol−1, respectively, were obtained for the solution-phase (acetonitrile) O–H bond dissociation enthalpies of the last three compounds relative to the O–H bond dissociation enthalpy in phenol, ΔDHosln(ArO–H) = DHosln(ArO–H) − DHosln(PhO–H). A value of 388.7 ± 3.7 kJ mol−1 was determined for the PhO–H bond dissociation enthalpy in acetonitrile. Density functional theory (MPW1PW91/aug-cc-pVDZ) calculations and complete basis set (CBS-4M) calculations were carried out to analyse intramolecular hydrogen bonding and to predict gas-phase O–H bond dissociation enthalpies, DHo(ArO–H). A microsolvation model, based on the DFT calculations, was used to study the differential solvation of the phenols and their radicals in acetonitrile and to bridge solution- and gas-phase data. The results strongly suggest that ΔDHosln(ArO–H) ≈ ΔDHo(ArO–H). Hence, to calculate absolute gas-phase O–H bond dissociation enthalpies in substituted phenols from the corresponding solution-phase values, the solvation enthalpies of the substituted phenols and their radicals are not required.

Estimates of quantum chemical molecular characteristics for complete basis sets

AbstractThe large number of quantum chemical procedures and modifications thereof has for decades made difficult the comparison of results from various laboratories. In the realm of nonempirical calculations it has become possible to overcome the most serious source of errors (and simultaneously to contribute to unification of procedures), that is, the truncation of the one‐electron basis set, which concerns all levels ranging from the Hartree‐Fock (HF) to highly correlated levels. In this paper, extrapolations to a complete basis set (CBS) have been carried out by means of the simplest two‐parameter equation (Fi = F∞ + a/ni, where Fi is energy or another molecular characteristic resulting from a calculation with a basis set having ni one‐electron functions, F∞ is the sought‐after characteristic for CBS, and a is a constant). Besides total energies, also HF orbital energies (and related physical characteristics), features of molecular geometry, characteristics derived from the wave function (electric dipole and quadrupole moments), as well as vibrational characteristics acquired on the basis of the Wilson matrix analysis have been studied. Because of the main interest in properties of polyatomic systems, in addition to the coupled‐cluster method (CCSD(T)), systematic attention has been paid to less demanding techniques (HF, density functional theory (DFT), and Møsller‐Plesset second‐order correlation energy correction (MP2)) suitable not only for bigger systems but also for fitting constants of empirical potentials. Besides correlation‐consistent polarized‐valence basis sets (cc‐pVXZ, where X mostly assumes values from 2 through 5), augmented basis sets have been used also for selected systems. Altogether, 39 systems (molecules, ions, radicals, radical‐ions, van der Waals molecules, and an activated complex) have been investigated. In order to keep the length of this paper within reasonable bounds, only illustrative results are presented, with all other results available on request from the authors. As energy and energy changes have a special position among investigated quantities, it is appropriate to mention that linear plots of total energies carried out with simple and augmented basis sets have a common limit for 1/n = 0. The same is true for energy differences (δE) where, moreover, also δE with and without considering the basis set superposition error assumes the same or nearly the same common limit. The result is that a fair estimate of the CBS energy change can be based on mere simple basis set calculations for two sufficiently good basis sets, e.g., TZ and QZ. In the scope of this study, the experience with DZ basis set calculations is not satisfactory, and therefore these calculations should not be included in extrapolations.

True stabilization energies for the optimal planar hydrogen-bonded and stacked structures of guanine...cytosine, adenine...thymine, and their 9- and 1-methyl derivatives: complete basis set calculations at the MP2 and CCSD(T) levels and comparison with experiment.

