Augmented Basis Sets Research Articles

On the stability of the cuboid singlet (S2)4 supermolecule: Benchmark ab initio studies

We report high level ab initio supermolecular calculations for the cuboid structure of the disulfur tetramer, (S2)4. Accurate geometries and interaction energies with respect to 4S2 ((3)Σg (-)) were obtained using four different methods, Möller-Plesset perturbation theory (MP2), complete-active-space SCF (CASSCF) + complete active space second-order perturbation (CASPT2), RCCSD(T), and a hybrid CASPT2(singlet-nonet)∕RCCSD(T)-nonet approach with systematic sequences of augmented correlation-consistent basis sets extrapolated to the complete basis set limit. Unlike the van der Waals-like (O2)4 cluster, (S2)4 is found to be much more chemically bound. Our best estimate of the dissociation energy to four S2 molecules is 65 kcal∕mol including the counterpoise correction and an intermolecular distance of 2.74 Å. The singlet ground state of (S2)4 is much less multiconfigurational than that of (O2)4 van der Waals complex, which allows a reliable CCSD(T) description of the singlet potential energy surface of the supermolecule around its equilibrium geometry. The electron pair localization function clearly reveals electron pairing between the S2 units in the complex at the ROHF and the CASSCF∕aug-cc-pVTZ levels. Vibrational analysis at the MP2∕cc-pV(D,T,Q)Z,aug-cc-pVTZ levels yield stable cuboid structures; however, at the CCSD∕aug-cc-pV(D,T)Z levels this analysis reveals a transition state with one imaginary frequency. Thus, further multireference-based studies with large basis sets are required to reliably settle the stability issue for this supermolecular sulfur species.

Benchmarks for 0–0 transitions of aromatic organic molecules: DFT/B3LYP, ADC(2), CC2, SOS-CC2 and SCS-CC2 compared to high-resolution gas-phase data

In the present study a benchmark set of medium-sized and large aromatic organic molecules with 10-78 atoms is presented. For this test set 0-0 transition energies measured in supersonic jets are compared to those calculated with DFT and the B3LYP functional, ADC(2), CC2 and the spin-scaled CC2 variants SOS-CC2 and SCS-CC2. Geometries of the ground and excited states have been optimized with these methods in polarized triple zeta basis sets. Zero-point vibrational corrections have been calculated with the same methods and basis sets. In addition the energies have been corrected by single point calculations with a triple zeta basis augmented with diffuse functions, aug-cc-pVTZ. The deviations of the theoretical results from experimental electronic origins, which have all been measured in the gas phase with high-resolution techniques, were evaluated. The accuracy of SOS-CC2 is comparable to that of unscaled CC2, whereas ADC(2) has slightly larger errors. The lowest errors were found for SCS-CC2. All correlated wave function methods provide significantly better results than DFT with the B3LYP functional. The effects of the energy corrections from the augmented basis set and the method-consistent calculation of the zero-point vibrational corrections are small. With this benchmark set reliable reference data for 0-0 transition energies for larger organic chromophores are available that can be used to benchmark the accuracy of other quantum chemical methods such as new DFT functionals or semi-empirical methods for excitation energies and structures and thereby augments available benchmark sets augments present benchmark sets which include mainly smaller molecules.

Accurate adsorption energies of small molecules on oxide surfaces: CO–MgO(001)

A hybrid MP2:DFT + D optimization method is applied using a 3 × 3 × 2 cluster model (Mg9O9) embedded in a 4 × 4 × 4 slab model. The calculated CO-Mg(2+) distance is 248 pm, and the calculated CO frequency (blue) shift is 20 cm(-1), 6 cm(-1) larger than the experimental value. For the structure obtained, MP2 calculations with basis set extrapolation on a series of cluster models of increasing size are performed. Taking into account the difference in the periodic limit at the DFT + D level, 20.9 ± 0.7 kJ mol(-1) is obtained as the estimate for the full periodic MP2 limit for the energy of CO desorption from the MgO(001) surface. CCSD(T) corrections are evaluated for the Mg9O9 cluster model using an augmented double-zeta basis set. Basis set extension effects are examined for smaller models. For a loading of Θ = 1/8, the estimated CCSD(T) value is 21.0 ± 1.0 kJ mol(-1), which is 0.4 ± 1.0 kJ mol(-1) larger than the (electronic) desorption energy derived in this study from TPD desorption barriers reported in the literature.

