Spectroscopic constants and molecular properties of CN−, SiH−, PO−, SO−, SF−, and SiS−: Density functional study

Spectroscopic constants and molecular properties of selected diatomic anions namely CN^?, SiH^?, PO^?, SO^?, SF^?, and SiS^? in their ground states have been studied in detail using the hybrid HF/DF B3LYP method. The consistency of the calculated values has been verified with four different basis sets, with improved quality. The spectroscopic constants and molecular properties calculated with the aug‐cc‐pVTZ basis set agree very well with the experimental and theoretical values wherever available. Most of the spectroscopic constants and molecular properties of the selected diatomic anions, particularly the spectroscopic constants and molecular properties of SO^? and SiS^? are reported for the first time. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Accurate ab intio determination of binding energies for rare-gas dimers by basis set extrapolation

To investigate the electron correlation effect on the binding energies of very weakly bound complexes at highly correlated levels, an extrapolation scheme exploiting the convergent behavior of the binding energy differences between two correlation levels with the correlation-consistent basis set aug-cc-pVXZ was explored. The scheme is based on extrapolating the binding energy differences between the lower and higher correlation levels (such as second-order Møller–Plesset perturbation theory and the single and double coupled-cluster method with perturbative triple correction level), CCSD(T), by X^–3 for relatively small basis set calculations to estimate the corresponding basis set limit, which is then added to the complete basis set(CBS) limit binding energy at the lower correlation level to derive the CBS limit binding energy at the higher level. Test results on rare-gas dimers Rg₂ (Rg is He, Ne, Ar) show that the CCSD(T) CBS limit binding energies estimated by this scheme with aug-cc-pVXZ and aug-cc-pV(X+1)Z basis sets are more accurate than the CBS limit estimated by direct extrapolation of correlation energies by X^–3 with aug-cc-pV(X+1)Z and aug-cc-pV(X+2)Z basis sets in most cases, which signifies the utility of the proposed extrapolation scheme as the level of electron correlation treatment increases. The nonnegligible discrepancy in the well depth near equilibrium between the experimental and the full connected single, double, and triple coupled-cluster method CBS limit estimate obtained by this procedure in the case of Ar₂ suggests that the previous semiempirical potential may be too attractive near equilibrium compared with the actual one.Acknowledgement The major portion of this work was carried out while the author was visiting the Quantum Theory Project (QTP) at the University of Florida. The author is thankful to Rodney Bartlett for hospitality and support during the visit. The author is also thankful to Ajith Perera for assistance in using the ACESII program package. Computational support from the QTP at the University of Florida and the Institute for Basic Science at Ajou University is gratefully acknowledged.     

Accurate spectroscopic constants of the lowest three electronic states in halonitrenes with multireference configuration interaction

Internally contracted multireference configuration interaction (icMRCI) calculations of the ground state (X³Σ⁻), the first excited state (a¹Δ) as well as the second excited state (b¹Σ⁺) have been performed for a series of halogenated nitrenes NXs (X = Cl, Br, and I). Accurate spectroscopic constants of these lowest three electronic states of each NX were obtained in this work using MRCI methods with aug‐cc‐pVXZ (X = T, Q, 5) basis sets and complete basis set (CBS) limit. In addition, various corrections, including the Davidson correction, scalar relativistic effect, core‐valence correlation, and spin‐orbit coupling effect, have been studied in calculating spectroscopic constants, especially for heavy‐atom nitrenes. Comparisons have been made with previous computational and experimental results where available. The icMRCI + Q calculations presented in this work provide a comprehensive series of results at a consistent high level of theory for all of the halogenated nitrenes.     

