Quintuple-zeta Basis Sets Research Articles

Accurate Full-Dimensional Global Diabatic Potential Energy Matrix for the Two Lowest-Lying Electronic States of the H + O2 ↔ HO + O Reaction.

A new and more accurate diabatic potential energy matrix (DPEM) is developed for the two lowest-lying electronic states of HO2, covering both the strong interaction region and reaction asymptotes. The ab initio calculations were performed at the Davidson corrected multireference configuration interaction level with the augmented correlation-consistent polarized valence quintuple-zeta basis set (MRCI+Q/AV5Z). The accuracy of the electronic structure calculations is validated by excellent agreement with the experimental HO2 equilibrium geometry, fundamental vibrational frequencies, and H + O2 ↔ OH + O reaction energy. Through the combination of an electronic angular momentum-method and a configuration interaction vector-based method, the mixing angle between the first two 2A″ states of HO2 was successfully determined. Elements of the 2×2 DPEM were fit to neural networks with a proper account of the complete nuclear permutation inversion symmetry of HO2. The DPEM correctly predicted the properties of conical intersection seams at linear and T-shape geometries, thus providing a reliable platform for studying both the spectroscopy of HO2 and the nonadiabatic dynamics for the H + O2 ↔ OH + O reaction.

Theoretical rovibronic spectroscopy of the calcium monohydroxide radical (CaOH).

The rovibronic (rotation-vibration-electronic) spectrum of the calcium monohydroxide radical (CaOH) is of interest to studies of exoplanet atmospheres and ultracold molecules. Here, we theoretically investigate the Ã2Π-X̃2Σ+ band system of CaOH using high-level ab initio theory and variational nuclear motion calculations. New potential energy surfaces (PESs) are constructed for the X̃2Σ+ and Ã2Π electronic states along with Ã-X̃ transition dipole moment surfaces (DMSs). For the ground X̃2Σ+ state, a published high-level ab initio PES is empirically refined to all available experimental rovibrational energy levels up to J = 15.5, reproducing the observed term values with a root-mean-square error of 0.06 cm-1. Large-scale multireference configuration interaction calculations using quintuple-zeta quality basis sets are employed to generate the Ã2Π state PESs and Ã-X̃ DMSs. Variational calculations consider both Renner-Teller and spin-orbit coupling effects, which are essential for a correct description of the spectrum of CaOH. Computed rovibronic energy levels of the Ã2Π state, line list calculations up to J = 125.5, and an analysis of Renner-Teller splittings in the ν2 bending mode of CaOH are discussed.

Computational Study of 3d Metals and Their Influence on the Acidity of Methane C-H Bonds.

CCSD(T) methods in conjunction with correlation consistent basis sets are used to predict the pKa for the deprotonation of methane in a 3d metal ion adduct, [M···CH4]+ (M = Sc–Cu), in dimethyl sulfoxide solvent, which is modeled by the SMD continuum solvent model. Results show that the coordination of methane to different M+ ions has a substantial difference of ∼27 pKa units, from most to least acidic, and increases the acidity of the methane C–H bond from ∼8 to 36 pKa units. Furthermore, even with the omission of the more expensive quadruple and quintuple zeta basis sets in the prediction process, similar trends in pKa(C–H) as a function of 3d metal ions are exhibited. This research serves to illustrate the substantial effect that metal ion identity has on the acidity of a coordinated hydrocarbon and the utility that correlation consistent basis sets have in lowering the computational cost of modeling larger systems.

Interatomic potentials for ground and excited states of Ar+He.

The potential energy curves (PECs) of the ground and excited states that correlate in the atomic limit with Ar([Ne]3s 23p 6,1S), Ar([Ne]3s 23p 54s 1, 3P, 1P), and Ar([Ne]3s 23p 54p 1, 3D, 3P, 3S, 1D, 1P, 1S) are calculated at the multireference configuration interaction (MRCI+Q) theoretical level with extrapolations to the complete basis set limit using all-electron correlation consistent triple-, quadruple-, and quintuple-zeta basis sets. Scalar relativistic corrections are calculated using second-order Douglas-Kroll-Hess Hamiltonian with the corresponding basis sets contracted for scalar relativistic Hamiltonians. For these calculations, the 3s orbitals of the Ar atom are not included in the active space but are correlated through single and double excitations. Spin-orbit eigenstates are computed by diagonalizing the Breit-Pauli matrix between internal configurations with no electrons in external orbitals and added to the scalar relativistic results. A total of 32 molecular PECs are computed with spin-orbit contributions, which correlate with 1s1, 1s5-2, and 2p10-1 atomic Ar energies in Paschen notation. Important features of the PECs and system crossings are discussed.

