Ajith Perera

Multireference coupled-cluster theory: The easy way

The multi-ionization equation-of-motion coupled-cluster (CC) method is developed for multireference (MR) problems. It is operationally single reference, depending upon a formal matrix diagonalization step to define the coefficients in the wavefunction in an unbiased way that allows for important MR character. The method is illustrated for the autoisomerization of cyclobutadiene, which has a very large multireference effect and compared to other MR-CC results. The newly implemented methods are also used to obtain the vertical double ionization (DI) potentials of several small molecules (H(2)O, CO, C(2)H(2), C(2)H(4)). Also, the performance of the new methods is analyzed by plotting the potential energy curve for twisted ethylene as a function of a dihedral angle between two methylenes. Evaluation of the total molecular energy via MR-DI-CC calculations makes it possible to avoid an unphysical cusp.

Benchmark studies on the building blocks of DNA. 1. Superiority of coupled cluster methods in describing the excited states of nucleobases in the Franck-Condon region.

Equation of motion excitation energy coupled-cluster (EOMEE-CC) methods including perturbative triple excitations have been used to set benchmark results for the excitation energy and oscillator strength of the building units of DNA, i.e., cytosine, guanine, adenine and thymine. In all cases the lowest twelve transitions have been considered including valence and Rydberg ones. Triple-ζ basis sets with diffuse functions have been used and the results are compared to CC2, CASPT2, TDDFT, and DFT/MRCI results from the literature. The results clearly show that it is only the EOMEE-CCSD(T) that is capable of providing accuracy of about 0.1 eV. EOMEE-CCSD systematically overshoots the energy of all types of transitions by 0.1-0.3 eV, whereas CC2 is surprisingly accurate for ππ* transitions but fails (often badly) for nπ* and Rydberg transitions. DFT and CASPT2 seem to give reliable results for the lowest transition, but the error increases fast with the excitation level. The differences in the excitation energies often change the energy ordering of the states, which should even influence the conclusions of excited state dynamics obtained with these approximate methods. The results call for further benchmark calculations on larger building blocks of DNA (nucleosides, basis pairs) at the CCSD(T) level.

Software design of ACES III with the super instruction architecture

The Advanced Concepts in Electronic Structure (ACES) III software is a completely rewritten implementation for parallel computer architectures of the most used capabilities in ACES II, including the calculation of the electronic structure of molecular ground states and excited states, and determination of molecular geometries and of vibrational frequencies using many‐body and coupled cluster methods. To achieve good performance on modern parallel systems while simultaneously offering a software development environment that allows rapid implementation of new methods and algorithms, ACES III was written using a new software infrastructure, the super instruction architecture comprising a domain‐specific language, super instruction assembly language (SIAL), and a sophisticated runtime environment, super instruction processor (SIP). The architecture of ACES III is described as well as the inner workings of SIAL and SIP. The execution performance of ACES III and the productivity of programming in SIAL are discussed.

Benchmarking for Perturbative Triple-Excitations in EE-EOM-CC Methods

Perturbative triples corrections ((T) and (T̃)) to the equation of motion coupled cluster singles and doubles (EOM-CCSD) are rederived and implemented in a pilot parallel code. The vertical excitation energies of molecules in the test set of Sauer et al. [J. Chem. Theor. Comput. 2009, 5, 555] are reported and compared to the iterative EOM-CCSDT-3 method. The average absolute deviations of EOM-CCSD(T) and EOM-CCSD(T̃) from EOM-CCSDT-3 over this wide test set are 0.06 and 0.18 eV, respectively. The poor performance of the latter suggests misbalanced handling of the (T̃) terms. Scaling curves for EOM-CCSD(T) are also presented to demonstrate the performance across multiple compute nodes, thus enabling the routine and accurate study of excited states for ever larger molecular systems.

Benchmark studies on the building blocks of DNA. 2. Effect of biological environment on the electronic excitation spectrum of nucleobases.

In the first paper of this series (Szalay; et al. J. Phys. Chem. A, 2012, 116, 6702) we have investigated the excited states of nucleobases. It was shown that it is only the equation of motion excitation energy coupled-cluster (EOMEE-CC) methods, which can give a balanced description for all type of the transitions of these molecules; if the goal is to obtain accurate results with uncertainty of about 0.1 eV only, triples corrections in the form of, e.g., the EOMEE-CCSD(T) method need to be included. In this second paper we extend this study to nucleobases in their biological environment, considering hydration, glycoside bond, and base pairing. EOMEE-CCSD and EOMEE-CCSD(T) methods are used with aug-cc-pVDZ basis. The effect of surrounding water was systematically investigated by considering one to five water molecules at different positions. It was found that hydration can modify the order of the excited states: in particular, nπ* states get shifted above the neighboring ππ* ones. The glycoside bonds effect is smaller, as shown by our calculations on cytidine and guanosine. Here the loss of planarity causes some intensity shift from ππ* to nπ* states. Finally, the guanine-cytosine (GC) Watson-Crick pair was studied; most of the states could be identified as local excitations on one of the bases, but there is also a low-lying charge-transfer state. Significant discrepancy with earlier CASPT2 and TDDFT studies was found for the GC pair and triples effects seem to be essential for all of these systems.