Lowest electronic states of neutral and ionic LiN

We have investigated the potential energy curves (PECs) of the LiN heteronuclear diatomic molecule, including its ionic species LiN⁺ and LiN⁻, using explicitly correlated multi-reference configuration interaction (MRCI-F12) calculations in conjunction with the correlation consistent quintuple-𝜁 basis set. The effect of core–valence correlation, scalar relativistic effects, and the size of the basis sets has been investigated. A comprehensive set of spectroscopic constants determined based on the above-mentioned calculations are also reported for the lowest electronic states and all systems, including dissociation energies, harmonic and anharmonic vibrational frequencies, and rotational constants. Additional parameters, such as the dipole moments, equilibrium spin-orbit constants, excitation energies, and rovibrational energy levels, are also documented. We found that the three triplet states of LiN, namely, X ³∑⁻, A ³Π, and 2 ³∑⁻, exhibit substantial potential wells in the PEC diagrams, while the quintet states are repulsive in nature. The ground state of the anion also shows a deep potential well in the vicinity of its equilibrium geometry. In contrast, the ground and excited states of the cation are very loosely bound. Charge transfer properties of each of these states are also analyzed to obtain an in-depth understanding of the interatomic interactions. We found that the core–valence correlation has a substantial effect on the calculated spectroscopic constants.     

Phosphorus mononitride: A difficult case for theory

Phosphorus nitride (PN) is the simplest molecule formed solely by phosphorus and nitrogen. It represents an interesting model for materials, where phosphorus is directly attached to nitrogen. Nevertheless, both theoretical and experimental studies often provide an incomplete picture on the structural, electronic, and spectral properties of PN. Theoretical predictions often suffer from insufficient level of theory, incomplete basis set, or from neglecting several effects, for example, zero-point vibrational correction (ZPVC). Therefore, we performed an extensive benchmark study on structural, electronic, and spectral properties of PN at the Hartree-Fock, density functional theory (DFT), or even the coupled-cluster levels. We paid special attention to the basis set effect. We tested three variants of Dunning's aug-cc-pVXZ basis sets with the size from double-ζ to sextuple-ζ, as well as Jensen's aug-pc-n, aug-pcJ-n, and aug-pcSseg-n basis sets, where n = 1-4. Obtained energetics, PN distance, dipole moment, vibrational frequencies, and nuclear magnetic resonance (NMR) parameters were extrapolated to the complete basis set limit (CBS) using three- or two-parameter formulas. The ³¹P NMR shieldings estimated with the aug-cc-pVXZ and aug-cc-pV(X + d)Z basis sets strongly depend on the basis set size providing scattered convergence patterns toward CBS. The Hartree-Fock self-consistent field (HF-SCF) NMR parameters evinced similar behavior as the coupled-cluster data. The only smooth convergence was achieved using the aug-cc-pCVXZ basis sets that include core-valence effects. The KT3 functional underestimated the phosphorus CBS shieldings by about 12 ppm compared to coupled cluster with singles and doubles (CCSD) (T). Nevertheless, KT3 unambiguously surpasses the HF-SCF and CCSD levels that provide ³¹P shieldings that are lower by about 150 ppm and 24 ppm compared to CCSD(T). The convergence of nitrogen shieldings was regular for all basis set hierarchies and all theoretical methods. Relativistic and vibrational effects on selected properties were also discussed.     

Calibration study of the CCSD(T)-F12a/b methods for C2 and small hydrocarbons

Explicitly correlated CCSD(T)-F12a/b methods combined with basis sets specifically designed for this technique have been tested for their ability to reproduce standard CCSD(T) benchmark data covering 16 small molecules composed of hydrogen and carbon. The standard method calibration set was obtained with very large one-particle basis sets, including some aug-cc-pV7Z and aug-cc-pV8Z results. Whenever possible, the molecular properties (atomization energies, structures, and harmonic frequencies) were extrapolated to the complete basis set limit in order to facilitate a direct comparison of the standard and explicitly correlated approaches without ambiguities arising from the use of different basis sets. With basis sets of triple-ζ quality or better, the F12a variant was found to overshoot the presumed basis set limit, while the F12b method converged rapidly and uniformly. Extrapolation of F12b energies to the basis set limit was found to be very effective at reproducing the best standard method atomization energies. Even extrapolations based on the small cc-pVDZ-F12/cc-pVTZ-F12 combination proved capable of a mean absolute deviation of 0.20 kcal/mol. The accuracy and simultaneous cost savings of the F12b approach are such that it should enable high quality property calculations to be performed on chemical systems that are too large for standard CCSD(T).     

