Triple-zeta Basis Set Research Articles

Assessment of the DLPNO Binding Energies of Strongly Noncovalent Bonded Atmospheric Molecular Clusters.

This work assesses the performance of DLPNO-CCSD(T0), DLPNO-MP2, and density functional theory methods in calculating the binding energies of a representative test set of 45 atmospheric acid–acid, acid–base, and acid–water dimer clusters. The performance of the approximate methods is compared to high level explicitly correlated CCSD(F12*)(T)/complete basis set (CBS) reference calculations. Out of the tested density functionals, ωB97X-D3(BJ) shows the best performance with a mean deviation of 0.09 kcal/mol and a maximum deviation of 0.83 kcal/mol. The RI-CC2/aug-cc-pV(T+d)Z level of theory severely overpredicts the cluster binding energies with a mean deviation of −1.31 kcal/mol and a maximum deviation up to −3.00 kcal/mol. Hence, RI-CC2/aug-cc-pV(T+d)Z should not be utilized for studying atmospheric molecular clusters. The DLPNO variants are tested both with and without the inclusion of explicit correlation (F12) in the wavefunction, with different pair natural orbital (PNO) settings (loosePNO, normalPNO, and tightPNO) and using both double and triple zeta basis sets. The performance of the DLPNO-MP2 methods is found to be independent of PNO settings and yield low mean deviations of −0.84 kcal/mol or below. However, DLPNO-MP2 requires explicitly correlated wavefunctions to yield maximum deviations below 1.40 kcal/mol. For obtaining high accuracy, with maximum deviation below ∼1.0 kcal/mol, either DLPNO-CCSD(T0)/aug-cc-pVTZ (normalPNO) calculations or DLPNO-CCSD(T0)-F12/cc-pVTZ-F12 (normalPNO) calculations are required. The most accurate level of theory is found to be DLPNO-CCSD(T0)-F12/cc-pVTZ-F12 using a tightPNO criterion which yields a mean deviation of 0.10 kcal/mol, with a maximum deviation of 0.20 kcal/mol, compared to the CCSD(F12*)(T)/CBS reference.

Six-dimensional ab initio potential energy surface and bound States for He-H2S complex

We present a new six-dimensional potential energy surface for He-H2S including the intramolecular Q1, Q2, and Q3 normal modes for the ν1 symmetric stretching, ν2 bending and ν3 asymmetric stretching of H2S. The potential was calculated at the coupled-cluster singles and doubles with noniterative inclusion of connected triples [CCSD(T)]-F12a level with augmented correlation-consistent polarized-valence triple-zeta (aug-cc-pVTZ) basis set plus the midpoint bond function (3s3p2d1f1g). Three vibrationally averaged potentials with H2S at the vibrational ground state ν1 as well as the excited states ν2 and ν3 were generated from the integration of the six-dimensional potential over the Q1, Q2 and Q3 coordinates. Each potential has a planar T-shaped global minimum, a planar local minimum, two inplane saddle points as well as an out-plane saddle point. The global minimum is located at R=3.46 Å, θ=109.9° and φ=0.0° with a well depth of 35.301 cm−1. The radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm were employed to calculate the rovibrational energy levels. The calculated band origins are blue-shifted (0.025 cm−1 and 0.031 cm−1) and (0.041 cm−1 and 0.060 cm−1) for He-(para-H2S) and He-(ortho-H2S) in the ν2 and ν3 region of the H2S molecule, respectively.

The structural, vibrational and electronic properties of the triel-bonded complexes of boron trifluoride with some cyclic ethers – An ab initio study

The properties (molecular structures, vibrational spectra and electronic distributions) of the triel-bonded complexes of boron trifluoride with the cyclic ethers oxirane, oxetane, tetrahydrofuran and tetrahydropyran have been computed. The calculations were carried out ab initio using the Gaussian 16 program at the second order level of Møller-Plesset perturbation theory (MP2) and with Dunning’s augmented correlation-consistent polarized valence triple-zeta basis sets (aug-cc-pVTZ). The results indicate that, with the exception of the oxirane complex, the interaction energies, the bond length and angle changes and the perturbations of the BF3 fragment vibrational wavenumbers are remarkably invariant to the ring size of the base. The unique position of the oxirane complex is associated with the extent of ring strain in the monomer relative to those of the other three bases.

