Equation-of-motion Coupled-cluster Singles Research Articles

ThAu2 -, ThAu2O-, and ThAuOH- anions: Photoelectron spectroscopic and theoretical characterization.

The thorium-gold negative ions ThAu2 -, ThAu2O-, and ThAuOH- have been observed and experimentally characterized by anion photoelectron spectroscopy. These experiments are accompanied by extensive ab initio electronic structure calculations using a relativistic composite methodology based primarily on coupled cluster singles and doubles with perturbative triples calculations. The theoretical electron affinities (EAs) at 0K agree with the experimental adiabatic EAs to within 0.02eV for all species. Two separate isomers were located in the calculations for ThAuOH-, and detachment from both of these appears to be present in the photoelectron spectrum. Excited electronic states of the neutral molecules are reported at the equation of motion-coupled cluster singles and doubles level of theory. Atomization energies and heats of formation are also calculated for each neutral species and have expected uncertainties of 3 and 4 kcal/mol, respectively. The σ bonds between Th and Au are determined by natural bond orbital analysis to consist of predominately sd hybrids on Th bonding with the Au 6s orbital. In order to investigate the correspondence between the bonding in Th-Au and Th-F molecules, a limited number of calculations were also carried out on most of the F-analogs of this study. These results demonstrate that Au does behave like F in these cases, although the Th-F σ bonds are much more ionic compared to Th-Au. This results in an EA for ThF2 that is 10 kcal/mol smaller than that of ThAu2. The EA values for the Th(IV) species, i.e., ThX2O and ThXOH, only differed, however, by 3-4 kcal/mol.

A periodic equation-of-motion coupled-cluster implementation applied to F-centers in alkaline earth oxides.

We present an implementation of the equation of motion coupled-cluster singles and doubles (EOM-CCSD) theory using periodic boundary conditions and a plane wave basis set. Our implementation of EOM-CCSD theory is applied to study F-centers in alkaline earth oxides employing a periodic supercell approach. The convergence of the calculated electronic excitation energies for neutral color centers in MgO, CaO, and SrO crystals with respect to the orbital basis set and system size is explored. We discuss extrapolation techniques that approximate excitation energies in the complete basis set limit and reduce finite size errors. Our findings demonstrate that EOM-CCSD theory can predict optical absorption energies of F-centers in good agreement with experiment. Furthermore, we discuss calculated emission energies corresponding to the decay from triplet to singlet states responsible for the photoluminescence properties. Our findings are compared to experimental and theoretical results available in the literature.

Unveiling the Photophysical Properties of Boron-dipyrromethene Dyes Using a New Accurate Excited State Coupled Cluster Method.

Boron-dipyrromethene (BODIPY) molecules form a class of fluorescent dyes known for their exceptional photoluminescence properties. Today, they are used extensively in various applications from fluorescent imaging to optoelectronics. The ease of altering the BODIPY core has allowed scientists to synthesize dozens of analogues by exploring chemical substitutions of various kinds or by increasing the length of conjugated groups. However, predicting the impact of any chemical change accurately is still a challenge, especially as most computational methods fail to describe correctly the photophysical properties of BODIPY derivatives. In this study, the recently developed coupled cluster method called "domain-based local pair natural orbital similarity transformed equation of motion-coupled cluster singles and doubles" (DLPNO-STEOM-CCSD) is employed to compute the lowest vertical excitation energies of more than 50 BODIPY molecules. The method performs remarkably well yielding an accuracy of about 0.06 eV compared to the experimental absorption maxima. We also provide an estimate to the error made by neglecting vibronic effects in the computed spectra. The dyes selected for investigation here span a large range of molecular sizes and chemical functionalities and are embedded in solvents with different polarities. We have also investigated if the method is able to correctly reproduce the impact of a single chemical modification on the absorption energy. To characterize the method in more specific terms, we have studied four large BODIPY analogues used in real-life applications due to their interesting chemical properties. These examples should illustrate the capacity of the DLPNO-STEOM-CCSD procedure to become a method of choice for the study of photophysical properties of medium to large organic compounds.

Communication: The pole structure of the dynamical polarizability tensor in equation-of-motion coupled-cluster theory.

In this letter, we investigate the pole structure of dynamical polarizabilities computed within the equation-of-motion coupled-cluster (EOM-CC) theory. We show, both theoretically and numerically, that approximate EOM-CC schemes such as, for example, the EOM-CC singles and doubles model exhibit an incorrect pole structure in which the poles that reflect the excitations from the target state (i.e., the EOM-CC state) are supplemented by artificial poles due to excitations from the CC reference state. These artificial poles can be avoided by skipping the amplitude response and reverting to a sum-over-states formulation. While numerical results are generally in favor of such a solution, its major drawback is that this scheme violates size extensivity.