Density Functional Theory and the Basis Set Truncation Problem with Correlation Consistent Basis Sets: Elephant in the Room or Mouse in the Closet?

Two recent papers in this journal called into question the suitability of the correlation consistent basis sets for density functional theory (DFT) calculations, because the sets were designed for correlated methods such as configuration interaction, perturbation theory, and coupled cluster theory. These papers focused on the ability of the correlation consistent and other basis sets to reproduce total energies, atomization energies, and dipole moments obtained from "quasi-exact" multiwavelet results. Undesirably large errors were observed for the correlation consistent basis sets. One of the papers argued that basis sets specifically optimized for DFT methods were "essential" for obtaining high accuracy. In this work we re-examined the performance of the correlation consistent basis sets by resolving problems with the previous calculations and by making more appropriate basis set choices for the alkali and alkaline-earth metals and second-row elements. When this is done, the statistical errors with respect to the benchmark values and with respect to DFT optimized basis sets are greatly reduced, especially in light of the relatively large intrinsic error of the underlying DFT method. When judged with respect to high-quality Feller-Peterson-Dixon coupled cluster theory atomization energies, the PBE0 DFT method used in the previous studies exhibits a mean absolute deviation more than a factor of 50 larger than the quintuple zeta basis set truncation error.

A full-dimensional ab initio potential energy surface and rovibrational energies of the Ar–HF complex

ABSTRACTWe report a new full-dimensional ab initio potential energy surface for the Ar–HF van der Waals complex at the level of coupled-cluster singles and doubles with noniterative inclusion of connected triples levels [CCSD(T)] using augmented correlation-consistent quintuple-zeta basis set (aV5Z) plus bond functions. Full counterpoise correction was employed to correct the basis-set superposition error. The hypersurface was fitted using artificial neural network method with a root mean square error of 0.1085 cm−1 for more than 8000 ab initio points. The complex was found to prefer a linear Ar–H–F equilibrium structure. The three-dimensional discrete variable representation method and the Lanczos propagation algorithm were then employed to calculate the rovibrational states without separating inter- and intra- molecular nuclear motions. The calculated vibrational energies of Ar–HF differ from the experiment values within about 1 cm−1 on the first four HF vibrational states, and the predicted pure rotational energies on (0000) and (1000) vibrational states are deviated from the observed value by about 1%, which shows the accuracy of our new PES.

Theoretical Study on the Spectroscopic Parameters and Transition Properties of MgH Radical Including Spin-orbit Coupling**Supported by the National Natural Science Foundation of China under Grant Nos 11564019, 11574114, 11147158, 91221301 and 11264020, and the Natural Science Foundation of Jilin Province under Grant No 20150101003JC.

An accurate theoretical study on the MgH radical is reported by adopting the high-level relativistic MRCI+Q method with a quintuple-zeta quality basis set. The reliable potential energy curves of the five Λ-S states of MgH are derived. Then the associated spectroscopic parameters are determined and found to be in good accordance with the available experimental results. The permanent dipole moments (PDMs) and the spin-orbit (SO) matrix elements of Λ-S states are computed. The results show that the abrupt changes of PDMs and SO matrix elements are attributed to the variations of electronic configurations at the avoided crossing point. The SOC effect leads to the five Λ-S states split into ten Ω states and results in the double potential well of (2)1/2 state. Finally, the transition properties from the (2)1/2, (1)3/2 and (3)1/2 states to the ground state X2Σ + 1/2 transitions are obtained, including the transition dipole moments, Franck-Condon factors and radiative lifetimes.

The low-lying electronic states of BeI: Accounting for spin–orbit effects on the energetic profile characterization and molecular properties

All electronic states correlating with the two lowest Λ+S and the four lowest Ω dissociation channels of BeI are characterized at the CASSCF/MRCI level of theory with quintuple-zeta basis sets. Spin–orbit interactions modify significantly the potential energy curves in regions of curve crossings and avoided crossings, and explain the scarcity of spectroscopic data. Trends in energetic and molecular properties are discussed for BeF, BeCl, BeBr, and BeI. For the A1 1/2(II)–X 1/2(I) and A2 3/2(I)–X 1/2(I) band systems, transition moments, transition probabilities, and Franck–Condon factors were computed; radiative and tunneling lifetimes completed the characterization of these states.