Planar H-bonded and stacked structures of guanine...cytosine (G.C), adenine...thymine (A...T), 9-methylguanine...1-methylcytosine (mG...mC), and 9-methyladenine...1-methylthymine (mA...mT) were optimized at the RI-MP2 level using the TZVPP ([5s3p2d1f/3s2p1d]) basis set. Planar H-bonded structures of G...C, mG...mC, and A...T correspond to the Watson-Crick (WC) arrangement, in contrast to mA...mT for which the Hoogsteen (H) structure is found. Stabilization energies for all structures were determined as the sum of the complete basis set limit of MP2 energies and a (DeltaE(CCSD(T)) - DeltaE(MP2)) correction term evaluated with the cc-pVDZ(0.25,0.15) basis set. The complete basis set limit of MP2 energies was determined by two-point extrapolation using the aug-cc-pVXZ basis sets for X = D and T and X = T and Q. This procedure is required since the convergency of the MP2 interaction energy for the present complexes is rather slow, and it is thus important to include the extrapolation to the complete basis set limit. For the MP2/aug-cc-pVQZ level of theory, stabilization energies for all complexes studied are already very close to the complete basis set limit. The much cheaper D-->T extrapolation provided a complete basis set limit close (by less than 0.7 kcal/mol) to the more accurate T-->Q term, and the D-->T extrapolation can be recommended for evaluation of complete basis set limits of more extended complexes (e.g. larger motifs of DNA). The convergency of the (DeltaE(CCSD(T)) - DeltaE(MP2)) term is known to be faster than that of the MP2 or CCSD(T) correlation energy itself, and the cc-pVDZ(0.25,0.15) basis set provides reasonable values for planar H-bonded as well as stacked structures. Inclusion of the CCSD(T) correction is essential for obtaining reliable relative values for planar H-bonding and stacking interactions; neglecting the CCSD(T) correction results in very considerable errors between 2.5 and 3.4 kcal/mol. Final stabilization energies (kcal/mol) for the base pairs studied are very substantial (A...T WC, 15.4; mA...mT H, 16.3; A...T stacked, 11.6; mA...mT stacked, 13.1; G...C WC, 28.8; mG...mC WC, 28.5; G...C stacked, 16.9; mG...mC stacked, 18.0), much larger than published previously. On the basis of comparison with experimental data, we conclude that our values represent the lower boundary of the true stabilization energies. On the basis of error analysis, we expect the present H-bonding energies to be fairly close to the true values, while stacked energies are still expected to be about 10% too low. The stacking energy for the mG...mC pair is considerably lower than the respective H-bonding energy, but it is larger than the mA...mT H-bonding energy. This conclusion could significantly change the present view on the importance of specific H-bonding interactions and nonspecific stacking interactions in nature, for instance, in DNA. Present stabilization energies for H-bonding and stacking energies represent the most accurate and reliable values and can be considered as new reference data.

Second-order Møller–Plesset calculations with dual basis sets

Following the pioneering work of Jurgens-Lutovsky and Almlöf [Chem. Phys. Lett. 178, 451 (1991)], a second-order Møller–Plesset program was developed which allows the use of a large basis set for the pair correlation functions and a more modest one for the self-consistent field (SCF) orbitals. For several test systems, correlation energies closely approximate the results of a large basis set calculation, at substantial savings. The SCF energy of the large basis set calculation can also be estimated using perturbation theory.

Stationary points for the OH − + CH 3F → CH 3OH + F − potential energy surface

Ab initio calculations at the HF, MP2, and CCSD(T) levels of theory, utilizing a range of basis sets including the large bases 6-311++G(2df,2pd) and aug-cc-pVTZ, are used to study the OH −+CH 3F→CH 3OH+F − potential energy surface (PES). Structures, vibrational frequencies, and energies are determined for the reactant and product asymptotic limits, the OH⋯CH 3F ion–dipole potential minimum, the [OH⋯CH 3⋯F] − central barrier, and the CH 3OH⋯F − hydrogen-bonded minimum. This PES does not have a post-reaction F −⋯CH 3OH minimum complementary to the pre-reaction OH −⋯CH 3F minimum. Except for the CH 3OH⋯F − minimum, the large basis sets and MP2 theory give a consistent set of structures and frequencies for the stationary points. Neither the structure nor the vibrational frequencies of the CH 3OH⋯F − minimum are converged by the MP2 and large basis set calculations. RHF theory does not describe the energy of the [OH⋯CH 3⋯F] − central barrier nor the reaction exothermicity, however, it does give OH −+CH 3F→OH −⋯CH 3F and F −+CH 3OH→CH 3OH⋯F − well depths in good agreement with the CCSD(T) values. Overall good agreement is found between the MP2/6-31+G ∗ and much higher level CCSD(T) energies for the stationary points. The MP2 and CCSD(T) calculations give a reaction exothermicity and F −+CH 3OH→CH 3OH⋯F − well depth in good agreement with the experimental values.

