Jesse J. Lutz

Thermochemical Kinetics for Multireference Systems: Addition Reactions of Ozone

The 1,3-dipolar cycloadditions of ozone to ethyne and ethene provide extreme examples of multireference singlet-state chemistry, and they are examined here to test the applicability of several approaches to thermochemical kinetics of systems with large static correlation. Four different multireference diagnostics are applied to measure the multireference characters of the reactants, products, and transition states; all diagnostics indicate significant multireference character in the reactant portion of the potential energy surfaces. We make a more complete estimation of the effect of quadruple excitations than was previously available, and we use this with CCSDT/CBS estimation of Wheeler et al. (Wheeler, S. E.; Ess, D. H.; Houk, K. N. J. Phys. Chem. A 2008, 112, 1798.) to make new best estimates of the van der Waals association energy, the barrier height, and the reaction energy to form the cycloadduct for both reactions. Comparing with these best estimates, we present comprehensive mean unsigned errors for a variety of coupled cluster, multilevel, and density functional methods. Several computational aspects of multireference reactions are considered: (i) the applicability of multilevel theory, (ii) the convergence of coupled cluster theory for reaction barrier heights, (iii) the applicability of completely renormalized coupled cluster methods to multireference systems, (iv) the treatment by density functional theory, (v) the multireference perturbation theory for multireference reactions, and (vi) the relative accuracy of scaling-type multilevel methods as compared with additive ones. It is found that scaling-type multilevel methods do not perform better than the additive-type multilevel methods. Among the 48 tested density functionals, only M05 reproduces the best estimates within their uncertainty. Multireference perturbation theory based on the complete-active-space reference wave functions constructed using a small number of reaction-specific active orbitals gives accurate forward barrier heights; however, it significantly underestimates reaction energies.

Electronic structure of the S1 state in methylcobalamin: Insight from CASSCF/MC-XQDPT2, EOM-CCSD, and TD-DFT calculations

The methylcobalamin cofactor (MeCbl), which is one of the biologically active forms of vitamin B12, has been the subject of many spectroscopic and theoretical investigations. Traditionally, the lowest‐energy part of the photoabsorption spectrum of MeCbl (the so‐called α/β band) has been interpreted as an S0→S1 electronic transition dominated by π→π* excitations associated with the CC stretching of the corrin ring. However, a more quantitative band‐shape analysis of the α/β spectral region, along with circular dichroism (CD), magnetic CD, and resonance Raman data, has revealed the presence of a second electronic transition that involves the CoCMe bond weakening. Conversely, the lowest‐energy excitations based on transient absorption spectroscopy measurements have been interpreted as metal‐to‐ligand charge transfer (MLCT) transitions. To resolve the existing controversy about the interpretation of the S1 state of MeCbl, calculations have been performed using two independent ab initio wavefunction‐based methods. These include the modified variant of the second‐order multiconfigurational quasi‐degenerate perturbation theory (MC‐XQDPT2), using complete active space self‐consistent field orbitals, and the equation‐of‐motion coupled‐cluster singles and doubles (EOM‐CCSD) approach using restricted Hartree–Fock orbitals. It is shown that both ab initio methods provide a consistent description of the S1 state as having an MLCT character. In addition, the performance of different types of functionals, including hybrid (B3LYP, MPW1PW91, TPSSh), generalized‐gradient‐approximation‐type (GGA‐type) (BP86, BLYP, MPWPW91), meta‐GGA (TPSS), and range‐separated (CAM‐B3LYP, LC‐BLYP) approaches, has been examined and the results of the corresponding time‐dependent density functional theory calculations have been benchmarked against the MC‐XQDPT2 and EOM‐CCSD data. The hybrid functionals support the interpretation in which the S1 state represents a π→π* transition localized on corrin, while pure GGA, meta‐GGA, and LC‐BLYP functionals produce results consistent with the MLCT assignment.