Aqueous microsolvation of HgClOH. A systematic MP2 study of the HgClOH–(H2O)n species with n = 1–4

We report a systematic study of aqueous microsolvation of HgClOH. The optimized structures, harmonic vibrational frequencies and binding energies of one to four water molecules coordinated with HgClOH have been computed with 2nd order Möller–Plesset perturbation theory. Accurate incremental water binding energies have been obtained at the complete basis set (CBS) limit using sequences of augmented correlation-consistent basis sets including the counterpoise correction. The main water-solute interactions arise from hydrogen bonding and hydrogen–halogen bonds. Although mercury establishes two direct orbital-driven interactions with water oxygens for n=3 and n=4, the intramolecular geometry of HgClOH is barely modified by the microsolvation environment. The CP-corrected MP2/CBS incremental binding energies are 5.20, 11.49, 6.63 and 10.00kcal/mol for n=1–4. The structural and vibrational analysis reveal that the strongest water-solute interaction appears for n=3.

Ab initiocalculations of the Ar-ethane intermolecular potential energy surface using bond function basis sets

The intermolecular potential energy surface (PES) of argon with ethane has been studied by ab initio calculations at the levels of second-order Møller-Plesset perturbation (MP2) theory and coupled-cluster theory with single, double, and noniterative triple configurations (CCSD(T)) using a series of augmented correlation-consistent basis sets. Two sets of bond functions, bf1 (3s3p2d) and bf2 (6s6p4d2f), have been added to the basis sets to show a dramatic and systematic improvement in the convergence of the entire PES. The PES of Ar-ethane is characterized by a global minimum at a near T-shaped configuration with a well depth of 0.611 kcal mol(-1), a second minimum at a collinear configuration with a well depth of 0.456 kcal mol(-1), and a saddle point connecting the two minima. It is shown that an augmented correlation-consistent basis set with a set of bond functions, either bf1 or bf2, can effectively produce results equivalent to the next larger augmented correlation-consistent basis set, that is, aug-cc-pVDZ-bf1 ≈ aug-cc-pVTZ, aug-cc-pVTZ-bf1 ≈ aug-cc-pVQZ. Very importantly, the use of bond functions improves the PES globally, resulting accurate potential anisotropy. Finally, MP2 method is inadequate for accurate calculations, because it gives a potentially overestimated well depth and, more seriously, a poor potential anisotropy.

The study of performance of DFT functional for van der Waals interactions

In the present study, the performance of different exchange–correlation functional of DFT for van der Waals molecules has been studied by optimising the structures with augmented cc-pVTZ basis sets. The structural parameters along with vibrational frequencies and rotational constants were calculated using 15 different exchange–correlations functional for 10 molecules and compared with experimental results. Further the interaction energies (basis set superposition error corrected) were calculated using different DFT exchange–correlation functional and compared with MP2 and CCSD(T) method. The error analysis was carried out using MUE (mean unsigned error) and MAPE (mean absolute percentage error) statistical methods.

Ab initio and DFT studies on 1-(thionitrosomethylene) hydrazine: conformers, energies, and intramolecular hydrogen-bond strength