A straightforward a posteriori method for reduction of density-fitting error in coupled-cluster calculations.

We present a simple method for a posteriori removal of a significant fraction of the density-fitting error from the calculated total coupled-cluster energies. The method treats the difference between the exact and density-fitted integrals as a perturbation, and simplified response-like equations allow us to calculate improved amplitudes and the corresponding energy correction. The proposed method is tested at the coupled-cluster singles and doubles level of theory for a diverse set of moderately-sized molecules. On average, error reductions by a factor of approximately 10 and 20 are observed in double-zeta and triple-zeta basis sets, respectively. Similar reductions are observed in calculations of interaction energies of several model complexes. The computational cost of the procedure is small in comparison with the preceding coupled-cluster iterations. The applicability of this method is not limited to the density-fitting approximation; in principle, it can be used in conjunction with an arbitrary decomposition scheme of the electron repulsion integrals.

How accurate are approximate quantum chemical methods at modelling solute-solvent interactions in solvated clusters?

In this paper, the performance of a wide range of DFT methods is assessed for the calculation of interaction energies of thermal clusters of a solute in water. Three different charge states (neutral, proton transfer transition state and zwitterion) of glycine were solvated by 1 to 40 water molecules as sampled from molecular dynamics simulations. While some ab initio composite methods that employ insufficiently large basis sets incurred significant errors even for a cluster containing only 5 water molecules relative to the W1X-2 benchmark, the DLPNO-CCSD(T)/CBS and DSD-PBEP86 (triple zeta basis set) levels of theory predicted very accurate interaction energies. These levels of theory were used to benchmark the performance of 16 density functionals from different rungs of Jacob's Ladder. Of the Rung 4 functionals examined, the ωB97M-V and ωB97X-V functionals stood out for predicting absolute interaction energies in 40-water clusters with mean absolute deviations (MAD) ∼4 kJ mol-1. The B3LYP-D3(BJ) functional performed exceptionally well with a MAD ∼1.7 kJ mol-1 and is the overall best performing method. Calculations of relative interaction energies allow for cancellation of systematic errors, including basis set truncation and superposition errors, and the ωB97M-V and B3LYP-D3(BJ) double zeta basis set calculations yielded relative interaction energies that are within ∼3 kJ mol-1 of the benchmark. The ONIOM approximation provides another strategy for accelerating the calculation of accurate absolute interaction energies provided that the calculations have converged with respect to the size of the "high-level-layer".

An accurate potential energy surface and ring polymer molecular dynamics study of the Cl + CH4 → HCl + CH3 reaction.

The reaction Cl + CH4 → HCl + CH3, a prototypical bimolecular reaction, has been established as an important proving ground for studying chemical reaction kinetics and dynamics of polyatomic molecules. In this work, a globally accurate full-dimensional potential energy surface (PES) for this reaction is developed by using the permutationally invariant polynomial neural network (PIP-NN) approach based on 74 000 points calculated at the level of the explicitly correlated unrestricted coupled cluster single, double, and perturbative triple level with the augmented correlation corrected valence triple-zeta basis set (UCCSD(T)-F12a/AVTZ). For points in the entrance channel, spin-orbit corrections stemming from Cl(2P) are determined at the level of complete active space self-consistent field (CASSCF) with the AVTZ basis set. With this PES, thermal rate coefficients and kinetic isotope effects are computed for reactions Cl + CH4 → HCl + CH3 and Cl + CD4 → DCl + CD3 using the ring polymer molecular dynamics (RPMD) method, which can provide reliable estimations for thermal rate coefficients effectively. Generally, the agreement with the scattered experimental results is reasonably satisfactory.