Molecular structure and spectra of titanium and vanadium trifluorides: Complete basis set CCSD(T) study

Quantum chemical study on TiF3 and VF3 molecules was carried out using the CCSD(T) coupled cluster method using the triple-, quadruple-, and quintuple-zeta basis set and an extrapolation to the complete basis set limit. The methods of multireference configuration interaction MRCISD+Q and perturbation theory MCQDPT2 were used also. The symmetry of the ground electronic state was determined: 2 A′1 and 3 E″ in TiF3 and VF3, respectively. The adiabatic excitation energies were evaluated: AEE(TiF3, \(\tilde A^2 E'' \leftarrow \tilde X^2 A'_1 \)) = 5000 cm−1, AEE(VF3, \(\tilde A^3 A'_2 \leftarrow \tilde X^3 E''\)) = 1000 cm−1. The Jahn-Teller effect in \(\tilde A^2 E''\) state of TiF3 and \(\tilde X^3 E''\) state of VF3 was investigated. The computed Jahn-Teller stabilization energy D 3h → C 2v amounts to 555 and 292 cm−1, respectively. The spin-orbit coupling effect on the VF3 molecular structure and spectrum of electronic states is shown to be quite significant. The calculated vibrational frequencies of TiF3 are in excellent agreement with IR spectroscopy data. The atomization enthalpies were evaluated: Δat H 298 pO = 430 kcal/mol (TiF3), 393 kcal/mol (VF3).

A theoretical contribution to the characterization of the low-lying electronic states of BeBr including spin–orbit effects

Electronic states of BeBr correlating with the first two dissociation channels are investigated at a high level of electronic structure theory (CASSCF/MRCI) along with quintuple-zeta quality basis sets. Very reliable potential energy curves are constructed and regions of both avoided and curve crossings that greatly resemble the ones for BeCl are identified. For both the ground state (X 2Σ+) and the first excited one (A 2Π), this study corroborates the present still limited experimental knowledge about this system and significantly extends its spectroscopic characterization. For the three doublets in the interval between 30000 and 40000cm−1, the inclusion of spin–orbit effects neatly accounts for the interactions between the relativistic states. For the A−X band system, transition moments were evaluated and transition probabilities, as expressed by the Einstein emission coefficients, computed; radiative lifetimes completed the characterization of the A state. The C 2Σ+ state was found to have two minima in the Λ+S representation, the first one with just one vibrational level; this shallow potential then disappears when perturbations by the B 2Π and the a 4Σ+ states are taken into account.

The low-lying electronic states of BeCl: Potential energy curves, transition moments, transition probabilities, and radiative lifetimes

High-level CASSCF/MRCI calculations with a quintuple-zeta quality basis set are reported characterizing a manifold of electronic states of the BeCl correlating with the two lowest-lying dissociation channels. A very reliable picture of the potential energy curves showing regions of both avoided and curve crossings over a wide range of internuclear distances and the associated spectroscopic parameters provide new data that can help better rationalize the transitions so far observed. Our calculations suggest that the assignments and data for the band system C 2Σ+−X 2Σ+ warrant new experimental studies. In fact we show that the C 2Σ+ state (B 2Σ+ in the experimental paper) has a double minimum. Also spin–orbit effects on the A 2Π state are shown to be relatively small. For the first time, transition moment functions for the major transitions are reported in the literature and used to estimate transition probabilities and radiative lifetimes.

Accuracy of basis-set extrapolation schemes for DFT-RPA correlation energies in molecular calculations

We construct a reference benchmark set for atomic and molecular random phase approximation (RPA) correlation energies in a density functional theory framework at the complete basis-set limit. This set is used to evaluate the accuracy of some popular extrapolation schemes for RPA all-electron molecular calculations. The results indicate that for absolute energies, accurate results, clearly outperforming raw data, are achievable with two-point extrapolation schemes based on quintuple- and sextuple-zeta basis sets. Moreover, we show that results in good agreement with the benchmark can also be obtained by using a semiempirical extrapolation procedure based on quadruple- and quintuple-zeta basis sets. Finally, we analyze the performance of different extrapolation schemes for atomization energies.