In the current study, we present an intramolecular HB, molecular structure, π-electrons delocalization and vibrational frequencies analysis of 25 possible conformers of 1-(thionitrosomethylene) hydrazine by means of DFT (B3LYP), MP2 methods in conjunction with the 6-311++G** and augmented correlation-consistent polarized-valence triple-zeta basis sets and G2MP2 theoretical level. The influence of the solvent on the stability order of conformers and the strength of intramolecular hydrogen-bonding was considered using the Tomasi’s polarized continuum model. Statistical analyses of quantitative definitions of aromaticity, nucleus independent chemical shift, harmonic oscillator model of aromaticity, aromatic fluctuation index, and the π-electron delocalization parameter (Q) as a geometrical indicator of a local aromaticity, evaluated for this conformers. Further verification of the obtained transition state structures were implemented via intrinsic reaction coordinate (IRC) analysis. Calculations of the 1H NMR chemical shift at GIAO/B3LYP/6-311++G** levels of theory are also presented. The calculated highest occupied molecular orbital (MO) and lowest unoccupied MO energies show that charge transfer occur within the molecule. Hydrogen-bond energies for H-bonded conformers were obtained from Espinosa method and the natural bond orbital theory and the atoms in molecules theory were also applied to get a more precise insight into the nature of such H-bond interactions.

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.

Theoretical study of the spectroscopically relevant parameters for the detection of HNPq and HPNq (q = 0, +1, −1) in the gas phase

High level ab initio electronic structure calculations at different levels of theory have been performed on HNP and HPN neutrals, anions, and cations. This includes standard coupled cluster CCSD(T) level with augmented correlation-consistent basis sets, internally contacted multi-reference configuration interaction, and the newly developed CCSD(T)-F12 methods in connection with the explicitly correlated basis sets. Core-valence correction and scalar relativistic effects were examined. We present optimized equilibrium geometries, harmonic vibrational frequencies, rotational constants, adiabatic ionization energies, electron affinities, vertical detachment energies, and relative energies. In addition, the three-dimensional potential energy surfaces of HNP(-1,0,+1) and of HPN(-1,0,+1) were generated at the (R)CCSD(T)-F12b∕cc-pVTZ-F12 level. The anharmonic terms and fundamentals were derived using second order perturbation theory. For HNP, our best estimate for the adiabatic ionization energy is 7.31 eV, for the adiabatic electron affinity is 0.47 eV. The higher energy isomer, HPN, is 23.23 kcal∕mol above HNP. HPN possesses a rather large adiabatic electron affinity of 1.62 eV. The intramolecular isomerization pathways were computed. Our calculations show that HNP(-) to HPN(-) reaction is subject to electron detachment.

Accurate theoretical study of PSq (q = 0,+1,−1) in the gas phase

Highly correlated ab initio methods were used in order to generate the potential energy curves and spin-orbit couplings of electronic ground and excited states of PS and PS(+). We also computed those of the bound parts of the electronic states of the PS(-) anion. We used standard coupled cluster CCSD(T) level with augmented correlation-consistent basis sets, internally contacted multi-reference configuration interaction, and the newly developed CCSD(T)-F12 methods in connection with the explicitly correlated basis sets. Core-valence correction and scalar relativistic effects were examined. Our data consist of a set of spectroscopic parameters (equilibrium geometries, harmonic vibrational frequencies, rotational constants, spin-orbit, and spin-spin constants), adiabatic ionization energies, and electron affinities. For the low laying electronic states, our calculations are consistent with previous works whereas the high excited states present rather different shapes. Based on these new computations, the earlier ultraviolet bands of PS and PS(+) were reassigned. For PS(-) and in addition to the already known anionic three bound electronic states (i.e., X(3)Σ(-), (1)Δ, and 1(1)Σ(+)), our calculations show that the (1)Σ(-), (3)Σ(+), and the (3)Δ states are energetically below their quartet parent neutral state (a(4)Π). The depletion of the J = 3 component of PS(-)((3)Δ) will mainly occur via weak interactions with the electron continuum wave.