A new four-dimensional ab initio potential energy surface and rovibrational spectra for the C2H2–Ar complex

ABSTRACT We report a new four-dimensional potential energy surface for the C2H2–Ar complex involving the and normal modes for the symmetric stretching and asymmetric stretching vibration of the C2H2 molecule. The potential was constructed at the coupled-cluster singles and doubles with noniterative inclusion of connected triples [CCSD(T)]-F12 level with augmented correlation-consistent polarized-valence triple-zeta (aug-cc-pVTZ) basis set supplemented with midpoint bond functions (3s3p2d1f1g). Two vibrationally averaged potentials with C2H2 at the vibrational ground and excited states were obtained by the integration of the potential over the and coordinates. It was found that each averaged potential has two equivalent T-shaped global minima, two equivalent local minima as well as three saddle points among them. The global minima are located at = 3.97 Å, = 61.4°/118.6° with a well depth of 125.47 cm−1. The rovibrational energy levels and bound states were calculated adopting radial discrete variable representation (DVR)/angular finite basis representation (FBR) and the Lanczos algorithm. The calculated band origin for C2H2–Ar is red-shift by −0.9937cm−1 in the region of C2H2, which reproduces the observed value of −1.0749cm−1 successfully. Furthermore, the calculated microwave and infrared transition frequencies are in well good agreement with the experiment data.

The Effects of Split Valence Basis Sets on Muon Hyperfine Interaction in Guanine Nucleobase and Nucleotide Structures

The DFT cluster method was employed to investigate the electronic structures and muonium hyperfine interactions in guanine nucleobase and nucleotide using three different basis sets. The total energy and Fermi contact values were calculated for muon trapped at carbon '8'. The three basis sets, 6-31G, 6-311G and 6-311G(d,p), were used in tandem with the B3LYP functional. There are significant quantitative differences in the calculated total energy. 6-311G(d,p) produced the lowest total energy as compared to the other basis sets. The lowering of the total energy is due to the increase in the number of basis functions to describe the atomic orbitals, which is consistent with the postulate on basis set completeness. The 6-31G basis set produced the muon Fermi contact value that is the closest to the experimental value. The calculated Fermi contact values for the nucleobase and nucleotide are significantly lowered in going from the double-zeta to the triple-zeta basis set by 5% and 4% respectively. The lowering of the Fermi contact value can be attributed to the extension of the triple-zeta basis set in describing the valence atomic orbitals. The presence of the sugar phosphate group in the nucleotide instead of the methyl group tends to lower the Fermi contact value. Thus, the sugar phosphate group should be taken into consideration when designing a calculation model.

Theoretical Study for the Ground Electronic State of the Reaction OH + SO → H + SO2.

The reaction OH + SO → H + SO2 plays an important role in the combustion of sulfur-containing fuels and the environment. Its reaction profile resembles that of OH + CO → H + CO2, which presents a prototypical reaction with the formation of deep complexes. In this work, a new potential energy surface (PES) for the OH + SO → H + SO2 reaction is developed based on ca. 39 200 data points calculated at the level of the explicitly correlated unrestricted coupled cluster method with single, double, and perturbative triple excitations with the augmented correlation-consistent polarized triple zeta basis set (CCSD(T)-F12a/AVTZ). The PES is invariant with respect to the permutation of the two identical oxygen atoms, which is guaranteed by the permutation-invariant polynomials as the input layer of the neural network. Using this PES, the quasiclassical trajectory method is employed to study the collision energy transfer between H and SO2 at the experimental translational energy of 59 kcal mol-1. The predicted large integral cross sections for trajectories producing SO2 with high vibrational energy and populations of the SO2 vibrational energy are in good agreement with the recent experimental and theoretical results. Detailed analysis shows that there are two possible mechanisms, a direct mechanism (without passing through HOSO or the HSO2 well) and an indirect one (passing through one or both wells). The latter dominates in producing SO2 with high vibrational energy.

A Comparison of NH2+5 and CH+5 Ions and Deuterated Variants of NHxD2+(5− x): Real or Artefactual Rotation?