Performance of the Vienna ab initio simulation package (VASP) in chemical applications

Five different density functionals in combination with ultra-soft pseudopotentials and plane wave basis sets were used to optimize the geometries of common chemical systems using solid state program Vienna ab initio simulation package (VASP). These systems included diatomics, N 2, O 2, F 2 and CO, and carbon based organic systems, ethane, ethylene, acetylene, 1,3-butadiene, 1,3,5-hexatriene, benzene, biphenyl, naphtalene graphene, polyethylene and all- trans-polyacetylene. The four functionals based on the generalized gradient approximation gave very good agreement on bond lengths and angles as compared with each other, with localized Gaussian basis set calculations and with experimental values. Reasonable results were also obtained for vibrational frequencies of selected normal modes of benzene and for torsional potentials of 1,3-butadiene and biphenyl. On the other hand, local density approximation tends to underestimate bond lengths. The performance of VASP for these properties is very similar to Gaussian type implementations of density functional theory explaining its successes in molecular, solid state, surface and polymer applications.

Spectroscopic Characteristics of Pentacene In Shpol'skii Matrixes

Absorption, fluorescence, and fluorescence excitation spectra of pentacene were measured in n-heptane, n-nonane, n-decane, n-dodecane, n-tetradecane, and n-hexadecane at temperature 5 K. We found that the band shift in different matrixes is well described by the intermolecular dispersive interactions with the Onsager cavity radius 5.5 ± 0.8 A. Analysis of the fluorescence vibronic structure indicated contribution of 12 totally symmetric vibrations in the frequency range below 2000 cm-1. The ab initio calculations with 6-31G(d) basis set and semiempirical AM1 calculations were carried out to explain the structure of the spectra.

Ab initio study of magnetochiral birefringence

The magnetically induced axial birefringence of six closed-shell chiral molecules (methyloxirane, C3H6O, fluoro- and methylcyclopropanone, C3H3OF and C4H6O, carvone, C10H14O, limonene, C10H16, and proline, C5H9NO2) is determined at the Hartree–Fock wave-function level by evaluating the frequency dependent quadratic response functions entering the molecular property expression, according to Barron and Vrbancich [Mol. Phys. 51, 715 (1984)]. Both the magnetic dipole and the electric quadrupole contributions are taken into account and their relative importance is discussed. A proof of the origin independence of the magnetochiral birefringence is presented for the exact wave function and the dependence on the origin is investigated in finite basis set calculations at the Hartree–Fock level. For carvone, limonene, and proline the results are compared with recent experimental data obtained by two different experimental groups, which are in disagreement with respect to the magnitude of the magnetochiral effect. A parallel study of the natural optical rotation shows that in the three larger molecules the optical rotatory strengths are strongly affected by changes in conformations. Nonetheless the magnetochiral birefringence computed for various different conformers—although varying remarkably—is much smaller in absolute value than experimentally observed. The disagreement—of more than three orders of magnitude—between some experimental data and theory appears to be hard to reconcile and to attribute entirely to limitations in the computational approach.

Toward true DNA base-stacking energies: MP2, CCSD(T), and complete basis set calculations.