A comparative assessment of the perturbative and renormalized coupled cluster theories with a noniterative treatment of triple excitations for thermochemical kinetics, including a study of basis set and core correlation effects.

The CCSD, CCSD(T), and CR-CC(2,3) coupled cluster methods, combined with five triple-zeta basis sets, namely, MG3S, aug-cc-pVTZ, aug-cc-pV(T+d)Z, aug-cc-pCVTZ, and aug-cc-pCV(T+d)Z, are tested against the DBH24 database of diverse reaction barrier heights. The calculations confirm that the inclusion of connected triple excitations is essential to achieving high accuracy for thermochemical kinetics. They show that various noniterative ways of incorporating connected triple excitations in coupled cluster theory, including the CCSD(T) approach, the full CR-CC(2,3) method, and approximate variants of CR-CC(2,3) similar to the triples corrections of the CCSD(2) approaches, are all about equally accurate for describing the effects of connected triply excited clusters in studies of activation barriers. The effect of freezing core electrons on the results of the CCSD, CCSD(T), and CR-CC(2,3) calculations for barrier heights is also examined. It is demonstrated that to include core correlation most reliably, a basis set including functions that correlate the core and that can treat core-valence correlation is required. On the other hand, the frozen-core approximation using valence-optimized basis sets that lead to relatively small computational costs of CCSD(T) and CR-CC(2,3) calculations can achieve almost as high accuracy as the analogous fully correlated calculations.

Extrapolating potential energy surfaces by scaling electron correlation: Isomerization of bicyclobutane to butadiene

The recently proposed potential energy surface (PES) extrapolation scheme, which predicts smooth molecular PESs corresponding to larger basis sets from the relatively inexpensive calculations using smaller basis sets by scaling electron correlation energies [A. J. C. Varandas and P. Piecuch, Chem. Phys. Lett. 430, 448 (2006)], is applied to the PESs associated with the conrotatory and disrotatory isomerization pathways of bicyclo[1.1.0]butane to buta-1,3-diene. The relevant electronic structure calculations are performed using the completely renormalized coupled-cluster method with singly and doubly excited clusters and a noniterative treatment of connected triply excited clusters, termed CR-CC(2,3), which is known to provide a highly accurate description of chemical reaction profiles involving biradical transition states and intermediates. A comparison with the explicit CR-CC(2,3) calculations using the large correlation-consistent basis set of the cc-pVQZ quality shows that the cc-pVQZ PESs obtained by the extrapolation from the smaller basis set calculations employing the cc-pVDZ and cc-pVTZ basis sets are practically identical, to within fractions of a millihartree, to the true cc-pVQZ PESs. It is also demonstrated that one can use a similar extrapolation procedure to accurately predict the complete basis set (CBS) limits of the calculated PESs from the results of smaller basis set calculations at a fraction of the effort required by the conventional pointwise CBS extrapolations.

Deviations from Born-Oppenheimer mass scaling in spectroscopy and ultracold molecular physics.

Abstract We investigate Born-Oppenheimer breakdown (BOB) effects (beyond the usual mass scaling) for the electronic ground states of a series of homonuclear and heteronuclear alkali-metal diatoms, together with the Sr 2 and Yb 2 diatomics. Several widely available electronic structure software packages are used to calculate the leading contributions to the total isotope shift for commonly occurring isotopologs of each species. Computed quantities include diagonal Born-Oppenheimer corrections (mass shifts) and isotopic field shifts. Mass shifts dominate for light nuclei up to and including K, but field shifts contribute significantly for Rb and Sr and are dominant for Yb. We compare the ab initio mass-shift functions for Li 2 , LiK and LiRb with spectroscopically derived ground-state BOB functions from the literature. We find good agreement in the values of the functions for LiK and LiRb at their equilibrium geometries, but significant disagreement with the shapes of the functions for all 3 systems. The differences may be due to contributions of nonadiabatic terms to the empirical BOB functions. We present a semiclassical model for the effect of BOB corrections on the binding energies of near-threshold states and the positions of zero-energy Feshbach resonances.