Protonated NH 5 2+ has unusual vibrational and rotational behavior because its three nonequivalent equilibrium structures have nearly identical energies and its five protons scramble freely, while in the CH 5 + structure, five hydrogen atoms are bonded to the carbon atom by sharing eight valence electrons. Although a few theoretical papers have been published on quantum mechanics of those systems. Better understanding requires spectral and conformational analyses. CASSCF (8, 9) calculations with the correlation consistent polarized valence double and triple zeta basis sets are accomplished for estimating the vibrational data and zero-point energies of those two ions. The present results indicate that normal modes agree qualitatively with NHxD (5- ) 2+ and one of the normal modes indicates that NH 5 2+ is highly fluxional and has a complex spectrum while the broken N-H bonds are reformed all the time. The spectrum of mode 10 is highly complex with red and some blue shifts. In particular, modes 6 and 12 are attributed to the rapid coupling of the N-H stretching normal mode to motions more closely related to isomerization, i.e., bending or rocking. There have been long debates whether NH 5 2+ has a structure at all or not and if the rotation is real or artefactual.

Optimal basis sets for CBS extrapolation of the correlation energy: oV x Z and oV(x+d)Z

We seek correlation consistent double- and triple-zeta basis sets that perform optimally for extrapolating the correlation energy to the one-electron complete basis set limit. Since the methods used are approximate, the novel basis sets become method specific in the sense of performing best for the chosen level of theory. Such basis sets are also shown to perform accurately for tensorial properties and do not significantly alter the Hartree-Fock energy. Quantitatively, the extrapolated correlation energies from (oVdZ, oVtZ) outperform typically by three- to fivefold those obtained from traditional ansatzes with similar flexibility, thus being (VtZ, VqZ) type or even better. They may even outperform explicitly correlated ones. Not surprisingly, the outperformance in relative energies (e.g., atomization and dissociation energies, and ionization potential) is somewhat downscaled, albeit consistently better than with traditional basis sets. As a case study, we also consider the polarizability of p-nitroaniline, a sizeable system for which complete basis set (CBS)(oVdZ, oVtZ) calculations are shown to outperform equally expensive CBS(VdZ, VtZ) results.

A Continuum from Halogen Bonds to Covalent Bonds: Where Do λ3 Iodanes Fit?

The intrinsic bonding nature of λ 3 -iodanes was investigated to determine where its hypervalent bonds fit along the spectrum between halogen bonding and covalent bonding. Density functional theory with an augmented Dunning valence triple zeta basis set ( ω B97X-D/aug-cc-pVTZ) coupled with vibrational spectroscopy was utilized to study a diverse set of 34 hypervalent iodine compounds. This level of theory was rationalized by comparing computational and experimental data for a small set of closely-related and well-studied iodine molecules and by a comparison with CCSD(T)/aug-cc-pVTZ results for a subset of the investigated iodine compounds. Axial bonds in λ 3 -iodanes fit between the three-center four-electron bond, as observed for the trihalide species IF 2 − and the covalent FI molecule. The equatorial bonds in λ 3 -iodanes are of a covalent nature. We explored how the equatorial ligand and axial substituents affect the chemical properties of λ 3 -iodanes by analyzing natural bond orbital charges, local vibrational modes, the covalent/electrostatic character, and the three-center four-electron bonding character. In summary, our results show for the first time that there is a smooth transition between halogen bonding → 3c–4e bonding in trihalides → 3c–4e bonding in hypervalent iodine compounds → covalent bonding, opening a manifold of new avenues for the design of hypervalent iodine compounds with specific properties.

Combined high resolution X-ray and DFT Bader analysis to reveal a proposed Ru–H⋯Si interaction in Cp(IPr)Ru(H)2SiH(Ph)Cl

The compound Cp(IPr)Ru(H)2SiH(Ph)Cl (IPr = 1,3-bis(2,6-diisopropylphenyl)-imidazol-2-ylidene) (1) was subject to low temperature (30 K), high resolution X-ray structural analysis to obtain a high quality electron density map. This map was subject to a Bader analysis to ascertain the possibility of a Ru–H⋯Si interaction. For comparison, DFT calculations employing the well known B3LYP functional in conjunction with a triple zeta basis set was employed. Thus, we not only report the results of a possible Ru–H⋯Si interaction but also benchmark the use of the employed level of theory against experimental results.

