EOM-CCSD Method Research Articles

Equation-of-motion regularized orbital-optimized second-order perturbation theory with the density-fitting approximation.

The density-fitted equation-of-motion (EOM) orbital-optimized second-order perturbation theory (DF-EOM-OMP2) method is presented for the first time. In addition, κ-DF-EOM-MP2 and κ-DF-EOM-OMP2 methods are implemented with the addition of κ-regularization. The accuracy of the DF-EOM-OMP2, κ-DF-EOM-MP2, and κ-DF-EOM-OMP2 methods are compared to the density-fitted EOM-MP2 (DF-EOM-MP2), EOM coupled-cluster (CC) singles and doubles (DF-EOM-CCSD), and EOM-CCSD with the triples excitation correction model [EOM-CCSD(fT)] for excitation energies of many closed- and open-shell chemical systems. The excitation energies computed using different test cases and methods were compared to the EOM-CCSD(fT) method and mean absolute errors (MAEs) are presented. The MAE values of closed- and open-shell cases (closed-shell organic chromophores set, open-shell set, peptide radicals set, and radical set) according to the EOM-CCSD(fT) method show that the κ-regularization technique yields highly accurate results for the first excited states. Our results indicate that the κ-DF-EOM-MP2 and κ-DF-EOM-OMP2 methods perform noticeably better than the DF-EOM-MP2 and DF-EOM-OMP2 methods. They approach the EOM-CCSD quality, at a significantly reduced cost, for the computation of excitation energies. Especially, the κ-DF-EOM-MP2 method provides outstanding results for most test cases considered. Overall, we conclude that the κ-versions of DF-EOM-MP2 and DF-EOM-OMP2 emerge as a useful computational tool for the study of excited-state molecular properties.

Efficient State-Specific Natural Orbital Based Equation of Motion Coupled Cluster Method for Core-Ionization Energies: Theory, Implementation, and Benchmark.

We have implemented a reduced-cost partial triples correction scheme to the equation of motion coupled cluster method for core-ionization energy based on state-specific natural orbitals. The second-order Algebraic Diagrammatic Construction (ADC) method is used to generate the state-specific natural orbital, which provides quicker convergence of the core-IP value with respect to the size of the virtual space than that observed in standard MP2-based natural orbitals. The error due to truncation of the virtual orbital can be reduced by using a perturbative correction. The accuracy of the method can be controlled by a single threshold, and there is a black box to use. The inclusion of the partial triples correction in the natural orbital based EOM-CCSD method greatly improves the agreement of the results with the experiment. The efficiency of the present implementation is demonstrated by calculating the core-ionization energy of a molecule containing 60 atoms and more than 2000 basis functions.

Constructing Multiresonance Thermally Activated Delayed Fluorescence Emitters for Organic LEDs: A Computational Investigation.

Multiple resonance thermally activated delayed fluorescence (MR-TADF) materials have acquired substantial attention due to their high electroluminescence efficiency with narrow emission spectra. However, the existing MR-TADF emitters suffer from substantial efficiency roll-off due to insufficient rate constants of the reverse intersystem crossing (kRISC) process compared to the traditional TADF materials. Herein, we employ the DLPNO-STEOM-CCSD method, which is computationally less expensive than the wave function-based EOM-CCSD method, to evaluate the electronic and photophysical properties of MR-TADF materials accurately. The predicted singlet-triplet energy gap (ΔEST), one of the critical parameters governing the TADF efficiency, exhibits remarkable agreement with the experimental measurement, with a standard deviation value of 0.026 eV (obtained based on five experimentally synthesized MR-TADF systems). The proposed technique was utilized to determine the suitability of 15 newly designed MR-TADF emitters via their computed radiative and nonradiative rates, luminescence efficiencies, and exciton characteristics. Moreover, most conceived molecules exhibit blue emission with decent to strong oscillator strengths, making them potential candidates for practical light-emitting applications. The proposed computational route will undoubtedly accelerate the designing and prescreening of potential MR-TADF emitters before their expensive laboratory synthesis and characterization.

Halogenation effects on the bridgehead position of the adamantane molecule

Halogen substitution effects on the bridgehead positioned carbon of adamantane molecule portraits many significant characteristics for the adamantane halides. As a result of the induction and electrostatic interaction caused by the substitution, large electron densities are formed around the halogens and a small positive electrostatic potential (σ-hole) is developed along the z-direction parallel to C-X bond axis. Computational study performed through EOM-CCSD method, B3LYP and WB97XD functionals of the density functional theory effectively supports this investigation in terms of molecular structure, vibrational properties, bonding behavior and electrostatic potential surfaces. Accordingly, substitution give rise to the change in the dipole moment and symmetry of the molecules. In addition, polarizabilities of the molecules along the C-X bond axis increases with respect to electron densities. HOMO-LUMO energy gap and positive σ-holes are found to decrease with the increase in the negative electron affinity. An anisotropic charge distribution developed upon substitution allows the adamantane halides to exhibit two different binding motifs like halogen and hydrogen bonding along the parallel and perpendicular directions of C-X bond. These characteristics feature of the halo adamantane finds applications in self-assembled monolayers, crystal engineering and biomedical applications.