The HOX⋯SO2 (X=F,Cl, Br,I) Binary Complexes: Implications for Atmospheric Chemistry

Sulfur dioxide and hypohalous acids (HOX, X=F, Cl, Br, I) are ubiquitous molecules in the atmosphere that are central to important processes like seasonal ozone depletion, acid rain, and cloud nucleation. We present the first theoretical examination of the HOX⋯SO₂ binary complexes and the associated trends due to halogen substitution. Reliable geometries were optimized at the CCSD(T)/aug-cc-pV(T+d)Z level of theory for HOF and HOCl complexes. The HOBr and HOI complexes were optimized at the CCSD(T)/aug-cc-pV(D+d)Z level of theory with the exception of the Br and I atoms which were modeled with an aug-cc-pwCVDZ-PP pseudopotential. 27 HOX⋯SO₂ complexes were characterized and the focal point method was employed to produce CCSDT(Q)/CBS interaction energies. Natural Bond Orbital analysis and Symmetry Adapted Perturbation Theory were used to classify the nature of each principle interaction. The interaction energies of all HOX⋯SO₂ complexes in this study ranged from 1.35 to 3.81 kcal mol⁻¹. The single-interaction hydrogen bonded complexes spanned a range of 2.62 to 3.07 kcal mol⁻¹, while the single-interaction halogen bonded complexes were far more sensitive to halogen substitution ranging from 1.35 to 3.06 kcal mol⁻¹, indicating that the two types of interactions are extremely competitive for heavier halogens. Our results provide insight into the interactions between HOX and SO₂ which may guide further research of related systems.     

Comment on: “Estimating the Hartree–Fock limit from finite basis set calculations” [Jensen F (2005) Theor Chem Acc 113:267]

We demonstrate that a minor modification of the extrapolation proposed by Jensen [(2005): Theor Chem Acc 113: 267] yields very reliable estimates of the Hartree–Fock limit in conjunction with correlation consistent basis sets. Specifically, a two-point extrapolation of the form yields HF limits E _HF,∞ with an RMS error of 0.1 millihartree using aug-cc-pVQZ and aug-cc-pV5Z basis sets, and of 0.01 millihartree using aug-cc-pV5Z and aug-cc-pV6Z basis sets.     

High-resolution infrared analysis of seven fundamental bands of gaseous isothiazole between 750 and 1500 cm−1

The gas phase IR spectrum of isothiazole, C₃H₃NS, between 550 and 1700 cm⁻¹ was recorded with a resolution of ca. 0.003 cm⁻¹. The rotational structure of seven fundamental bands in the region 750–1500 cm⁻¹ has been assigned and analysed by the Watson Hamiltonian model. A number of local resonances in the bands have been identified and explained qualitatively in terms of Coriolis interactions. For each band upper state spectroscopic constants, including band center, rotational constants, and quartic centrifugal distortion constants are given. From observed crossings due to resonances we locate the weak bands ν₉(A′) and ν₁₃(A′) at 1041.9(2) and 642.0(3) cm⁻¹, respectively. The anharmonic frequencies have been determined using a cc-pVTZ basis set, at the MP2 and B3LYP levels; the two theoretical methods give very similar results for rotational constants, anharmonic band center frequencies and distortion constants, and many of these are in good agreement with experiment.     

Theoretical study of spectroscopic constants and molecular properties of diatomic anions using B3LYP method

Structure, spectroscopic constants and molecular properties of selected diatomic anions in their ground states have been studied in detail using HF/DF B3LYP method. The consistency of the calculated values of spectroscopic constants and molecular properties has been tested using four basis sets with improved quality. The spectroscopic constants and molecular properties of these diatomic ions agree well with the experimental and theoretical values wherever available. Most of the spectroscopic constants and molecular properties of these ions, in particular the spectroscopic constants of SiO⁻, CS⁻ and the molecular properties of SiN⁻, CP⁻, SiO⁻ are first reported.     