Stacking energies in low-energy geometries of pyrimidine, uracil, cytosine, and guanine homodimers were determined by the MP2 and CCSD(T) calculations utilizing a wide range of split-valence, correlation-consistent, and bond-functions basis sets. Complete basis set MP2 (CBS MP2) stacking energies extrapolated using aug-cc-pVXZ (X = D, T, and for pyrimidine dimer Q) basis sets equal to -5.3, -12.3, and -11.2 kcal/mol for the first three dimers, respectively. Higher-order correlation corrections estimated as the difference between MP2 and CCSD(T) stacking energies amount to 2.0, 0.7, and 0.9 kcal/mol and lead to final estimates of the genuine stacking energies for the three dimers of -3.4, -11.6, and -10.4 kcal/mol. The CBS MP2 stacking-energy estimate for guanine dimer (-14.8 kcal/mol) was based on the 6-31G(0.25) and aug-cc-pVDZ calculations. This simplified extrapolation can be routinely used with a meaningful accuracy around 1 kcal/mol for large aromatic stacking clusters. The final estimate of the guanine stacking energy after the CCSD(T) correction amounts to -12.9 kcal/mol. The MP2/6-31G(0.25) method previously used as the standard level to calculate aromatic stacking in hundreds of geometries of nucleobase dimers systematically underestimates the base stacking by ca. 1.0-2.5 kcal/mol per stacked dimer, covering 75-90% of the intermolecular correlation stabilization. We suggest that this correction is to be considered in calibration of force fields and other cheaper computational methods. The quality of the MP2/6-31G(0.25) predictions is nevertheless considerably better than suggested on the basis of monomer polarizability calculations. Fast and very accurate estimates of the MP2 aromatic stacking energies can be achieved using the RI-MP2 method. The CBS MP2 calculations and the CCSD(T) correction, when taken together, bring only marginal changes to the relative stability of H-bonded and stacked base pairs, with a slight shift of ca. 1 kcal/mol in favor of H-bonding. We suggest that the present values are very close to ultimate predictions of the strength of aromatic base stacking of DNA and RNA bases.

Assessment of simple exchange-correlation energy functionals of the one-particle density matrix

An improved density matrix functional (DMF) combining the properties of the “corrected Hartree” (CH) and “corrected Hartree–Fock” (CHF) approximations is proposed. Functionals of the CH/CHF type and the closely related natural orbital functional of Goedecker and Umrigar (GU) are tested in fully variational finite basis set calculations of light atoms, the lowest energy singlet methylene, and, for the first time, potential energy curves of diatomic molecules. Although CH/CHF-style DMFs may give reasonable energies for atoms and molecules near equilibrium geometries, they predict unrealistically shallow minima in the potential energy curves for diatomic molecules with more than two electrons. The calculated CH and CHF molecular dissociation curves exhibit the same patterns of over- and under-correlations as the corresponding correlation energy plots for the homogeneous electron gas undergoing a transition from high to low densities. In contrast, the GU functional yields not only accurate atomic and molecular energies but also plausible dissociation curves. The reasons behind the observed performance are analyzed.

Implementation of RI-CC2 triplet excitation energies with an application to trans-azobenzene

Triplet excitation energies within the approximate coupled cluster singles and doubles model CC2 have been implemented using an explicitly spin coupled basis and the resolution of the identity approximation for two-electron integrals. This approach reduces substantially the requirements for CPU time, disk space and memory, and extends the applicability of CC2 for triplet excited states to molecules that could not be studied before with this method. We report an application to the lowest singlet and triplet vertical excitation energies of trans-azobenzene. An accurate ab initio geometry optimized at the MP2/cc-pVTZ level is presented, and CC2 calculations in the aug-cc-pVTZ basis set with 874 basis functions are combined with coupled cluster singles and doubles (CCSD) calculations in modest basis sets to obtain the best possible estimates for the vertical excitation energies. The results show that recently reported SOPPA calculations are unreliable. Good agreement with experiment is obtained for the lowest excited singlet state S1, but for the lowest triplet state T1 the results indicate a large difference between the vertical excitation energy and the experimentally observed transition.

