Equation-of-motion Coupled-cluster Calculations Research Articles

Reassessing the potential of TlCl for laser cooling experiments via four-component correlated electronic structure calculations.

Following the interest in the experimental realization of laser cooling for thallium fluoride (TlF), determining the potential of thallium chloride (TlCl) as a candidate for laser cooling experiments has recently received attention from a theoretical perspective [Yuan et al., J. Chem. Phys. 149, 094306 (2018)]. From these ab initio electronic structure calculations, it appeared that the cooling process, which would proceed from transitions between a3Π0 + and X1Σ0 + states, had as a potential bottleneck the long lifetime (6.04 µs) of the excited state a3Π0 +, that would make it very difficult to experimentally control the slowing zone. In this work, we revisit the electronic structure of TlCl by employing four-component Multireference Configuration Interaction (MRCI) and Polarization Propagator (PP) calculations and investigate the effect of such approaches on the computed transition dipole moments between a3Π0 + and a3Π1 excited states of TlCl and TlF (the latter serving as a benchmark between theory and experiment). Whenever possible, MRCI and PP results have been cross-validated by four-component equation of motion coupled-cluster calculations. We find from these different correlated approaches that a coherent picture emerges in which the results of TlF are extremely close to the experimental values, whereas for TlCl the four-component calculations now predict a significantly shorter lifetime (between 109 and 175ns) for the a3Π0 + than prior estimates. As a consequence, TlCl would exhibit rather different, more favorable cooling dynamics. By numerically calculating the rate equation, we provide evidence that TlCl may have similar cooling capabilities to TlF. Our analysis also indicates the potential advantages of boosting stimulated radiation in optical cycles to improve cooling efficiency.

Examining fundamental and excitation gaps at the thermodynamic limit: A combined (QTP) DFT and coupled cluster study on trans-polyacetylene and polyacene.

Interest in ab initio property prediction of π-conjugated polymers for technological applications places significant demand on "cost-effective" and conceptual computational methods, particularly effective, one-particle theories. This is particularly relevant in the case of Kohn-Sham Density Functional Theory (KS-DFT) and its new competitors that arise from correlated orbital theory, the latter defining the QTP family of DFT functionals. This study presents large, ab initio equation of motion-coupled cluster calculations using the massively parallel ACESIII to target the fundamental bandgap of two prototypical organic polymers, trans-polyacetylene (tPA) and polyacene (Ac), and provides an assessment of the new quantum theory project (QTP) functionals for this problem. Further results focusing on the 1Ag (1Ag), 1Bu (1B2u), and 3Bu (3B2u) excited states of tPA (Ac) are also presented. By performing calculations on oligomers of increasing size, extrapolations to the thermodynamic limit for the fundamental and all excitation gaps, as well as estimations of the exciton binding energy, are made. Thermodynamic-limit results for a combination of "optimal" and model geometries are presented. Calculated results for excitations that are adequately described using a single-particle model illustrate the benefits of requiring a KS-DFT functional to satisfy the Bartlett ionization potential theorem.

The role of high-order electron correlation effects in a model system for non-valence correlation-bound anions.

The diffusion Monte Carlo (DMC), auxiliary field quantum Monte Carlo (AFQMC), and equation-of-motion coupled cluster (EOM-CC) methods are used to calculate the electron binding energy (EBE) of the non-valence anion state of a model (H2O)4 cluster. Two geometries are considered, one at which the anion is unbound and the other at which it is bound in the Hartree-Fock (HF) approximation. It is demonstrated that DMC calculations can recover from the use of a HF trial wave function that has collapsed onto a discretized continuum solution, although larger EBEs are obtained when using a trial wave function for the anion that provides a more realistic description of the charge distribution and, hence, of the nodal surface. For the geometry at which the cluster has a non-valence correlation-bound anion, both the inclusion of triples in the EOM-CC method and the inclusion of supplemental diffuse d functions in the basis set are important. DMC calculations with suitable trial wave functions give EBE values in good agreement with our best estimate EOM-CC result. AFQMC using a trial wave function for the anion with a realistic electron density gives a value of the EBE nearly identical to the EOM-CC result when using the same basis set. For the geometry at which the anion is bound in the HF approximation, the inclusion of triple excitations in the EOM-CC calculations is much less important. The best estimate EOM-CC EBE value is in good agreement with the results of DMC calculations with appropriate trial wave functions.