An ab initio study of the (H2O)20H+ and (H2O)21H+ water clusters

The study of the minimum Born–Oppenheimer structures of the protonated water clusters, (H2O)nH+, is performed for n=20 and 21. The structures belonging to four basic morphologies are optimized at the Hartree–Fock, second-order many-body perturbation theory and coupled cluster level, with the 6–31G, 6-31G∗, and 6-311G∗∗ basis sets, using the parallel ACES III program. The lowest energy structure for each n is found to be the cagelike form filled with H2O, with the proton located on the surface. The cage is the distorted dodecahedron for the 21-mer case, and partially rearranged dodecahedral structure for the 20-mer. The results confirm that the lowest energy structure of the magic number n=21 clusters corresponds to a more stable form than that of the 20-mer clusters.

Benchmark studies on the building blocks of DNA. 3. Watson-Crick and stacked base pairs.

Excited states of stacked adenine-thymine and guanine-cytosine pairs as well as the Watson-Crick pair of guanine-thymine have been investigated using the equation of motion coupled-cluster (EOM-CC) method with single and double as well as approximate triple excitations. Transitions have been assigned, and the form of the excitations has been analyzed. The majority of the excitations could be classified as localized on the nucleobases, but for all three studied systems, charge-transfer (CT) transitions could also be identified. The main aim of this study was to compare the performance of lower-level methods (ADC(2) and TDDFT) to the high-level EOM-CC ones. It was shown that both ADC(2) and TDDFT with long-range correction have nonsystematic error in excitation energies, causing alternation of the energetic ordering of the excitations. Considering the high costs of the EOM-CC calculations, there is a need for reliable new approximate methods.

Singlet–triplet separations of di-radicals treated by the DEA/DIP-EOM-CCSD methods

The singlet–triplet splittings of the di-radicals methylene, trimethylene–methane, ortha-, meta- and para-benzynes, and cyclobutane-1,2,3,4-tetrone have become test systems for the applications of various multi-reference (MR) coupled-cluster methods. We report results close to the basis set limit computed with double ionization potential (DIP) and double electron attachment (DEA) equation-of-motion coupled-cluster methods. These di-radicals share the characteristics of a 2-hole 2-particle MR problem and are commonly used to assess the performance of MR methods, and yet require more careful study unto themselves as benchmarks. Here, using our CCSD(T)/6-311G(2d,2p) optimized geometries, we report DIP/DEA-CC results and single-reference (SR) CCSD, CCSD(T), ΛCCSD(T) and CCSDT results for comparison.

Approximating electronically excited states with equation-of-motion linear coupled-cluster theory

A new perturbative approach to canonical equation-of-motion coupled-cluster theory is presented using coupled-cluster perturbation theory. A second-order Møller-Plesset partitioning of the Hamiltonian is used to obtain the well known equation-of-motion many-body perturbation theory equations and two new equation-of-motion methods based on the linear coupled-cluster doubles and linear coupled-cluster singles and doubles wavefunctions. These new methods are benchmarked against very accurate theoretical and experimental spectra from 25 small organic molecules. It is found that the proposed methods have excellent agreement with canonical equation-of-motion coupled-cluster singles and doubles state for state orderings and relative excited state energies as well as acceptable quantitative agreement for absolute excitation energies compared with the best estimate theory and experimental spectra.

A crossed molecular beam and ab-initio investigation of the reaction of boron monoxide (BO; X2Σ+) with methylacetylene (CH3CCH; X1A1): competing atomic hydrogen and methyl loss pathways.

The gas-phase reaction of boron monoxide ((11)BO; X(2)Σ(+)) with methylacetylene (CH3CCH; X(1)A1) was investigated experimentally using crossed molecular beam technique at a collision energy of 22.7 kJ mol(-1) and theoretically using state of the art electronic structure calculation, for the first time. The scattering dynamics were found to be indirect (complex forming reaction) and the reaction proceeded through the barrier-less formation of a van-der-Waals complex ((11)BOC3H4) followed by isomerization via the addition of (11)BO(X(2)Σ(+)) to the C1 and/or C2 carbon atom of methylacetylene through submerged barriers. The resulting (11)BOC3H4 doublet radical intermediates underwent unimolecular decomposition involving three competing reaction mechanisms via two distinct atomic hydrogen losses and a methyl group elimination. Utilizing partially deuterated methylacetylene reactants (CD3CCH; CH3CCD), we revealed that the initial addition of (11)BO(X(2)Σ(+)) to the C1 carbon atom of methylacetylene was followed by hydrogen loss from the acetylenic carbon atom (C1) and from the methyl group (C3) leading to 1-propynyl boron monoxide (CH3CC(11)BO) and propadienyl boron monoxide (CH2CCH(11)BO), respectively. Addition of (11)BO(X(2)Σ(+)) to the C1 of methylacetylene followed by the migration of the boronyl group to the C2 carbon atom and/or an initial addition of (11)BO(X(2)Σ(+)) to the sterically less accessible C2 carbon atom of methylacetylene was followed by loss of a methyl group leading to the ethynyl boron monoxide product (HCC(11)BO) in an overall exoergic reaction (78 ± 23 kJ mol(-1)). The branching ratios of these channels forming CH2CCH(11)BO, CH3CC(11)BO, and HCC(11)BO were derived to be 4 ± 3%, 40 ± 5%, and 56 ± 15%, respectively; these data are in excellent agreement with the calculated branching ratios using statistical RRKM theory yielding 1%, 38%, and 61%, respectively.