Conformations, vibrational frequencies and Raman intensities of short-chain fatty acid methyl esters using DFT with 6-31G(d) and Sadlej pVTZ basis sets

Density functional calculations, using B3LPY/6-31G(d) methods, have been used to investigate the conformations and vibrational (Raman) spectra of three short-chain fatty acid methyl esters (FAMEs) with the formula C n H 2 n O 2 ( n=3–5). In all three FAMEs, the lowest energy conformer has a simple ‘all- trans’ structure but there are other conformers, with different torsions about the backbone, which lie reasonably close in energy to the global minimum. One result of this is that the solid samples we studied do not appear to consist entirely of the lowest energy conformer. Indeed, to account for the ‘extra’ bands that were observed in the Raman data but were not predicted for the all- trans conformer, it was necessary to add-in contributions from other conformers before a complete set of vibrational assignments could be made. Provided this was done, the agreement between experimental Raman frequencies and 6-31G(d) values (after scaling) was excellent, RSD=12.6 cm −1. However, the agreement between predicted and observed intensities was much less satisfactory. To confirm the validity of the approach followed by the 6-31G(d) basis set, we used a larger basis set, Sadlej pVTZ, and found that these calculations gave accurate Raman intensities and simulated spectra (summed from two different conformers) that were in quantitative agreement with experiment. In addition, the unscaled Sadlej pVTZ, and the scaled 6-31G(d) calculations gave the same vibrational mode assignments for all bands in the experimental data. This work provides the foundation for calculations on longer-chain FAMEs (which are closer to those found as triglycerides in edible fats and oils) because it shows that scaled 6-31G(d) calculations give equally accurate frequency predictions, and the same vibrational mode assignments, as the much more CPU-expensive Sadlej pVTZ basis set calculations.

Aggregation and Solvation of Steroid Molecules in Different Solvents

Ab initio quantum chemical studies at the Hartree−Fock (HF) level with the 6-31G** basis set and molecular dynamics calculations were performed on two pharmaceutical compounds, namely, the budesonide and beclomethasone dipropionate molecules. The possible water binding positions in the budesonide molecule were analyzed using the PM3 Hamiltonian, which gives fairly good geometries for budesonide−water complexes but underestimates dramatically the stabilization energies of the complexes as compared to Hartree−Fock calculations. The most stable complex according to our Hartree−Fock calculations is one where water is bound to the keto group. Its stabilization energy is −30.2 kJ/mol. In the molecular dynamics simulations, clear differences in aggregation of steroid molecules were observed in different solvents. The conformations of steroid molecules from molecular dynamics simulations differ from structures predicted from quantum chemical calculations showing the importance of evaluation of structure in different solvents.

Polarized atomic orbitals for linear scaling methods

We present a modified version of the polarized atomic orbital (PAO) method [M. S. Lee and M. Head-Gordon, J. Chem. Phys. 107, 9085 (1997)] to construct minimal basis sets optimized in the molecular environment. The minimal basis set derives its flexibility from the fact that it is formed as a linear combination of a larger set of atomic orbitals. This approach significantly reduces the number of independent variables to be determined during a calculation, while retaining most of the essential chemistry resulting from the admixture of higher angular momentum functions. Furthermore, we combine the PAO method with linear scaling algorithms. We use the Chebyshev polynomial expansion method, the conjugate gradient density matrix search, and the canonical purification of the density matrix. The combined scheme overcomes one of the major drawbacks of standard approaches for large nonorthogonal basis sets, namely numerical instabilities resulting from ill-conditioned overlap matrices. We find that the condition number of the PAO overlap matrix is independent from the condition number of the underlying extended basis set, and consequently no numerical instabilities are encountered. Various applications are shown to confirm this conclusion and to compare the performance of the PAO method with extended basis-set calculations.