Computational Benchmarking for Ultrafast Electron Dynamics: Wave Function Methods vs Density Functional Theory.

Attosecond electron dynamics in small- and medium-sized molecules, induced by an ultrashort strong optical pulse, is studied computationally for a frozen nuclear geometry. The importance of exchange and correlation effects on the nonequilibrium electron dynamics induced by the interaction of the molecule with the strong optical pulse is analyzed by comparing the solution of the time-dependent Schrödinger equation based on the correlated field-free stationary electronic states computed with the equationof-motion coupled cluster singles and doubles and the complete active space multi-configurational self-consistent field methodologies on one hand, and various functionals in real-time time-dependent density functional theory (TDDFT) on the other. We aim to evaluate the performance of the latter approach, which is very widely used for nonlinear absorption processes and whose computational cost has a more favorable scaling with the system size. We focus on LiH as a toy model for a nontrivial molecule and show that our conclusions carry over to larger molecules, exemplified by ABCU (C10H19N). The molecules are probed with IR and UV pulses whose intensities are not strong enough to significantly ionize the system. By comparing the evolution of the time-dependent field-free electronic dipole moment, as well as its Fourier power spectrum, we show that TD-DFT performs qualitatively well in most cases. Contrary to previous studies, we find almost no changes in the TD-DFT excitation energies when excited states are populated. Transitions between states of different symmetries are induced using pulses polarized in different directions. We observe that the performance of TD-DFT does not depend on the symmetry of the states involved in the transition.

Assessment of low-scaling approximations to the equation of motion coupled-cluster singles and doubles equations.

Methods for fast and reliable computation of electronic excitation energies are in short supply, and little is known about their systematic performance. This work reports a comparison of several low-scaling approximations to the equation of motion coupled cluster singles and doubles (EOM-CCSD) and linear-response coupled cluster singles and doubles (LR-CCSD) equations with other single reference methods for computing the vertical electronic transition energies of 11 small organic molecules. The methods, including second order equation-of-motion many-body perturbation theory (EOM-MBPT2) and its partitioned variant, are compared to several valence and Rydberg singlet states. We find that the EOM-MBPT2 method was rarely more than a tenth of an eV from EOM-CCSD calculated energies, yet demonstrates a performance gain of nearly 30%. The partitioned equation-of-motion approach, P-EOM-MBPT2, which is an order of magnitude faster than EOM-CCSD, outperforms the CIS(D) and CC2 in the description of Rydberg states. CC2, on the other hand, excels at describing valence states where P-EOM-MBPT2 does not. The difference between the CC2 and P-EOM-MBPT2 can ultimately be traced back to how each method approximates EOM-CCSD and LR-CCSD. The results suggest that CC2 and P-EOM-MBPT2 are complementary: CC2 is best suited for the description of valence states while P-EOM-MBPT2 proves to be a superior O(N(5)) method for the description of Rydberg states.

Theoretical Study of the Electronic Spectrum of Disulfur Monoxide

The near ultraviolet-visible absorption spectrum of disulfur monoxide ( S2O) has been theoretically studied by using the time-dependent density functional theory (TD-DFT) and the equation of motion coupled-cluster singles and doubles approach (EOM-CCSD) combined with the AUG-cc-PVQZ basis set. From this, analytical expressions for the absorption coefficient over the 250 - 340 nm range are reported for the first time. The computed molecular structure and the vibrational frequencies for the ground and third electronically excited state S2O (C 1Aʹ), responsible of the observed spectrum, are compared with available data.

Using the ONIOM hybrid method to apply equation of motion CCSD to larger systems: Benchmarking and comparison with time-dependent density functional theory, configuration interaction singles, and time-dependent Hartree–Fock

Equation of motion coupled-cluster singles and doubles (EOM-CCSD) is one of the most accurate computational methods for the description of one-electron vertical transitions. However, its O(N(6)) scaling, where N is the number of basis functions, often makes the study of molecules larger than 10-15 heavy atoms prohibitive. In this work we investigate how accurately less expensive methods can approximate the EOM-CCSD results. We focus on our own N-layer integrated molecular orbital molecular mechanics (ONIOM) hybrid scheme, where the system is partitioned into regions which are treated with different levels of theory. For our set of benchmark calculations, the comparison of conventional configuration interaction singles (CIS), time-dependent Hartree-Fock (TDHF), and time-dependent density functional theory (TDDFT) methods and ONIOM (with different low level methods) showed that the best accuracy-computational time combination is obtained with ONIOM(EOM:TDDFT), which has a rms of the error with respect to the conventional EOM-CCSD of 0.06 eV, compared with 0.47 eV of the conventional TDDFT.