Infinite Basis Set Extrapolation for Double Hybrid Density Functional Theory 2: Effect of Adding Diffuse Basis Functions

AbstractWe applied the Infinite Basis (IB) set extrapolation and Double Hybrid Density Functional Theory (DHDF) to calculate the electron affinities, reaction barrier heights, proton affinities, non‐covalent interactions, atomization, ionization, and alkyl bond dissociation energies. We previously found that the mean unsigned error of the B2KPLYP‐IB calculation with the combination of cc‐pVTZ and cc‐pVQZ reach the chemical accuracy limit (∼2 kcal/mol) where the largest deviation occurred in the electron affinity calculations and the weak interactions between noble gases and nonpolar molecules. Here, we investigated the basis set effect using the B2KPLYP‐IB extrapolation scheme that involves (1) the addition of extra tight d basis functions to the second row elements (i.e. cc‐pV(L+d)Z), (2) the addition of extra s, p, and d diffuse basis functions, and (3) a comparison between Dunning's Correlation Consistent and Jensen's Polarization Consistent (pc‐L) basis sets. We found that the addition of extra s and p diffuse basis functions formed the minimal augmented basis sets proposed by Truhlar. This addition permitted the B2KPLYP‐IB to reach the chemical accuracy limit with the combination of the double ζ and triple ζ basis sets. Adding extra s, p diffuse functions to the pc‐L series permitted only a small improvement. This small improvement is due to the fact that the pc‐L basis sets already contain a large number of functions for the p block elements. Taken together, the results suggest that this minimal augmented basis sets is useful for due to its accuracy and affordable computational cost.

Electronic vertical excitation spectrum of the weak H⋯BF complex

The counterpoise-corrected adiabatic interaction energy (IE) of the ground H(2S)⋯BF(X1Σ+) and excited H(2S)⋯BF(a3Π) electronic states of the H⋯BF van der Waals (vdW) complex is firstly studied in the present contribution in the framework of the supermolecule approach at the CCSD(T) and the partially spin-restricted RCCSD(T) levels of theory, respectively, using the aug-cc-pVQZ augmented basis set complemented with a set of 33211 standard midbond functions. Calculations predict a single minimum for the X2A′ ground state; the most stable configuration occurring at β=74°, distance R=6.60 ao and equilibrium dissociation energy De=46.84cm−1. The calculated IE for the excited 4A′ state reveals two local minima and a global minimum separated by saddle points, where the most stable configuration occurs at β=122°, R=6.44 ao with De=41.09cm−1. The resulting IE of the excited 4A″ state reveals a single minimum. The most stable configuration occurs at β=79°, R=6.43 ao with De=52.71cm−1. A basis set extrapolation procedure was employed to estimate the complete basis set limit of the bonding parameters. The corresponding vertical excitation-energy shifts in the fluorescent spectrum with respect to the isolated BF molecule are calculated as a guideline for future theoretical and experimental work.

Dipole matrix element approach versus Peierls approximation for optical conductivity

We develop a computational approach for calculating the optical conductivity in the augmented plane wave basis set of Wien2K and apply it for thoroughly comparing the full dipole matrix element calculation and the Peierls approximation. The results for SrVO3 and V2O3 show that the Peierls approximation, which is commonly used in model calculations, works well for optical transitions between the d orbitals. In a typical transition metal oxide, these transitions are solely responsible for the optical conductivity at low frequencies. The Peierls approximation does not work, on the other hand, for optical transitions between p- and d-orbitals which usually became important at frequencies of a few eVs

A Multilevel Strategy for the Exploration of the Conformational Flexibility of Small Molecules.

Predicting the conformational preferences of flexible compounds is still a challenging problem with important implications in areas such as molecular recognition and drug design. In this work, we describe a multilevel strategy to explore the conformational preferences of molecules. The method relies on the predominant-state approximation, which partitions the conformational space into distinct conformational wells. Moreover, it combines low-level (LL) methods for sampling the conformational minima and high-level (HL) techniques for calibrating their relative stability. In the implementation used in this study, the LL sampling is performed with the semiempirical RM1 Hamiltonian, and solvent effects are included using the RM1 version of the MST continuum solvation model. The HL refinement of the conformational wells is performed by combining geometry optimizations of the minima at the B3LYP (gas phase) or MST-B3LYP (solution) level, followed by single point MP2 computations using Dunning's augmented basis sets. Then, the effective free energy of a conformational well is estimated by combining the MP2 energy, supplemented with the MST-B3LYP solvation free energy for a conformational search in solution, with the local curvature of the well sampled at the semiempirical level. Applications of this strategy involve the exploration of the conformational preferences of 1,2-dichloroethane and neutral histamine in both the gas phase and water solution. Finally, the multilevel strategy is used to estimate the reorganization cost required for selecting the bioactive conformation of HIV reverse transcriptase inhibitors, which is estimated to be at most 1.3 kcal/mol.

