This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Møller–Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.

The first total synthesis of roquefortine C is achieved by implementation of a novel elimination strategy to construct the thermodynamically unstable E-dehydrohistidine moiety. Molecular modeling studies are presented which explain the instability of the roquefortine C structure compared to that of isoroquefortine C.

Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.

The structures and energies of axial and equatorial conformers and rotamers of 4-substituted tetrahydro-2H-thiopyran-1,1-dioxides (tetrahydrothiopyran-1,1-dioxides, thiacyclohexane-1,1-dioxides, thiane-1,1-dioxides, and 1,1-dioxothianes; CH3, CH2OH, CHO, COCH3, CN, F, Cl, Br, and OCOCH3) were calculated using the hybrid density functionals B3LYP, B3P86, and B3PW91, as well as MP2 and the 6-31G(d), 6-31G(2d), 6-31G(3d), 6-31G(d,p), and 6-31+G(d) basis sets. MP2/6-31+G(d)/ /HF/6-31+G(d) [−ΔG° = 1.73 kcal/mol], B3P86/6-31G(d) [−ΔG° = 1.75 kcal/mol], and B3PW91/6-31G(d) [−ΔG° = 1.85 kcal/mol] gave conformational free energy (ΔG°) values at 180 K for 4-methyltetrahydro-2H-thiopyran-1,1-dioxide which were similar to the reported experimental values for methylcyclohexane (−ΔG° = 1.80 kcal/mol), 4-methyltetrahydro-2H-thiopyran (−ΔG° = 1.80 kcal/mol), and other 4-methyl-substituted heterocycles. All levels of theory showed that the conformational preferences of the 4-methanoyl (4-formyl), 4-ethanoyl (4-acetyl), and 4-cyano substituents were small. The HF calculations gave conformational free energy (ΔG°) values for 4-chlorotetrahydro-2H-thiopyran-1,1dioxide which were closer to the experimental value than the MP2 and density functional methods. The best agreement with available experimental data for 4-bromotetrahydro-2H-thiopyran-1,1-dioxide was obtained from the HF/6-31G(2d), HF/6-31G(3d), and B3LYP/6-31G(2d) calculations, and, for 4-acetoxytetrahydro-2H-thiopyran-1,1-dioxide, from the HF/6–31G(3d) calculations. The conformational free energies (ΔG°) and relative energies (ΔE) of the conformers and rotamers have been compared with the correspondingly substituted cyclohexanes and tetrahydro-2H-thiopyrans and are discussed in terms of dipole–dipole (electrostatic) interactions and repulsive nonbonded interactions (steric) in the most stable axial and equatorial conformers. The axial S=O bond lengths are shorter than the equatorial S=O bond lengths and the C2–C3 bond lengths in the substituents with carbon-bonded to the ring are shorter than the C3–C4 and C4–C-5 bond lengths. In contrast, the C2–C3 bond lengths in the 4-halogen and 4-acetoxy substituents are longer than the C3–C4 and C4–C-5 bond lengths.

Ab initio molecular orbital theory with the 6-31G(d), 6-31G(2d), 6-31+G(d), 6-31G(d,p), 6-31+G(d,p), and 6-311G(d,p) basis sets and the hybrid density functionals B3LYP, B3P86, and B3PW91 have been used to calculate the optimized geometries and relative energies of the chair, half-chair, sofa, twist, and boat structures of 2-thiaoxacyclohexane (1,2-oxathiane). The values of the energy difference (ΔE, kcal/mol) between the chair and 3,6-twist structures of 1,2-oxathiane were 4.92 (HF), 4.73 (MP2), and 4.66 (DFT). The HF chair–twist energy difference (ΔGc–to) for 1,2-oxathane was 5.16 kcal/mol. Intrinsic reaction coordinate (IRC) calculations connected a transition state (TS-A) between the chair conformation and the less stable 2,5-twist form and connected two transition states (TS-B, TS-C) between the chair conformation and the more stable 3,6-twist conformer. The DFT energy differences between the chair and TS-A, TS-B, and TS-C were 11.4, 10.8, and 12.6 kcal/mol, respectively. Hyperconjugative stereoelectronic interactions were observed in the chair (no → \(\sigma _{{\text{C}}6 - {\text{H}}_{{\text{ax}}} }^*\) and \(\sigma _{{\text{C}} - {\text{H}}_{{\text{ax}}} } \) → \(\sigma _{{\text{C}} - {\text{H}}_{{\text{ax}}} }^* \)) and 3,6-twist (nS → \(\sigma _{{\text{C3}} - {\text{His}}_{{\text{oa}}} }^* \) and nO → \(\sigma _{{\text{C6}} - {\text{His}}_{{\text{oa}}} }^* \)) conformers of 1,2-oxathiane. The chair conformation of 1,2-oxthiane is 9.6 and 10.0 kcal/mol, respectively, less stable than the chair conformations of 3-thiaoxacyclohexane (1,3-oxathiane) and 4-thiaoxacyclohexane (1,4-oxathiane, thioxane).