Efficient formulation and computer implementation of the active-space electron-attached and ionized equation-of-motion coupled-cluster methods

The efficient, general-purpose implementations of the active-space electron-attached (EA) and ionized (IP) equation-of-motion coupled-cluster (EOMCC) methods including up to 3p-2h and 3h-2p excitations, called EA-EOMCCSDt and IP-EOMCCSDt, respectively, are discussed. The details of the algorithm that enables one to achieve a high degree of code vectorization for the active-space methods and the factorized forms of the EA- and IP-EOMCCSDt equations that maximize the benefits of using active orbitals in the process of selecting the dominant 3p-2h and 3h-2p excitations are presented. The results of benchmark calculations for the low-lying doublet and quartet states of the CH and SH radicals reveal that the active-space EA-EOMCCSDt and IP-EOMCCSDt methods are capable of producing results for the electronic excitations in open-shell systems that match the high accuracy of EA- and IP-EOMCC calculations with a full treatment of 3p-2h and 3h-2p excitations, even when the excited states of interest display a manifestly multideterminantal nature, with the costs that can be on the same order of those characterizing the basic EOMCC singles and doubles approach.

Extension of the active‐space equation‐of‐motion coupled‐cluster methods to radical systems: The EA‐EOMCCSDt and IP‐EOMCCSDt approaches

AbstractThe development of the active‐space variants of the electron‐attached (EA) and ionized (IP) equation‐of‐motion coupled‐cluster (EOMCC) methods, in which higher‐than‐doubly excited components of the cluster operator T and higher than 2p‐1h or 2h‐1p components of the electron attaching and ionizing operators R are defined through the use of active orbitals, is discussed. As shown by preliminary test calculations of adiabatic excitation energies and potential energy curves for the low‐lying states of the CH and OH radicals, the basic active‐space EA‐EOMCC and IP‐EOMCC methods, referred to as the EA‐EOMCCSDt and IP‐EOMCCSDt approaches, are capable of accuratelydescribing the ground and excited states of open‐shell systems, even at the moderately stretched nuclear geometries and even for states with a strong multi‐determinantal or doubly excited character, at the low costs that are on the order of those characterizing the standard EOMCC singles and doubles method. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

Extension of the method of moments of coupled-cluster equations to excited states: The triples and quadruples corrections to the equation-of-motion coupled-cluster singles and doubles energies

The recently proposed extension of the method of moments of coupled-cluster equations (MMCC) to excited states via the equation-of-motion coupled-cluster (EOMCC) formalism [K. Kowalski and P. Piecuch, J. Chem. Phys. 115, 2966 (2001)] is developed further. A new approximate variant of the excited-state MMCC theory, termed the MMCC(2,4) method, is proposed and tested. In the MMCC(2,4) method, relatively simple noniterative corrections due to triples and quadruples are added to the excited-state energies obtained in the standard EOMCCSD (EOMCC singles and doubles) calculations. The performance of the MMCC(2,4) approach is illustrated by the results of calculations for the excited states of N2, C2, and CH+. The MMCC(2,4) energies are compared with the results of the MMCC(2,3) calculations, in which noniterative corrections due to triples only are added to the EOMCCSD energies, and with the results of other EOMCC calculations, including various EOMCC triples schemes.

Excited-state potential energy curves of CH +: a comparison of the EOMCCSDt and full EOMCCSDT results

The recently developed equation-of-motion coupled-cluster (EOMCC) method with singles, doubles, and a selected set of triples defined through active orbitals (EOMCCSDt) is applied to the excited-state potential energy curves of the CH + ion. The results are compared with the EOMCCSD (EOMCC singles and doubles), EOMCCSDT (EOMCC singles, doubles, and triples), and full configuration interaction results. It is demonstrated that the EOMCCSDt method provides the excited-state potentials of the EOMCCSDT quality and that the EOMCCSDt and EOMCCSDT methods restore the asymptotic degeneracy of excited states, which is broken by the EOMCCSD and other EOMCC doubles models.

New type of noniterative energy corrections for excited electronic states: Extension of the method of moments of coupled-cluster equations to the equation-of-motion coupled-cluster formalism

The recently proposed method of moments of coupled-cluster equations (MMCC) is extended to excited states via the equation-of-motion coupled-cluster (EOMCC) formalism. The main idea of the new MMCC theory is that of the noniterative energy corrections which, when added to the excited-state energies obtained in standard approximate EOMCC calculations, recover the exact energies. The MMCC corrections are expressed in terms of the generalized moments of the EOMCC equations. Approximate variants of the excited-state MMCC formalism, including the MMCC(2,3) approach, are introduced. In the MMCC(2,3) method, very simple energy corrections, expressed in terms of matrix elements of the triples-reference, triples-singles, and triples-doubles blocks of the EOMCCSD (EOMCC singles and doubles) similarity-transformed Hamiltonian, are added to the excited-state energies obtained in EOMCCSD calculations. The performance of the MMCC(2,3) approach is illustrated by the results of pilot calculations for the potential energy curves of ground and excited states of CH+.