An Ab Initio Investigation of the Ground and Excited Electronic State Properties of a Series of Bromine- and Iodine-Containing Singlet Carbenes

Ab initio calculations have been performed to determine the structure and energies of the ground and first excited electronic states of bromine- and iodine-containing singlet carbenes. Effective core potential basis sets augmented with polarization functions were utilized at the CASSCF, CASPT2, and CISD levels of theory. Validation of the effective core potential basis sets for the ground and excited states of the singlet carbenes was carried out by comparison with previous results from all-electron basis set calculations. As was the case in previous studies of chlorine- and fluorine-containing halocarbenes, the bromine- and iodine-containing singlet carbenes are characterized by small bond angles in their ground states, ranging from 100° to 112°, and dramatically larger bond angles in their first excited states, ranging from 125° to 132°. This increase is due to the promotion of an electron from a carbon lone pair orbital coplanar with the carbon−halogen bonds to a carbon p-type orbital perpendicular to the bonds. Adiabatic transition energies for transitions from the ground to first excited state for the singlet carbenes determined at the CASPT2(18,12) and CISD levels range from 21 277 to 10 870 cm-1 and are in excellent agreement with experimental measurements where comparisons are available.

First-principles studies of the structural and electronic properties of pyriteFeS2

We present a study of the structural and electronic properties of Pyrite FeS 2 performed using both localized basis set and plane wave first-principles calculations Calculations performed using either Gaussian or plane wave basis sets yield results consistent with each other. Small differences in the computed geometries are shown to be due to the choice of pseudopotential employed in the plane wave calculations. The computed densities of states are relatively insensitive to the form of basis set and pseudopotential used. We find that density functional and hybrid approaches predict properties such as geometry and densities of states in good agreement with experiment hut that the agreement between the results from Hartree-Fock (HF) calculations and experiment is poor. The reasons for the poor performance of HF theory in this system are examined and are found to be due to the neglect of electronic correlation.

DFT Calculations of Photoabsorption Spectra in the VUV Region for Design of Photoresist Materials for 157 nm Lithography.

Time-dependent density functional theory (TD-DFT) calculations using the B3LYP hybrid functional were performed to investigate the transparencies of organic molecules and polymers in the vacuum ultraviolet (VUV) region. The calculated photoabsorption spectra obtained from the combination of geometry optimization using the 6-311G(d) basis set and subsequent calculations of transition energies and oscillator strengths using the 6-311++G(d, p) basis set agree well with the experimental spectra. This method is a useful to infer the transparency of polymers in the VUV region, and in particular helpful for design of photoresist materials for F2 lithography (157nm). The transparencies of the model compounds relating to the representative polymer platforms were estimated, and the calculated spectra demonstrate the effectiveness of judicious introduction of -F and -CF3 groups in reducing optical absorption at the wavelength. In addition, the absorption spectra of model compounds having a sulfonyl fluoride (-SO2F) and sulfonyl ester (-SO2OR) groups, which were proposed by the present authors as novel resist platforms, were calculated and compared with the experimental spectra of corresponding homopolymers.

The Dirac equation in the algebraic approximation: VIII. Comparison of finite basis set and finite element molecular Dirac–Hartree–Fock calculations for the H2, LiH, and BH ground states

AbstractUsing basis sets of distributed s‐type Gaussian functions with positions and exponents optimized so as to support Hartree–Fock total energies with an accuracy approaching the sub‐μHartree level, Dirac–Hartree–Fock–Coulomb calculations are reported for the ground states of the H2, LiH, and BH molecules at their respective equilibrium geometries. The calculated energies are compared with those obtained by Kullie et al. using the finite element technique for the Dirac–Hartree–Fock–Coulomb problem. Finite basis set calculations using the Dirac–Hartree–Fock–Breit approximation are also reported and compared with a first‐order treatment of the frequency‐independent Breit interaction. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

Finite-basis-set implementation of subspace density-functional theory for excited states

The aim of this paper is to study the peculiarities arising in a finite-basis-set implementation of the subspace density-functional theory (SDFT) for the excited states of molecules. The accuracy of different basis-set calculations is discussed within the framework of the local-density approximation. Small basis sets with adjustable parameters, optimized for each subspace energy, were found to provide a balanced description of states. On the contrary, basis sets adjusted to the ground state yield a poor approximation for the excited states. For the molecules under consideration $({\mathrm{H}}_{2},$ HeH, and LiH), the SDFT accuracy for excited states compares well with ground-state density-functional theory calculations. Despite the limited basis set used the excitation energies calculated are in agreement with the more accurate ones obtained within the wave-function formalism by the configuration interaction methods.