Ab initio molecular orbital theory with the 6-31G(d), 6-31+G(d), 6-31G(d,p), 6-311G(d,p), 6-311+G(d,p), 6-31G(2d), 6-311G(2d), and 6-311G(2d,p) basis sets have been used to calculate the conformational enthalpies (ΔH°), entropies (ΔS°), and free energies (ΔG°) of the axial and equatorial conformers of 2-methyl-, 3-methyl-, and 4-methyltetrahydro-2H-pyran (tetrahydropyran, oxacyclohexane, oxane) and methylcyclohexane (toluene). Although HF and MP2 generally gave higher conformational free energies (ΔG°) than the experimentally reported values, other MP2 calculations gave ΔG° values in excellent agreement with experimental results for methylcyclohexane [6-311G(d,p)] and 3-methyltetrahydro-2H-pyran [6-31+G(d), 6-311+G(d,p)]. Consistent with solution studies, the MP2 calculations gave larger ΔG° values for 4-methyltetrahydro-2H-pyran than for methylcyclohexane.

Ab initio theory with the 3-21G, 6-31G(d), 6-31G(d,p), 6-311 G(d,p), 6-31 +G(d), and 6-311 +G(d,p) basis sets and density functional theory (SVWN, pBP, BLYP), including the hybrid density functional methods B3LYP, B3PW91, and B3P86, have been used to calculate the energies of the chair, half-chair, sofa, twist, and boat conformers of tetrahydro-2H-pyran (oxacyclohexane, oxane, pentamethylene oxide, tetrahydropyran, THP). The enthalpies (DeltaH degrees), entropies (DeltaS degrees), and free energies (DeltaG degrees) of the conformers were also determined. The energy difference (DeltaE, kcal/mol) between the chair and the 2,5-twist conformer is 5.92 to 6.10 (HF), 5.78 to 6.10 (MP2), 6.71 to 6.82 (SVWN), 6.04 to 6.12 (pBP), and 5.84 to 5.95 (BLYP, B3LYP, B3PW91, B3P86). The energy difference! (AE, kcal/mol) between the chair and the 1,4-boat conformer is 6.72 to 7.05 (HF), 6.76 to 7.16 (MP2), 6.97 to 7.20 (SVWN), 6.26 to 6.36 (pBP), and 6.23 to 6.46 (BLYP, B3LYP, B3PW91, B3P86). The transition state between the chair conformation and the 2,5-twist conformation is 11 kcal/mol higher in energy than the chair conformer.