Electron Attachment to DNA Base Pairs: An Interplay of Dipole- and Valence-Bound States.

We have investigated the electron-attached states in Watson-Crick guanine-cytosine and adenine-thymine base pairs using the highly accurate equation-of-motion coupled-cluster (EOM-CC) method and extended basis sets. Both base pairs have two bound anionic states. The dipole-bound state is stable even at the neutral geometry, but the valence-bound state is only adiabatically bound. The initial electron attachment results in the formation of a dipole-bound state that acts as a doorway to the valence-bound anionic state. The adiabatic potential energy surface of ground and first excited states of an anion shows an avoided crossing, indicating mixing of the electronic and nuclear degrees of freedom. We have calculated the coupling strength between the valence- and dipole-bound states by fitting a simple diabatic model potential to a cut through the two adiabatic surfaces of the anions obtained from the EOM-CC calculations. The transfer of the electron from the initial dipole-bound to the final valence-bound state has been found to happen at an ultrafast time scale.

Double Photodetachment of F–·H2O: Experimental and Theoretical Studies of [F·H2O]+

Double photodetachment of the cluster F-·H2O in a strong laser field is explored in a combined experimental-theoretical study. Products are observed experimentally by coincidence photofragment imaging following double ionization by intense laser pulses. Theoretically, equation of motion coupled cluster calculations (EOM-CC), suitable for modeling strong correlation effects in the electronic wave function, shed light on the Franck-Condon region, and ab initio molecular dynamics simulations also performed using EOM-CC methods reveal the fragmentation dynamics in time on the lowest-lying singlet and triplet states of [F·H2O]+. The simulations show the formation of H2O+ + F, which is the predominant experimentally observed product channel. Suggestions are proposed for the formation mechanisms of the minor products, for example, the very interesting H2F+, which involves significant geometrical rearrangement. Analysis of the results suggests interesting future directions for the exploration of photodetachment of anionic clusters in an intense laser field.

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.

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.

Visible Light Absorption of N-Doped TiO2 Rutile Using (LR/RT)-TDDFT and Active Space EOMCCSD Calculations

We have performed detailed ground- and excited-state calculations of pure and N-doped TiO2 rutile to model and analyze the experimentally observed UV/vis spectrum. Using our embedding model, we have performed both linear response (LR) and real-time (RT) TDDFT calculations of the excited states of the pure and N-doped systems. We have also studied the lowest excitations using high-level active space equation-of-motion coupled cluster (EOMCC) approaches involving all single and interband double excitations. We compare and contrast the nature of the excitations in detail for the pure and doped systems and also provide an analysis of the excited-state density using our RT-TDDFT calculations. Our calculations indicate a lowering of the band gap and verify the role of the N3– states on the observed spectrum of N-doped TiO2 rutile as suggested by experimental findings. Both RT-TDDFT and EOMCC calculations show that the excitations in pure TiO2 are more delocalized compared with the N-doped system.