Shifts in Excitation Energies Induced by Hydrogen Bonding: A Comparison of the Embedding and Supermolecular Time-Dependent Density Functional Theory Calculations with the Equation-of-Motion Coupled-Cluster Results

Shifts in the π → π∗ excitation energy of the cis-7-hydroxyquinoline chromophore induced by hydrogen bonding with small molecules, obtained with the frozen-density embedding theory (FDET), are compared with the results of the high-level equation-of-motion coupled-cluster (EOMCC) calculations with singles, doubles, and noniterative triples, which provide the reference ab initio data, the supermolecular time-dependent density functional theory (TDDFT) calculations, and the available experimental data. It is demonstrated that the spectral shifts resulting from the FDET calculations employing nonrelaxed environment densities and their EOMCC counterparts are in excellent agreement with one another, whereas the analogous shifts obtained with the supermolecular TDDFT approach do not agree with the EOMCC reference data. Among the discussed issues are the effects of higher-order correlations on the excitation energies and complexation-induced excitation energy shifts resulting from the EOMCC calculations, and the choice of the approximants that represent the nonadditive kinetic energy contributions to the embedding potential of FDET.

Geometries and adiabatic excitation energies of the low-lying valence states of CNC, C2N, N3 and NCO studied with the electron-attached and ionized equation-of-motion coupled-cluster methodologies

The full and active-space variants of the electron-attached (EA) equation-of-motion (EOM) coupled-cluster (CC) method with up to three-particle–two-hole (3p–2h) excitations in the electron-attaching operator Rμ(N+1) that use the CC singles and doubles (CCSD) approach to obtain the ground state of the reference N-electron closed-shell system, abbreviated as EA-EOMCCSD(3p–2h), and their ionized (IP) counterparts with up to three-hole–two-particle (3h–2p) excitations in the ionizing operator Rμ(N−1), abbreviated as IP-EOMCCSD(3h–2p), are used to optimize the geometries of the ground and low-lying excited states of four open-shell molecules, CNC, C2N, NCO and N3, and determine the corresponding adiabatic excitation energies. The full and active-space EA-EOMCCSD(3p–2h) results for the CNC and C2N molecules, obtained with the correlation-consistent basis sets as large as cc-pVTZ and cc-pVQZ, respectively, are compared with one another, with the corresponding EA-EOMCCSD(2p–1h) calculations, with the previously generated small basis set EA-EOMCC and symmetry-adapted-cluster configuration-interaction (SAC-CI-SDT-R/PS) data, and, wherever possible, with experiment. The analogous comparison of the full and active-space IP-EOMCCSD(3h–2p) results with the IP-EOMCCSD(2h–1p), SAC-CI-SDT-R/PS and experimental data is performed for the NCO and N3 molecules. It is shown that the active-space EA-EOMCCSD(3p–2h) and IP-EOMCCSD(3h–2p) approaches using small numbers of active orbitals, which have computational costs that are of the order of the CCSD calculations, provide excitation energies and optimized geometries that are in excellent agreement with the results of the significantly more expensive parent EA-EOMCCSD(3p–2h) and IP-EOMCCSD(3h–2p) calculations, independent of the basis set. It is also demonstrated that the basic EA-EOMCCSD(2p–1h) and IP-EOMCCSD(2h–1p) methods, while generally inadequate for a reliable description of the excitation energies, describe the geometries in a reasonable manner, including excited states dominated by two-electron transitions. Although the full and active-space EA-EOMCCSD(3p–2h) calculations for the most challenging CNC and C2N molecules improve the EA-EOMCCSD(2p–1h) excitation energies, some differences with the available experimental data remain in spite of the use of larger correlation-consistent basis sets and complete basis set extrapolations.