Quantum dynamics of vibrationally activated OH-CO reactant complexes

The MP2 complete basis set (CBS) limit for the binding energy of the two low-lying water octamer isomers of D2d and S4 symmetry is estimated at -72.7+/-0.4 kcal/mol using the family of augmented correlation-consistent orbital basis sets of double through quintuple zeta quality. The largest MP2 calculation with the augmented quintuple zeta (aug-cc-pV5Z) basis set produced binding energies of -73.70 (D2d) and -73.67 kcal/mol (S4). The effects of higher correlation, computed at the CCSD(T) level of theory, are estimated at <0.1 kcal/mol. The newly established MP2/CBS limit for the water octamer is reproduced quite accurately by the newly developed all atom polarizable, flexible interaction potential (TTM2-F). The TTM2-F binding energies of -73.21 (D2d) and -73.24 kcal/mol (S4) for the two isomers are just 0.5 kcal/mol (or 0.7%) larger than the MP2/CBS limit.     

Anion Cryptates: Synthesis,Crystal Structures,and Complexation Constants of Fluoride and Chloride Inclusion Complexes of Polyammonium Macrobicyclic Ligands

Three macrobicyclic octamines 1–3 and the macrotricyclic hexadecamine 14 have been synthesized. The octamines 1–3 bind anionic substrates when protonated. The stability constants of the complexes between the protonated forms of the macrobicyclic polyamines and halide anions have been determined by pH-metric measurements. The stability constants in H₂O are very high; 1 in its hexaprotonated form binds F⁻ with high selectivity (selectivity F⁻/Cl⁻ > 10⁸), while 3 exhibits strong stability constants for both F⁻ and Cl⁻. Three X-ray structures have been obtained, one where F⁻ is held inside the cavity of 1 · 6H⁺, one where Cl⁻ is included in 3 · 6H⁺, and 3 · 6H⁺ where the cavity is empty.     

Optimal diffuse augmented atomic basis sets for extrapolation of the correlation energy

We seek correlation-consistent diffuse-augmented double-zeta and triple-zeta basis sets that perform optimally in extrapolating the correlation energy to the one-electron complete basis set limit, denoted oAVXZ and oAV(X + d)Z. The novel basis sets are method-dependent in that they are trained to perform optimally for the correlation energy at each specific level of theory. They are shown to yield accurate results in calculating both the energy and tensorial properties such as polarizabilities while not significantly altering the Hartree-Fock energy. Quantitatively, complete basis set limit (CBS)-/(oAVdZ,oAVtZ)-extrapolated correlation energies typically outperform, by 3- to 5-fold, the ones calculated with traditional ansatzes of similar flexibility. Attaining energies of CBS/(AVtZ,AVqZ) type or better accuracy, they frequently outperform expensive raw explicitly correlated ones. Promisingly, a limited test on CBS-extrapolated energies based on conventional basis sets has shown that they compare well even with extrapolated explicitly correlated ones. Calculated atomization and dissociation energies, molecular geometries, ionization potentials, and electron affinities also tend to outperform the ones obtained with traditional Dunning's ansatzes from which the new basis sets have been determined. The method for basis set generation is simple, and there is no reason of principle why the approach could not be adapted for handling other bases in the literature.     

Structures and heats of formation of the neutral and ionic PNO, NOP, and NPO systems from electronic structure calculations

High level ab initio electronic structure calculations using the coupled cluster CCSD(T) method with augmented correlation-consistent basis sets extrapolated to the complete basis set limit have been performed on the PNO, NOP, and NPO isomers and their corresponding anions and cations. Geometries for all species were optimized up through the aug-cc-pV(Q+d)Z level and vibrational frequencies were calculated with the aug-cc-pV(T+d)Z basis set. The most stable of the three isomers is NPO and it is predicted to have a heat of formation of 23.3 kcal/mol. PNO is predicted to be only 1.7 kcal/mol higher in energy. The calculated adiabatic ionization potential of NPO is 12.07 eV and the calculated adiabatic electron affinity is 2.34 eV. The calculated adiabatic ionization potential of PNO is 10.27 eV and the calculated adiabatic electron affinity is only 0.24 eV. NOP is predicted to be much higher in energy by 29.9 kcal/mol. The calculated rotational constants for PNO and NPO should allow for these species to be spectroscopically distinguished. The adiabatic bond dissociation energies for the P[Single Bond]N, P[Single Bond]O, and N[Single Bond]O bonds in NPO and PNO are the same within approximately 10 kcal/mol and fall in the range of 72-83 kcal/mol.     