Structure and spectra of the molecules of manganese, iron, and cobalt trifluorides: A CCSD(T) study in the complete basis set

The coupled-cluster singles and doubles with perturbative triples (CCSD(T)) method in triple-, quadruple-, and quintuple-zeta basis sets with extrapolation to the complete basis set limit is used to analyze the properties of MnF3, FeF3, and CoF3 molecules. The relative energies of low-lying electronic states are determined. The Jahn-Teller effect is investigated in the ground electronic state 5 E′ of the MnF3 molecule and the first excited electronic state 5 E″ of the CoF3 molecule. Geometric parameters, atomization enthalpies, vibrational frequencies, intensities in the infrared and Raman spectra are found with high accuracy. The assignment of the bands observed in the low-frequency region of the IR and Raman spectra of MnF3 and CoF3 molecules are revised.

Theoretical investigation of the He–I2(E3Πg) ion-pair state: Ab initio intermolecular potential and vibrational levels

We present a theoretical study on the potential energy surface and vibrational bound states of the E electronic excited state of the HeI(2) van der Waals system. The interaction energies are computed using accurate ab initio methods and large basis sets. Relativistic small-core effective core potentials in conjunction with a quintuple-zeta quality basis set are employed for the heavy iodine atoms in multireference configuration interaction calculations for the (3)A' and (3)A" states. For the representation of the potential energy surface we used a general interpolation technique for constructing potential surfaces from ab initio data based on the reproducing kernel Hilbert space method. The surface presents global and local minima for T-shaped configurations with well-depths of 33.2 and 4.6 cm(-1), respectively. Vibrational energies and states are computed through variational quantum mechanical calculations. We found that the binding energy of the HeI(2)(E) T-shaped isomer is 16.85 cm(-1), in excellent agreement with recent experimental measurements. In lieu of more experimental data we also report our predictions on higher vibrational levels and we analyze the influence of the underlying surface on them. This is the first attempt to represent the potential surface of such a highly excited electronic state of a van der Waals complex, and it demonstrates the capability of the ab initio technology to provide accurate results for carrying out reliable studies to model experimental data.

Ab initio study of scandium fluoride molecules: ScF, ScF2, AND ScF3

Equilibrium geometric parameters, normal mode frequencies and intensities in IR spectra, atomization enthalpy, and relative energies of low-lying electronic states of scandium fluoride molecules (ScF, ScF2, and ScF3) are calculated by the coupled-cluster method (CCSD(T)) in triple-, quadruple, and quintuple-zeta basis sets with the subsequent extrapolation of the calculation results to the complete basis set limit. The ScF molecule is also studied by the CCSDT technique. The error in the approximate calculation of triple excitations in the CCSD(T) method does not exceed 0.002 A for the equilibrium internuclear distance Re, 4 cm−1 for the vibrational frequency, and 0.2 kcal/mol for the dissociation energy of the molecule. In the ground electronic state \(\tilde X^2 \)A1(C2ν) of ScF2 molecules, Re(Sc-F) = 1.827 A and αe(F-Sc-F) = 124.2°; the energy barrier to bending (linearization) h = Emin(Dg8h) − Emin(C2ν) = 1652 cm−1. The relative energies of A2Δg and \(\tilde B^2 \)Πg electronic states are 3522 cm−1 and 14633 cm−1 respectively. The bond distance in the ScF3 molecule (\(\tilde X^1 \)A′1, D3h) is refined: Re(Sc-F) = 1.842 A. The atomization enthalpies ΔatH2980 of ScFk molecules are 139.9 kcal/mol, 289.0 kcal/mol, and 444.8 kcal/mol for k = 1, 2, 3 respectively.

A theoretical contribution characterizing a potentially new molecular species: MgAs

A new molecular species, MgAs, is investigated theoretically for the first time at the CASSCF/MRCI level using quintuple-zeta quality basis sets. Potential energy curves for the lowest-lying electronic states are presented as well as the associated spectroscopic constants. Dipole and transition moment functions for selected states complement this characterization. Estimates of transition probabilities and radiative lifetimes for the most important transitions are also reported. The effect of spin–orbit interactions is clearly reflected on the potential energy curves. Comparisons with BeAs, BeN, and BeP are made where pertinent.