New zinc phthalocyanine derivatives for nitrogen dioxide sensors: A theoretical optoelectronic investigation

Zinc-phthalocyanines ZnPc derivatives including quinoleinoxy groups have been studied through DFT calculations. The most stable geometries were characterized for the unsubstituted to the tetra substituted ZnPcs. The energy gap decreased from 2.146 eV for ZnPc to 2.050 eV for ZnPcR4, in agreement with the experimental trend, and indicating the reliability of the electrochemical evaluation of LUMO and HOMO energy levels. Optical transitions computed at the CAM-B3LYP-D3 with triple zeta basis sets were found to be in good agreement with experimental values for both the B and Q bands. Subsequently, structures were also characterized for NO2 adsorbed complexes, in order to assess the potential role of ZnPc as a NO2 sensor. A clear sigma bonding chemisorption of NO2 on Zn atom is observed for all derivatives, followed by a charge transfer from the π Pc conjugated system to the Zn-NO2 moiety. More importantly, after NO2 chemisorption on ZnPc derivative a remarkable red-shift is observed in the optical spectra, particularly for NO2/ZnPcR4 complex, thus offering a good index to detect the binding of NO2. The optical spectra and the vibrational spectra can therefore be used to detect the presence of NO2 and ZnPc derivatives show appropriate properties to constitute good NO2 sensors.

A comparison of NH52+ and CH5+ ions and deuterated variants of NHx D(5–x)2+: Real or artefactual rotation?

Protonated NH52+ has unusual vibrational and rotational behavior because its three nonequivalent equilibrium structures have nearly identical energies and its five protons scramble freely, while in the CH5+ structure, five hydrogens are bonded to the carbon atom by sharing eight valence electrons. Although a few theoretical papers have been published on the quantum mechanics of those systems. Better understanding requires spectral and conformational analysis. CASSCF (8, 9) calculations with the correlation consistent polarized valence double and triple zeta basis sets are accomplished for estimating the vibrational data and zero-point energies of two those ions .The present results indicate the normal modes agree qualitatively with NHxD(5-x)2+ and one of the normal modes indicates that NH52+ is highly fluxional and has a complex spectrum while the broken N—H bonds are reformed all the time. The spectrum of mode 10 is highly complex with red and some blue shifts. In particular, modes 6 and 12 are attributed to the rapid coupling of the N—H stretching normal mode to motions more closely related to isomerization, i.e., bending or rocking. There have been long debates whether NH52+ has a structure at all or not and if the rotation is real or artefactual.

Explicitly correlated potential energy surface of the CO2-CO van der Waals dimer and applications.

The four-dimensional-potential energy surface (4D-PES) of the CO2-CO van der Waals complex is generated using the explicitly correlated coupled cluster with single, double, and perturbative triple excitation (CCSD(T)-F12) method in conjunction with the augmented correlation-consistent triple zeta (aug-cc-pVTZ) basis set. This 4D-PES is developed over the set of inter-molecular coordinates and where the CO2 and CO monomers are treated as rigid rotors. Afterwards, analytic fits of this 4D-PES are carried out. In addition to the already known C-bound and O-bound stable structures of CO2-CO, we characterise a new isomer: it has a T-shaped structure where the O atom of the CO2 moiety points into the centre of mass of CO. We also find the saddle points connecting these minimal structures. This new isomer may play a role during the intramolecular isomerization processes at low energies. Then, the 4D-PES expansion is incorporated into bound vibrational state computations of C-bound and O-bound complexes. We also computed the temperature dependence of the second virial coefficient for CO2-CO. A good agreement with experiments is found.

Dissection of the multichannel reaction of acetylene with atomic oxygen: from the global potential energy surface to rate coefficients and branching dynamics.