Ab initio theory and density functional theory (B3LYP) have been used to calculate the geometry optimized structures, configurational isomer energy differences (Δ E ), and the configurational enthalpies (Δ H 0 ), entropies (Δ S 0 ), and free energies (Δ G 0 ) of 4-alkyl equatorial tetrahydro-2 H -thiopyran-1-oxides (tetrahydrothiopyran-1-oxides, thiacyclohexane-1-oxides, thiane-1-oxides (Me, Et, neo -Pent, i -Pr, tert -Bu) and 4-trimethylsilyl equatorial tetrahydro-2 H -thiopyran-1-oxide. The calculated structural data indicate that repulsive steric interactions between the axial alkyl group and the ring atoms are the major contributors to the equatorial preference. The configurational isomer energy differences (Δ E ), configurational enthalpies (Δ H 0 ) and free energies (Δ G 0 ) of the 4-alkyl equatorial tetrahydro-2 H -thiopyran-1-oxides have been compared with the reported experimental conformational enthalpies (Δ H 0 ) and free energies (Δ G 0 ) of the corresponding alkylcyclohexanes and 4-alkyltetrahydro-2 H -thiopyrans. The use of the configurational isomer energy differences (Δ E ) and/or configurational free energies (Δ G 0 ) of 4-alkyl equatorial tetrahydro-2 H -thiopyran-1-oxides as possible models for assigning the difference in the steric requirements of an alkyl substituent in axial and equatorial positions is also discussed.

Ab initio molecular orbital theory with the 6-31G(d), 6-31+G(d), 6-31G(d,p), and 6-31G(2d) basis sets has been used to calculate the geometry optimized structures and the relative energies (ΔE) of the rotamers of the chair conformers of 3-substituted equatorial tetrahydro-2H-thiopyran-1-oxides (tetrahydrothiopyran-1-oxides, thiacyclohexane-1-oxides, thiane-1-oxides; CH3, CF3, CHO, COCH3, CN, F, Cl, Br). The conformational free energies (ΔG°) and relative energies (ΔE) of the conformers and rotamers are discussed in terms of the repulsive nonbonded interactions in both conformers.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTA Comparison of the ab Initio Calculated and Experimental Conformational Energies of AlkylcyclohexanesMarc L. Kasner , Fillmore Freeman , Zufan M. Tsegai , and Warren J. Hehre View Author Information Department of Chemistry and Biochemistry, Montclair State Univerity, Upper Montclair, NJ 07043 Department of Chemistry, University of California, Irvine, Irvine, CA 92697-2025 Department of Chemistry, University of California, Irvine, Irvine, CA 92697, and Wavefunction, Inc., Irvine CA 92612Cite this: J. Chem. Educ. 2000, 77, 5, 661Publication Date (Web):May 1, 2000Publication History Received3 August 2009Published online1 May 2000Published inissue 1 May 2000https://pubs.acs.org/doi/10.1021/ed077p661https://doi.org/10.1021/ed077p661research-articleACS PublicationsRequest reuse permissionsArticle Views310Altmetric-Citations26LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose SUBJECTS:Energy,Molecular structure Get e-Alerts

Ab initio Hartree–Fock calculations using the 6-31G(d), 6-31G(2d), 6-31G(d,p), 6-311G(d,p), 6-31+G(d), and 6-311+G(d,p) basis sets, second-order Møller–Plesset perturbation theory (MP2) using the same basis sets, and density functional theory [SVWN/DN∗, SVWN/DN∗∗, pBP/DN∗, pBP/DN∗∗, BLYP/6–31G(d), B3BLYP/6–31G(d)] were used to calculate the geometry optimized structure of tetrahydro-2H-thiopyran (tetrahydrothiopyran, thiacyclohexane, thiane) and the conformational enthalpy (ΔH°), entropy (ΔS°), and free energy (ΔG°) of the chair conformers of methylcyclohexane and 2-methyl-, 3-methyl-, and 4-methyltetrahydro-2H-thiopyran. The DFT methods generally overestimate the conformational free energies (−ΔG°) while some of the MP2 methods give values closer to the experimental results. The MP2/6-311G(d,p) calculated value (−ΔG°=1.46kcal/mol) for 2-methyltetrahydro-2H-thiopyran is in excellent agreement with the experimentally reported value and the MP2/6-21G(2d) calculated value (−ΔG°=1.46kcal/mol) for 3-methyltetrahydro-2H-thiopyran is also in excellent agreement with the experimentally reported value. The equatorial preference of the methyl group is discussed in terms of the repulsive nonbonded interactions in the equatorial conformer, gauche butane (torsional) interactions in the axial conformer, and repulsive nonbonded interactions of the axial methyl group with the ring carbons and hydrogens.