Ab Initio Treatment of Bond-Breaking Reactions: Accurate Course of HO3 Dissociation and Revisit to Isomerization.

An efficient scheme is devised for accurate studies of bond-breaking/forming reactions and illustrated for HO3. It is suggested and numerically demonstrated that an accurate dissociation path for the title system can be obtained by defining the central OO bond as the reaction coordinate. The approach consists of optimizing the dissociation path at the full-valence-complete-active space level of theory followed by single-point multireference configuration interaction calculations along it. Using large diffusely augmented basis sets of the correlation consistent type, accurate dissociation curves are then obtained for both the cis- and trans-HO3 isomers by extrapolating the calculated raw energies to the complete basis set limit. The profiles show a weak van der Waals type minimum and a small barrier, both lying below the dissociation asymptote. It is shown that this barrier arises at the break-off of the central OO chemical bond and onset of the OH···O2 hydrogen bond. The calculated dissociation energies (De) are 4.5 ± 0.1 and 4.7 ± 0.1 kcal mol(-1) for the cis- and trans-HO3 isomers, respectively, with a very conservative estimate of the dissociation energy (D0) for trans-HO3 being 2.7 ± 0.2 kcal mol(-1) and a more focused one being 2.8 ± 0.1 kcal mol(-1). This result improves upon our previous estimate of this quantity while overlapping in the lower range of 2.9 ± 0.1 kcal mol(-1), the commonly accepted value from the low-temperature CRESU experiments. Since the cis-HO3 isomer is predicted to be 0.15 kcal mol(-1) less stable than trans-HO3, this may partly explain the failure to obtain a clear characterization of the former. The isomerization (torsional) potential is also revisited and a comparison presented with a curve inferred from spectroscopic measurements. Good agreement is observed, with the accuracy of the new calculated data commending its use for the reanalysis of the available vibrational-rotational spectroscopic data.

Photodissociation of N2O: Triplet states and triplet channel

The role of triplet states in the UV photodissociation of N(2)O is investigated by means of quantum mechanical wave packet calculations. Global potential energy surfaces are calculated for the lowest two (3)A' and the lowest two (3)A'' states at the multi-reference configuration interaction level of electronic structure theory using the augmented valence quadruple zeta atomic basis set. Because of extremely small transition dipole moments with the ground electronic state, excitation of the triplet states has only a marginal effect on the far red tail of the absorption cross section. The calculations do not show any hint of an increased absorption around 280 nm as claimed by early experimental studies. The peak observed in several electron energy loss spectra at 5.4 eV is unambiguously attributed to the lowest triplet state 1(3)A'. Excitation of the 2(1)A' state and subsequent transition to the repulsive branch of the 2(3)A'' state at intermediate NN-O separations, promoted by spin-orbit coupling, is identified as the main pathway to the N(2)((1)Σ(g)(+))+O((3)P) triplet channel. The yield, determined in two-state wave packet calculations employing calculated spin-orbit matrix elements, is 0.002 as compared to 0.005 ± 0.002 measured by Nishida et al. [J. Phys. Chem. A 108, 2451 (2004)].