The O(3P) + C2H2 reaction is the first step in acetylene oxidation. The accurate kinetic data and the understanding of the reaction dynamics is of great importance. To this end, a full-dimensional global potential energy surface (PES) for the ground triplet state of the O(3P) + C2H2 reaction is constructed based on approximately 85 000 ab initio points calculated at the level of explicitly correlated unrestricted coupled cluster single, double, and perturbative triple excitations with the explicitly correlated polarized valence triple zeta basis set (UCCSD(T)-F12b/VTZ-F12). The PES is fit using the permutation invariant polynomial-neural network (PIP-NN) approach with a total root mean square error of 0.21 kcal mol-1. The key topographic features of the PES, including multiple potential wells and saddle points along different reaction pathways, are well represented by this fit PES. The kinetics and dynamics of the O(3P) + C2H2 reaction are investigated using the quasi-classical trajectory (QCT) method. The calculated rate coefficients are in good agreement with experimental data over a wide temperature range, especially when the temperature is lower than 1500 K. The product branch ratio has also been determined, which indicates the H + HCCO channel as the dominant reaction pathway at 298-3000 K, accounting for 80-90% of the overall rate coefficient, in agreement with experimental observations. The dynamics of the reaction is analyzed in detail.

An accurate full-dimensional permutationally invariant potential energy surface for the interaction between H2O and CO.

The interaction between H2O and CO has been the subject of numerous experimental and theoretical investigations for a long time due to their important roles in various environments, such as the atmosphere, combustion of hydrocarbons, and the interstellar medium. In this work, the first full-dimensional accurate potential energy surface (PES) was developed for the CO + H2O system based on ca. 102 000 points calculated at the level of an explicitly correlated coupled-cluster method with single, double, and perturbative triple excitations with the augmented correlation-consistent polarized triple zeta basis set (CCSD(T)-F12a/AVTZ) using the permutation invariant polynomial-neural network (PIP-NN) method. The geometries, energies, and frequencies of the two complex wells, CO-H2O and OC-H2O, and one transition state connecting them, as well as some interconversions between different conformers, are accurately reproduced by the PES, thanks to the small fitting error of only 1.08 meV. With full-dimensional degrees of freedom considered in the PES, we found that there exist strong dependences of the CO and OH bond lengths on the OC-H2O and CO-H2O interaction energies, which is not possible in reduced dimensional PESs. Finally, classical dynamics was carried out to study the energy transfer between H2O and CO with different initial vibrational energies in H2O and different vibrational states in CO.

Study of $${\text{CD}}_{5}^{ + }$$ Ions and Deuterated Variants( $${\text{C}}{{{\text{H}}}_{x}}{\text{D}}_{{(5 - x)}}^{ + }$$ ): An Artefactual Rotation

Deuterated methane, $${\text{CD}}_{5}^{ + }$$ , has unusual vibrational and rotational behavior because its three nonequivalent equilibrium structures have nearly identical energies and its five protons scramble freely. Although a few theoretical papers have been published on the quantum mechanics of these systems, a better understanding requires spectral and conformational analysis. Post Hartree-Fock, Moller-Plesset and DFT calculations with the correlation consistent polarized valence double and triple zeta basis sets have been accomplished for estimating the thermodynamic data and zero-point energies of $${\text{C}}{{{\text{H}}}_{x}}{\text{D}}_{{(5 - x)}}^{ + }$$ . The present results indicates the normal modes agree with qualitative of $${\text{C}}{{{\text{H}}}_{x}}{\text{D}}_{{(5 - x)}}^{ + }$$ which modes 10 indicates $${\text{CD}}_{5}^{ + }$$ is highly fluxional and has a complex spectrum while the C–D bonds which are broken and reformed all the time. The spectrum of mode 12 is highly complex with red-and some blue shifts. In particular, modes 8 and 10 be attributed to the rapid coupling of the CD-stretching normal mode to motions more closely related to isomerization, i.e., bending or rocking. There has thus been a long debate whether $${\text{CD}}_{5}^{ + }$$ has a structure at all or not and is it real rotational motions or artefactual.

Accurate Ionization Potentials, Electron Affinities and Electronegativities of Single-Walled Carbon Nanotubes by State-of-the-Art Local Coupled-Cluster Theory

Abstract Single-walled carbon nanotubes (SWCNTs) possess novel conducting properties and high potential as a building block for molecular electronic devices. In this paper, we report accurate ionization potentials, electron affinities and electronegativities for large SWCNTs using our state-of-the-art implementations of reduced-scaling coupled-cluster method (DLPNO-CCSD(T)) using triple zeta basis set.