The active-space equation-of-motion coupled-cluster methods for excited electronic states: Full EOMCCSDt

The full version of the equation-of-motion coupled-cluster (EOMCC) method with all singles and doubles, and a selected set of triples defined through active orbitals (EOMCCSDt) has been implemented and tested using the H8, H2O, N2, C2, and CH+ systems. It is demonstrated that the full EOMCCSDt method provides the results of the full EOMCCSDT (EOMCC singles, doubles, and triples) quality at the fraction of the computer effort associated with the EOMCCSDT calculations. This includes excited states that are dominated by doubles and states that have large triexcited components. The excellent performance of the EOMCCSDt approach is observed even when the ground electronic state has a quasidegenerate character, which means that we can apply the EOMCCSDt formalism to excited states that cannot be adequately described by the perturbative triples models. The EOMCCSDt method is equivalent to the EOMCCSDT approach if all orbitals used in the EOMCCSDt calculations are active.

Low-lying excited states of HOOOCl and HOOOBr

A theoretical investigation of the low-lying singlet and triplet electronic states of HOOOCl and HOOOBr is presented. Calculations of excitation energies and oscillator strengths using CASSCF, first-order CI, MRCI and the equation of motion coupled-cluster singles and doubles methods are presented. The calculations predict that for HOOOCl and HOOOBr there are two singlet states that are accessible by wavelengths longer than 235 nm. These transitions, however, are predicted to be relatively weak. Spin–orbit calculations yield oscillator strengths for the lowest two triplet states of HOOOBr that are only one order of magnitude smaller than those of its low-lying singlet states.

Analytic energy derivatives for the equation-of-motion coupled-cluster method: Algebraic expressions, implementation and application to theS 1 state of HFCO

The general theory of analytic derivatives for the equation-of-motion coupled cluster (EOM-CC) method is reviewed. Special attention is paid to the EOM-CC singles and doubles (EOM-CCSD) approximation, which has the same computational scaling properties as the coupled-cluster singles doubles (CCSD) ground state method and is therefore applicable to a wide range of molecular systems. The detailed spin orbital equations that must be solved in EOM-CCSD gradient calculations are presented for the first time, and some guidelines are discussed regarding their computational implementation. Finally, use of the EOM-CCSD gradient method is illustrated by determining the structure, dipole moment components, harmonic frequencies and infrared intensities of formyl fluoride (HFCO) in its singlet excited (n, π*) state.

Analytic energy gradients for the equation-of-motion coupled-cluster method: Implementation and application to the HCN/HNC system

A recently developed theory for calculating analytic first derivatives of the energy for excited states treated by the equation-of-motion coupled-cluster (EOM-CC) method has been implemented and applied to study potential energy surfaces in the HCN/HNC system. The EOM-CC singles and doubles (EOM-CCSD) approximation is used to predict equilibrium structures, energies, dipole moments, harmonic vibrational frequencies and infrared intensities of HCN and HNC isomers in both the à 1A″ and B̃ 1A′ excited states. In addition, the activated complex for HCN→HNC isomerization in these states is investigated theoretically for the first time.

Does chlorine peroxide exhibit a strong ultraviolet absorption near 250 nm?

A theoretical investigation of the low-lying singlet electronic states of chlorine peroxide (ClOOCl) is presented. Calculations of excitation energies and oscillator strengths at the equation of motion coupled-cluster singles and doubles level predict that six excited states of ClOOCl are accessible at photon wavelengths above 200 nm. These states occur in three sets of pairs which can be approximately represented as symmetrized and antisymmetrized excitations of electrons from lone pair and Cl–O bonding orbitals to antibonding Cl–O orbitals. While small oscillator strengths are predicted for transitions to the lowest two ‘‘pairs’’ of states, sizable values are predicted for the X 1A→E 1A and X 1A→F 1B transitions (0.02 and 0.08, respectively). Furthermore, our estimation of the vertical excitation energy for these processes is ≊5.20 eV, in satisfactory agreement with the experimentally observed band maximum of ClOOCl at 5.04 eV. The results of this work lend strong support to the contention that photodissociation of ClOOCl plays an important role in the catalytic destruction of stratospheric ozone.