Theoretical study of spectroscopic and molecular properties of several low‐lying electronic states of CO molecule

The potential energy curves (PECs) of eight low‐lying electronic states (X¹Σ⁺, a³Π, a′³Σ⁺, d³Δ, e³Σ^?, A¹Π, I¹Σ^?, and D¹Δ) of the carbon monoxide molecule have been studied by an ab initio quantum chemical method. The calculations have been performed using the complete active space self‐consistent field method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with the correlation‐consistent aug‐cc‐pV5Z basis set. The effects on the PECs by the core‐valence correlation and relativistic corrections are included. The way to consider the relativistic corrections is to use the third‐order Douglas–Kroll Hamiltonian approximation at the level of a cc‐pV5Z basis set. Core‐valence correlation corrections are performed using the cc‐pCVQZ basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are corrected for size‐extensivity errors by means of the Davidson modification (MRCI+Q). The spectroscopic parameters (D_e, T_e, R_e, ω_e, ω_ex_e, ω_ey_e, B_e, α_e, and γ_e) of these electronic states are calculated using these PECs. The spectroscopic parameters are compared with those reported in the literature. Using the Breit–Pauli operator, the spin–orbit coupling effect on the spectroscopic parameters is discussed for the a³Π electronic state. With the PECs obtained by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations, the complete vibrational states of each electronic state have been determined. The vibrational manifolds have been calculated for each vibrational state of each electronic state. The vibrational level G(ν), inertial rotation constant B_ν, and centrifugal distortion constant D_ν of the first 20 vibrational states when the rotational quantum number J equals zero are reported and compared with the experimental data. Comparison with the measurements demonstrates that the present spectroscopic parameters and molecular constants determined by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations are both reliable and accurate. © 2012 Wiley Periodicals, Inc.     

Accurate analytic potential energy function and spectroscopic study for CH(XΠ) radical using coupled-cluster theory in combination with the correlation-consistent quintuple basis set

The coupled-cluster singles-doubles-approximate-triples [CCSD(T)] theory in combination with the correlation-consistent quintuple basis set (aug-cc-pV5Z) is used to investigate the spectroscopic properties of the CH(X²Π) radical. The accurate adiabatic potential energy curve is calculated over the internuclear separation ranging from 0.07 to 2.45 nm and is fitted to the analytic Murrell–Sorbie function, which is employed to determine the spectroscopic parameters, ω_eχ_e, α_e and B_e. The present D_e, R_e, ω_e, ω_eχ_e, α_e and B_e values are of 3.6261 eV, 0.11199 nm, 2856.312 cm⁻¹, 64.9321 cm⁻¹, 0.5452 cm⁻¹ and 14.457 cm⁻¹, respectively. Excellent agreement is obtained when they are compared with the available measurements. With the potential obtained at the CCSD(T)/aug-cc-pV5Z level of theory, a total of 18 vibrational states is predicted when J = 0 by numerically solving the radial Schrödinger equation of nuclear motion. The complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are reproduced for the CH(X²Π) radical when J = 0 for the first time, which are in good agreement with the available RKR data.     

Coupled cluster,B2PLYP and M06-2X investigation of the thermochemistry of five-membered nitrogen containing heterocycles,furan, and thiophene