Embedding vs Supermolecular Strategies in Evaluating the Hydrogen-Bonding-Induced Shifts of Excitation Energies

Shifts in the excitation energy of the organic chromophore, cis-7-hydroxyquinoline (cis-7HQ), corresponding to the π→π* transition in cis-7HQ and induced by the complexation with a variety of small hydrogen-bonded molecules, obtained with the frozen-density embedding theory (FDET), are compared with the results of the supermolecular equation-of-motion coupled-cluster (EOMCC) calculations with singles, doubles, and non-iterative triples, which provide the reference theoretical data, the supermolecular time-dependent density functional theory (TDDFT) calculations, and experiment. Unlike in the supermolecular EOMCC and TDDFT cases, where each complexation-induced spectral shift is evaluated by performing two separate calculations, one for the complex and another one for the isolated chromophore, the FDET shifts are evaluated as the differences of the excitation energies determined for the same many-electron system, representing the chromophore fragment with two different effective potentials. By considering eight complexes of cis-7HQ with up to three small hydrogen-bonded molecules, it is shown that the spectral shifts resulting from the FDET calculations employing non-relaxed environment densities and their EOMCC reference counterparts are in excellent agreement with one another, whereas the analogous shifts obtained with the supermolecular TDDFT method do not agree with the EOMCC reference data. The average absolute deviation between the complexation-induced shifts, which can be as large, in absolute value, as about 2000 cm-1, obtained using the non-relaxed FDET and supermolecular EOMCC approaches that represent two entirely different computational strategies, is only about 100 cm-1, i.e., on the same order as the accuracy of the EOMCC calculations. This should be contrasted with the supermolecular TDDFT calculations, which produce the excitation energy shifts that differ from those resulting from the reference EOMCC calculations by about 700 cm-1 on average. Among the discussed issues are the choice of the electronic density defining the environment with which the chromophore interacts, which is one of the key components of FDET considerations, the basis set dependence of the FDET, supermolecular TDDFT, and EOMCC results, the usefulness of the monomer vs supermolecular basis expansions in FDET considerations, and the role of approximations that are used to define the exchange-correlation potentials in FDET and supermolecular TDDFT calculations.

TD-CI Simulation of the Electronic Optical Response of Molecules in Intense Fields: Comparison of RPA, CIS, CIS(D), and EOM-CCSD

A number of different levels of theory have been tested in TD-CI simulations of the response of butadiene interacting with very short, intense laser pulses. Excitation energies and transition dipoles were calculated with linear-response time-dependent Hartree-Fock (also known as the random phase approximation, RPA), configuration interaction in the space of single excitations (CIS), perturbative corrections to CIS involving double excitations [CIS(D)], and the equation-of-motion coupled-cluster (EOM-CC) method using the 6-31G(d,p) basis set augmented with n = 0-3 sets of diffuse sp functions on all carbons and only on the end carbons [6-31 n+ G(d,p) and 6-31(n+)G(d,p), respectively]. Diffuse functions are particularly important for transitions between the pseudocontinuum states above the ionization threshold. Simulations were carried out with a three-cycle Gaussian pulse (ω = 0.06 au, 760 nm) with intensities up to 1.26 × 10(14) W cm(-2) directed along the vector connecting the end carbons. Depending on the basis set, up to 500 excited states were needed for the simulations. Under the conditions selected, the response was too weak with the 6-31G(d,p) basis set, and the difference between levels of theory was more pronounced. When two or three set of diffuse functions were included on all of the carbons, the RPA, CIS, and EOM-CC results were comparable, but the CIS(D) response was too large compared to the more accurate EOM-CC calculations. Even though the frequency of the pulse is not resonant with any of the ground-to-excited transitions, excitations to valence and pseudocontinuum states occur readily above a threshold in the intensity.