Ab initio molecular orbital theory using the 3-21G(∗), 6-31G∗, 6-31G∗∗, 6-311G∗∗ basis sets, Møller-Plesset perturbation theory [MP2/3-21G(∗)//3-21G(∗), MP2/6-31G∗//6-31G∗, MP2/6-31G∗∗//6-31G∗∗, MP2/6-311G∗∗//6-311G∗∗], and density functional theory (pBP/DN∗∗) were used to calculate the geometries and energies of dihydrodioxins (3,4-dihydro-1,2-dioxin, 3,6-dihydro-1,2-dioxin, 4H-1,3-dioxin (1,3-diox-4-ene), and 2,3-dihydro-1,4-dioxin (1,4-dioxene). Frequency calculations show that the four dihydrodioxins exist in the half-chair conformation and that their boat conformers are transition states. Hyperconjugative orbital interactions (stereoelectronic effects) including nO(3)→σ∗C(2)–O(1), nO(3)→σ∗C(2)–Hax, are observed in 4H-1,3-dioxin. Ab initio (3-21G(∗), 6-31G∗) and MP2/6-31G∗//6-31G∗ calculations were used to obtain geometry optimized structures and conformational energies (−ΔG° or “A values”, kcal/mol) of the rotamers in the half-chair conformers of 2-alkyl-4H-1,3-dioxins and 2-trimethylsilyl-4H-1,3-dioxin [MP2/6-31G∗//6-31G∗: CH3(2.95), C2H5(2.89), iso-C3H7(2.97), tert-C4H9(7.34), neo-C5H11(2.16), Si(CH3)3(4.45)]. The calculated conformational energies of the 2-alkyl-4H-1,3-dioxins and 2-trimethylsilyl-4H-1,3-dioxin are larger than those calculated for the corresponding alkylcyclohexanes and 4-alkylcyclohexenes. Plots of the calculated conformational energies of the 2-alkyl-4H-1,3-dioxins and 2-trimethylsilyl-4H-1,3-dioxin versus the calculated −ΔG° values of the correspondingly substituted cyclohexanes (slope=1.320 and r=0.989) and 4-substituted cyclohexenes (slope=2.150 and r=0.968) are linear. Hyperconjugative orbital interactions are also observed in the 2-alkyl-4H-1,3-dioxins. The C(2)–Hax bond lengths are longer than the C(2)–Heq bond lengths and the C(2)–O(1) bond lengths are longer than the C(2)–O(3) bond lengths in 4H-1,3-dioxin and in the 2-substituted 4H-1,3-dioxins. The C(4)–O(3) bond lengths in the 4H-1,3-dioxins are generally 1.407 or 1.408Å. In the 2-substituted 4H-1,3-dioxins, the O(1)–C(2)–O(1) bond angles vary from 110.4 to 112.8° and the C(2)–O(3)–C(4) and C(7)–C(2)–O(3) bond angles in the most stable axial conformer are larger that the corresponding angles in its most stable equatorial conformer.

Ab initio Hartree–Fock and Density Functional Theory calculations were used to obtain the geometries and relative energies of the rotamers in the chair conformations of 2-alkyltetrahydro-2H-pyrans and 2-(trimethylsilyl)tetrahydro-2H-pyran. The MP2/6-31G*//6-31G* conformational energies (−ΔG°or A values, kcal/mol) of the 2-alkyltetrahydro-2H-pyrans (Me=3.18; Et=3.04; i-Pr=3.03; t-Bu=7.56; neo Pent=2.84) and 2-(trimethylsilyl)tetrahydro-2H-pyran (SiMe3=4.77) are larger than those calculated for the corresponding alkylcyclohexanes and 2-alkyltetrahydro-2H-thiopyrans (tetrahydrothiopyrans, thiacyclohexanes, thianes). Plots of the calculated conformational energies for the 2-substituted tetrahydro-2H-pyrans versus the calculated −ΔG° values for the corresponding alkylcyclohexanes (slope=1.34 and r=0.983) and for the corresponding 2-substituted tetrahydro-2H-thiopyrans (slope=2.01 and r=0.986) are linear.