Herein, the thermochemical properties of five-membered rings heterocycles were studied employing the CCSD(T) methodology coupled with the correlation consistent basis sets and including corrections for relativistic and core-valence effects as well as anharmonicities of the potentials. For pyrrole, furan, imidazole, pyrazole, 1H-1,2,4-triazole, and 1H-tetrazole, the mean absolute deviation (MAD) of the \Updelta \textH_{\textf, 2 9 8}^\texto \Updelta {\text{H}}_{{{\text{f}}, 2 9 8}}^{\text{o}} , computed at the CCSD(T) level, is 0.5 kcal/mol with respect to the experimental values. In the case of 1H-1,2,3-triazole, 2H-1,2,3-triazole, 4H-1,2,3-triazole, 4H-1,2,4-triazole, 2H-tetrazole, and pentazole, we propose the following \Updelta \textH_{\textf, 2 9 8}^\texto \Updelta {\text{H}}_{{{\text{f}}, 2 9 8}}^{\text{o}} : 62.6, 59.2, 85.0, 54.2, 77.7, and 107.5 kcal/mol, respectively. For thiophene, we revisit our previous result and propose a value of 26.0 kcal/mol. The theoretical estimations were used to study the performance of the M06-2X and B2PLYP functionals. Also, the convergence toward the complete basis set limit (CBS) was analyzed. M06-2X did not show a smooth convergence toward the CBS limit. Particularly, for the cc-pVTZ and cc-pVQZ basis sets, some problems were detected. Yet, along the cc-pVQZ, cc-pV5Z, and cc-pV6Z basis sets, the TAE smoothly decreased. The diminution of the TAE upon increase in basis set was not expected because the opposite behavior is more frequently observed. The MAD of the total atomization energies determined at the M06-2X level was 0.42 kcal/mol, with respect to the CCSD(T) results. In the case of the double hybrid B2PLYP functional, a smooth convergence toward the CBS limit was detected, even though the performance seriously degradated when the basis set was increased. At the CBS limit, the MAD with respect to the CCSD(T) TAEs was 8.26 kcal/mol.     

Quantum chemical calculations of geometries and gas‐phase deprotonation energies of linear polyyne chains

The molecular geometries of polyyne chains H(CC)_nH with their deprotonated forms (anions) have been optimized using ab initio LCAO‐SCF molecular orbital (MO) method and density functional theory at different basis set levels. The polyynes possess a series of alternating single and triple bonds. On the theoretical side the persistence of bond alternation and the effect of chain lengthening on the individual bond length in linear conjugated polyyne chains has been investigated. The common conclusion has been drawn that the bond alternation will persist and that bond length variation will be small. The triple bond length increases progressively toward the asymptotic limits as the value of n increases progressively. If the split‐valence basis set was employed, the total charges obtained using the Mulliken population analysis yielded unrealistic values. Using natural bond orbital (NBO) analysis or Bader's analysis, the net charges of the individual atoms converge very rapidly to their asymptotic limits, and the central atoms have almost zero charges in contrast to the Mulliken population analysis results. The reliability of deprotonation energies of neutral polyynes and their monoanionic derivatives calculated from the differences in molecular energy of the parent chains and the corresponding anions E(H(CC)_n⁻)–E(H(CC)_nH) and E(⁻(CC)_n⁻)–E(H(CC)_n⁻) was tested for different basis sets. The increase of the number of CC bonds in the chain decreases these differences asymptotically. The studied compounds are the best available building blocks in bimetallic compounds with useful properties in molecular electronics and nonlinear optics. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 73–85, 2001     

Can halogen bond energy be reliably estimated from electron density properties at bond critical point? The case of the (A)nZ—Y•••X− (X,Y = F,Cl, Br) interactions

Relationships between the Y•••X bond critical point (BCP) properties or the Y•••X distance and the halogen bond interaction energy were analyzed in detail by theoretical methods for the series of structures [(A)_nZ—Y•••X]⁻ (X,Y = F, Cl, Br; totally 441 structures). No relationship was found for the whole set of structures or for the series [(A)_nZ—F•••X]⁻, [(A)_nZ—Cl•••X]⁻, and [(A)_nZ—Br•••X]⁻. The interaction energies may be roughly estimated from the BCP properties for the series [(A)_nZ—Y•••F]⁻, [(A)_nZ—Y•••Cl]⁻, and [(A)_nZ—Y•••Br]⁻ as well as for [(A)_nZ—Y•••X]⁻ (when (A)_nZ is variable, X and Y are constant) with the mean absolute deviation values 2.04-4.38 kcal/mol. The corresponding recommended relationships are provided and they are significantly different from the popular dependencies deduced previously for other types of noncovalent interactions. Tremendous effect of the computational method and basis set on the relationships under analysis was discovered. Computational results clearly indicate that, for practical purposes, the E_int(BCP property) dependencies should be established not simply for each global type of interactions (hydrogen bond, halogen bond, chalcogen bond, etc.) but for each combination of the first and second order atoms taking into account also the computational method and basis set.