Two-dimensional (2+n) resonance enhanced multiphoton ionization of HCl: Photorupture channels via the FΔ21 Rydberg state and ab initio spectra

Mass spectra were recorded for (2+n) resonance enhanced multiphoton ionization (REMPI) of HCl as a function of resonance excitation energy in the 82 600-88 100 cm(-1) region to obtain two-dimensional REMPI data. Analysis of ion-mass signal intensities for excitations via the F (1)Delta(2)(v(')=0-2) and the V (1)Sigma(+)(v(')) states as a function of rotational quantum numbers in the intermediate states either revealed near-resonance interactions or no significant coupling between the F (1)Delta(2) and the V (1)Sigma(+) states, depending on quantum levels. Ion-signal intensities and power dependence measurements allowed us to propose photoionization mechanisms in terms of intermediate state involvement. Based on relative ion-signal intensities and rotational line positions we quantified the contributions of Rydberg and valence intermediate states to the photoionization product formation and evaluated coupling strengths for state mixing. Time-dependent density functional theory (TD-DFT), equation-of-motion coupled cluster (EOM-CC), and completely renormalized EOM-CC calculations with various basis sets were performed to derive singlet state potential energy curves, relevant spectroscopic parameters, and to calculate spectra. Experimentally observed spectra and older calculations are compared with the reported ab initio results.

Anharmonic vibrational state calculations in the electronic excited states studied by time-dependent density functional theory

Time-dependent density functional theory (TDDFT) is combined with the correlation-corrected vibrational self-consistent field method to calculate the fundamental vibrational frequencies of the electronic excited states of diatomic, triatomic, and tetraatomic molecules. Equation of motion coupled-cluster calculations are also carried out for comparison. TDDFT is shown to provide the harmonic and anharmonic frequencies for various excited states with reasonable accuracy by using hybrid functionals, except that several vibrational modes such as hydrogen atom stretching exhibit sizable discrepancies due to the lack of orbital relaxation process in TDDFT.

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.

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+.

What Parameters Determine N−N and O−O Coupling Constants (2hJX-X) Across X−H+−X Hydrogen Bonds?

Equation of motion coupled-cluster calculations (EOM-CCSD) have been performed to obtain 15N−15N and 17O−17O coupling constants (2hJX-X) across N−H+−N and O−H+−O hydrogen bonds in a series of protonated dimers. 2hJX-X values are dominated by the Fermi-contact term and are distance dependent. Large coupling constants are associated with symmetric hydrogen bonds, short hydrogen bond distances, and low electron densities on the hydrogen-bonded proton, and are not related to the binding energies of these complexes. The magnitudes of coupling constants do not appear to be related to the nature of the covalent bonding of the hydrogen-bonded nitrogen and oxygen atoms, although this bonding indirectly determines the coupling constant by determining the N−N or O−O distance. Complexes with sp2-hybridized oxygens are more sensitive to the trans or cis orientation of the hydrogen-bonded pairs than are the corresponding nitrogen complexes. One-bond coupling constants (1hJX-H) are greater than two-bond couplings (2hJX-...

Ab initio coupled-cluster study of 2II radicals in ground and excited states: application to NCO and NCS

In this paper we report EOM-CC (equation-of-motion coupled-cluster) calculations on the X ̃ 2Π and B ̃ 2Π states of NCO and NCS radicals. Equilibrium bond length, rotational constant, harmonic vibrational frequencies, Renner—Teller parameter and spin—orbit splitting values are presented and compared to the available experimental data. The results show clearly that the calculated molecular parameters are accurate enough to be used in assigning experimental spectra.

Calculation of size-intensive transition moments from the coupled cluster singles and doubles linear response function

Coupled cluster singles and doubles linear response (CCLR) calculations have been carried out for excitation energies and dipole transition strengths for the lowest excitations in LiH, CH+, and C4 and the results compared with the results from a CI-like approach to equation of motion coupled cluster (EOMCC). The transition strengths are similar in the two approaches for single molecule calculations on small systems. However, the CCLR approach gives size-intensive dipole transition strengths, while the EOMCC formalism does not. Thus, EOMCC calculations can give unphysically dipole transition strengths, e.g., in EOMCC calculations on a sequence of noninteracting LiH systems we obtained a negative dipole strength for the lowest totally symmetric dipole allowed transition for 19 or more noninteracting LiH systems. The CCLR approach is shown to be a very attractive ‘‘black box’’ approach for the calculation of transition moments.