Predictive coupled-cluster isomer orderings for some SinCm (m, n ≤ 12) clusters: A pragmatic comparison between DFT and complete basis limit coupled-cluster benchmarks

The accurate determination of the preferred Si12C12 isomer is important to guide experimental efforts directed towards synthesizing SiC nano-wires and related polymer structures which are anticipated to be highly efficient exciton materials for the opto-electronic devices. In order to definitively identify preferred isomeric structures for silicon carbon nano-clusters, highly accurate geometries, energies, and harmonic zero point energies have been computed using coupled-cluster theory with systematic extrapolation to the complete basis limit for set of silicon carbon clusters ranging in size from SiC3 to Si12C12. It is found that post-MBPT(2) correlation energy plays a significant role in obtaining converged relative isomer energies, suggesting that predictions using low rung density functional methods will not have adequate accuracy. Utilizing the best composite coupled-cluster energy that is still computationally feasible, entailing a 3-4 SCF and coupled-cluster theory with singles and doubles extrapolation with triple-ζ (T) correlation, the closo Si12C12 isomer is identified to be the preferred isomer in the support of previous calculations [X. F. Duan and L. W. Burggraf, J. Chem. Phys. 142, 034303 (2015)]. Additionally we have investigated more pragmatic approaches to obtaining accurate silicon carbide isomer energies, including the use of frozen natural orbital coupled-cluster theory and several rungs of standard and double-hybrid density functional theory. Frozen natural orbitals as a way to compute post-MBPT(2) correlation energy are found to be an excellent balance between efficiency and accuracy.

Reference dependence of the two-determinant coupled-cluster method for triplet and open-shell singlet states of biradical molecules

We study the performance of the two-determinant (TD) coupled-cluster (CC) method which, unlike conventional ground-state single-reference (SR) CC methods, can, in principle, provide a naturally spin-adapted treatment of the lowest-lying open-shell singlet (OSS) and triplet electronic states. Various choices for the TD-CC reference orbitals are considered, including those generated by the multi-configurational self-consistent field method. Comparisons are made with the results of high-level SR-CC, equation-of-motion (EOM) CC, and multi-reference EOM calculations performed on a large test set of over 100 molecules with low-lying OSS states. It is shown that in cases where the EOMCC reference function is poorly described, TD-CC can provide a significantly better quantitative description of OSS total energies and OSS-triplet splittings.

Valence and charge-transfer optical properties for some SinCm (m, n ≤ 12) clusters: Comparing TD-DFT, complete-basis-limit EOMCC, and benchmarks from spectroscopy

Accurate optical characterization of the closo-Si12C12 molecule is important to guide experimental efforts toward the synthesis of nano-wires, cyclic nano-arrays, and related array structures, which are anticipated to be robust and efficient exciton materials for opto-electronic devices. Working toward calibrated methods for the description of closo-Si12C12 oligomers, various electronic structure approaches are evaluated for their ability to reproduce measured optical transitions of the SiC2, Si2Cn (n = 1-3), and Si3Cn (n = 1, 2) clusters reported earlier by Steglich and Maier [Astrophys. J. 801, 119 (2015)]. Complete-basis-limit equation-of-motion coupled-cluster (EOMCC) results are presented and a comparison is made between perturbative and renormalized non-iterative triples corrections. The effect of adding a renormalized correction for quadruples is also tested. Benchmark test sets derived from both measurement and high-level EOMCC calculations are then used to evaluate the performance of a variety of density functionals within the time-dependent density functional theory (TD-DFT) framework. The best-performing functionals are subsequently applied to predict valence TD-DFT excitation energies for the lowest-energy isomers of SinC and Sin-1C7-n (n = 4-6). TD-DFT approaches are then applied to the SinCn (n = 4-12) clusters and unique spectroscopic signatures of closo-Si12C12 are discussed. Finally, various long-range corrected density functionals, including those from the CAM-QTP family, are applied to a charge-transfer excitation in a cyclic (Si4C4)4 oligomer. Approaches for gauging the extent of charge-transfer character are also tested and EOMCC results are used to benchmark functionals and make recommendations.