Density functional study of multiplicity-changing valence and Rydberg excitations of p-block elements: Delta self-consistent field, collinear spin-flip time-dependent density functional theory (DFT), and conventional time-dependent DFT

A database containing 17 multiplicity-changing valence and Rydberg excitation energies of p-block elements is used to test the performance of density functional theory (DFT) with approximate density functionals for calculating relative energies of spin states. We consider only systems where both the low-spin and high-spin state are well described by a single Slater determinant, thereby avoiding complications due to broken-symmetry solutions. Because the excitations studied involve a spin change, they require a balanced treatment of exchange and correlation, thus providing a hard test for approximate density functionals. We test three formalisms for predicting the multiplicity-changing transition energies. First is the ΔSCF method; we also test time-dependent density functional theory (TDDFT), both in its conventional form starting from the low-spin state and in its collinear spin-flip form starting from the high-spin state. Very diffuse basis functions are needed to give a qualitatively correct description of the Rydberg excitations. The scalar relativistic effect needs to be considered when quantitative results are desired, and we include it in the comparisons. With the ΔSCF method, most of the tested functionals give mean unsigned errors (MUEs) larger than 6 kcal/mol for valence excitations and MUEs larger than 3 kcal/mol for Rydberg excitations, but the performance for the Rydberg states is much better than can be obtained with time-dependent DFT. It is surprising to see that the long-range corrected functionals, which have 100% Hartree-Fock exchange at large inter-electronic distance, do not improve the performance for Rydberg excitations. Among all tested density functionals, ΔSCF calculations with the O3LYP, M08-HX, and OLYP functionals give the best overall performance for both valence and Rydberg excitations, with MUEs of 2.1, 2.6, and 2.7 kcal/mol, respectively. This is very encouraging since the MUE of the CCSD(T) coupled cluster method with quintuple zeta basis sets is 2.0 kcal/mol; however, caution is advised since many popular density functionals give poor results, and there can be very significant differences between the ΔSCF predictions and those from TDDFT.

A global ab initio potential energy surface for HNO (a3A″) and quantum mechanical studies of vibrational states and reaction dynamics

A new global potential energy surface for the lowest triplet electronic state (a(3)A") of HNO has been developed by a three-dimensional cubic spline interpolation of more than 13,000 ab initio points, which were calculated at the multireference configuration interaction level with Davidson correction using the augmented correlation-consistent polarized valence quintuple zeta basis set. Two minima and five saddle points were found on the potential energy surface. Low-lying vibrational states were obtained in this new potential using the Lanczos method and assigned. In addition, thermal rate constants for the N + OH → H + NO reactions were obtained using an exact wave packet method. Reasonably good agreement with experimental data was obtained.

Theoretical study of the low-lying electronic states of the CN 2+ dication

Ab initio computations are performed using multi-reference configuration interaction technique and augmented quintuple-zeta basis set to investigate the low-lying electronic states of the CN 2+ dication. The electronic ground state of this dication appears to be of X 4Σ − nature and possesses a potential well of about 0.85 eV. Several excited states of this doubly charged molecule also depict such potential wells. The rotational and vibrational spectroscopic constants of these bound metastable states have been computed. The adiabatic double ionization energy of CN was deduced at 37.5 eV from the potential energy curves of the electronic ground states of the CN and CN 2+ species. The double ionization spectra of CN was also simulated by the computations of the Franck–Condon factors.

The electronic states of SeF: A reinterpretation of the chemiluminescent emission of the reaction of selenium with fluorine

The low-lying doublet and quartet electronic states of the species SeF correlating with the first dissociation channel are investigated theoretically at a high-level of electronic correlation treatment, namely, the complete active space self-consistent field/multireference single and double excitations configuration interaction (CASSCF/MRSDCI) using a quintuple-zeta quality basis set including a relativistic effective core potential for the selenium atom. Potential energy curves for (Lambda+S) states and the corresponding spectroscopic properties are derived that allows for an unambiguous assignment of the only spectrum known experimentally as due to a spin-forbidden X (2)Pi-a (4) summation (-) transition, and not a A (2)Pi-X (2)Pi transition as assumed so far. For the bound excited doublets, yet unknown experimentally, this study is the first theoretical characterization of their spectroscopic properties. Also the spin-orbit coupling constant function for the X (2)Pi state is derived as well as the spin-orbit coupling matrix element between the X (2)Pi and a (4) summation (-) states. Dipole moment functions and vibrationally averaged dipole moments show SeF to be a very polar species. An overview of the lowest-lying spin-orbit (Omega) states completes this description.