A systematical comparison of DFT methods in reproducing the interaction energies of halide series with protein moieties

A systematic theoretical investigation on the interaction energies of halogen-ionic bridges formed between halide ions and the polar H atoms bonded to N of protein moieties has been carried out by employing a variety of density functional methods. In this procedure, full geometry optimizations are performed at the Møller-Plesset second-order perturbation (MP2) level of theory in conjunction with the Dunning's augmented correlation-consistent basis set, aug-cc-pVDZ. Subsequently, two distinct basis sets, i.e. 6-311++G(df,pd) and aug-cc-pVTZ, are employed in the following single-point calculations so as to check the stability of the results obtained at the different levels of DFT. The performance of DFT methods has been evaluated by comparing the results with those obtained from the rigorous MP2 theory. It is shown that the B98, B97-1, and M05 give the lowest root-mean-square error (RMSE) for predicting fluoride-binding energies, M05-2X, MPW1B95, and MPW1PW91 have the best performance in reproducing chloride-binding energies, B97-1, PBEKCIS, and PBE1KCIS present the optimal result for bromide-binding energies, while B97-1, MPW1PW91, and TPSS perform most well on iodide-binding energies. The popular B3LYP functional seems to be quite modest for studying halide-protein moiety interactions. In addition, the PBE1KCIS functional provide accuracies close to the computationally expensive MP2 method for the calculation of interaction energies of all halide-binding systems.

Perspectives on Basis Sets Beautiful: Seasonal Plantings of Diffuse Basis Functions.

We present a perspective on the use of diffuse basis functions for electronic structure calculations by density functional theory and wave function theory. We especially emphasize minimally augmented basis sets and calendar basis sets. We base our conclusions on our previous experience with commonly computed quantities, such as bond energies, barrier heights, electron affinities, noncovalent (van der Waals and hydrogen bond) interaction energies, and ionization potentials, on Stephens et al.'s results for optical rotation and on our own new calculations (presented here) of polarizabilities and of potential energy curves of van der Waals complexes. We emphasize the benefits of partial augmentation of the higher-zeta basis sets in preference to full augmentation at a lower ζ level. Benefits and limitations of the use of fully, partially, and minimally augmented basis sets are reviewed for different electronic structure methods and molecular properties. We have found that minimal augmentation is almost always enough for density functional theory (DFT) when applied to ionization potentials, electron affinities, atomization energies, barrier heights, and hydrogen-bond energies. For electric dipole polarizabilities, we find that augmentation beyond minimal has an average effect of 8% at the polarized triple-ζ level and 5% at the polarized quadruple-ζ level. The effects are larger for potential energy curves of van der Waals complexes. The effects are also larger for wave function theory (WFT). Even for WFT though, full augmentation is not needed for most purposes, and a level of augmentation between minimal and full is optimal for most problems. The calendar basis sets named after the months provide a convergent sequence of partially augmented basis sets that can be used for such calculations. The jun-cc-pV(T+d)Z basis set is very useful for MP2-F12 calculations of barrier heights and hydrogen bond strengths.

Ab initio study of the ground and excited states of the zinc sulfide diatomic system, ZnS

The electronic structure of the ground and excited states of the ZnS species has been investigated by variational multireference and, in some cases, coupled-cluster techniques employing augmented basis sets of quintuple-ζ quality. Full potential energy curves are reported for 18 states. The nature of the bonding for the lowest electronic states is discussed in some detail.

Assessment of theoretical procedures for hydrogen-atom abstraction by chlorine, and related reactions

We have examined a number of hydrogen-abstraction reactions and assessed various theoretical procedures with regard to their performance for geometry optimization and for calculating barriers and reaction energies. We find that the BH&H-LYP and M05-2X procedures with the 6-31+G(d,p) basis set provide reasonable predictions for the geometries of the transition structures and also yield reasonable imaginary frequencies when compared with our benchmark QCISD/6-31+G(d,p) and CCSD(T)/6-311+G(3df,2p) values. For the calculation of barriers and reaction energies, M05-2X appears to be the most accurate of the hybrid functionals. The double-hybrid functionals, B2K-PLYP, UB2-PLYP-09, ROB2-PLYP, and DSD-B-LYP-D3, when used in combination with an augmented triple-zeta basis set, give very good agreement with the benchmark URCCSD(T)/aug-cc-pVQZ energies. We find that for wavefunction procedures, use of CCSD(T) in combination with an augmented triple-zeta quality basis set is required for the accurate prediction of barriers and reaction energies for these reactions.