EOM-CCSD-based neural network diabatic potential energy matrix for 1πσ*-mediated photodissociation of thiophenol

A new diabatic potential energy matrix (PEM) of the coupled 1ππ* and 1πσ* states for the 1πσ*-mediated photodissociation of thiophenol was constructed using a neural network (NN) approach. The diabatization of the PEM was specifically achieved by our recent method [Chin. J. Chem. Phys. 34, 825 (2021)], which was based on adiabatic energies without the associated costly derivative couplings. The equation of motion coupled cluster with single and double excitations (EOM-CCSD) method was employed to compute adiabatic energies of two excited states in this work due to its high accuracy, simplicity, and efficiency. The PEM includes three dimensionalities, namely the S−H stretch, C−S−H bend, and C−C−S−H torsional coordinates. The root mean square errors of the NN fitting for the S1 and S2 states are 0.89 and 1.33 meV, respectively, suggesting the high accuracy of the NN method as expected. The calculated lifetimes of the S1 vibronic 00 and 31 states are found to be in reasonably good agreement with available theoretical and experimental results, which validates the new EOM-CCSD-based PEM fitted by the NN approach. The combination of the diabatization scheme solely based on the adiabatic energies and the use of EOM-CCSD method makes the construction of reliable diabatic PEM quite simple and efficient.

A Core-Valence Separated Similarity Transformed EOM-CCSD Method for Core-Excitation Spectra.

We present the theory and implementation of a core-valence separated similarity transformed EOM-CCSD (STEOM-CCSD) method for K-edge core excitation spectra. The method can select an appropriate active space using CIS natural orbitals and near "black box" to use. The second similarity transformed Hamiltonian is diagonalized in the space of single excitation. Therefore, the final diagonalization step is free from the convergence problem arising due to the coupling of the core-excited states with the continuum of doubly excited states. Convergence trouble can appear for the preceding core-ionized state calculation in STEOM-CCSD. A core-valence separation (CVS) scheme compatible with the natural orbital based active space selection (CVS-STEOM-CCSD-NO) is implemented to overcome the problem. The CVS-STEOM-CCSD-NO has a similar accuracy to that of the standard CVS-EOM-CCSD method but comes with a lower computational cost. The modification required in the CVS scheme to make use of the CIS natural orbital is highlighted. The suitability of the CVS-STEOM-CCSD-NO method for chemical application is demonstrated by simulating the K-edge spectra of glycine and thymine.

The Challenge of Accurate Computation of Two-Photon Absorption Properties of Organic Chromophores in the Condensed Phase.

Two strategies are applied to evaluate the effect of the environment on the two-photon absorption (TPA) cross sections for two characteristic excited states of C2H4 upon complexation with H2O. The supermolecular strategy provides the reference complexation-induced shifts and uses either the EOM-CCSD or ADC(2) method. The embedding strategy is based on frozen-density-embedding theory (FDET) and uses only fundamental constants. The TPA cross sections from high-level supermolecular calculations are extremely basis-set-sensitive. Literature data and the present study indicate that accuracy of the absolute TPA cross sections below 100 atomic units and their shifts below 10 atomic units remains a challenge. The obtained FDET results show a similar basis-set behavior. For the largest basis set (d-aug-cc-pVQZ), TPA cross sections obtained from these two strategies are in excellent agreement. The complexation-induced shifts have the correct sign of the effect and a small (12-33%) relative error in magnitude. The deviations of the FDET-derived shifts from the reference are of similar magnitude as the reliability threshold of the reference shifts.

Electronic properties and primary dissociation channels of fluoromethane compounds

We investigated fluoromethane compounds (CF4, CF3, CHF3, CH2F2, and CH3F) to examine their electronic properties and primary dissociation channels by using computational chemistry. For the electron attachment process, it was very important to represent the observed negative mass spectrum as a function of electron energy that calculation by the MP2 method for the negative ion and subsequent calculation by the EOMCCSD method were used to more accurately estimate the ground and the first excited states of the negative ion. In the evaluation of dissociation channels through the excitation process, the structure change of the excited fragment (from pyramidal to planar) was taken into account. Evaluation of Jahn–Teller distortion for the highly symmetrical CHF3 and CH3F was also very important to estimate the fragmentation process through the excitation. The calculated results after these treatments gave satisfactory representation of the experimental values. Moreover some predictions of experimentally unknown values are proposed.

Approximate equation-of-motion coupled-cluster methods for electron affinities of closed-shell molecules.

We investigate performance of the equation-of-motion coupled-cluster method at the single and doubles level (EOM-CCSD) and a series of approximate methods based on EOM-CCSD on electron affinities (EA) of closed-shell cations and neutral molecules with positive and negative EAs in this work. Our results confirm that P-EOM-MBPT2 can provide reasonable EAs when molecules with significant multireference character are not considered and its mean absolute error on EAs of these molecules is around or less than 0.2 eV. Its accuracy is comparable to that of the more expensive EOM-CCSD(2) method. Results of EOM-CCSD(2), P-EOM-MBPT2, and CIS(D∞) indicate that the [[H, ac +], T2] term in the 1h2p-1h block is more important on EAs than the term neglected in the 1h2p-1h2p block in P-EOM-MBPT2. We proposed an economical method where EAs from CIS(D∞) are corrected by treating this [[H, ac +], T2] term in the 1h2p-1h block perturbatively [corr-CIS(D∞)]. EAs with corr-CIS(D∞) agree very well with those of P-EOM-MBPT2 with a difference of less than 0.02 eV. Computational scaling of this method is N4 for the iterative part and N5 for some non-iterative steps. Its storage requirement is only of OV3. Corr-CIS(D∞) is an economical and reliable method on EAs, and it can be applied to EAs of large molecules.

A TDDFT study of some dinuclear compounds containing CpM(CO)3 or CpM(CO)2 groups

The electronic structure and spectroscopy of some representative dinuclear compounds containing CpM(CO)3 and CpM(CO)2 groups were studied using TDDFT (Time Dependent Density Functional Theory). These compounds contain Cp (cyclopentadienyl) as a ligand, and M can be Cr, Mo or W. Their main electronic transitions were calculated and the results are in good agreement with the experimental data. This allows the assignment of some bands whose origin was not clear. In all the cases, the carbonyls and Cp groups restrict the symmetry. The molecular orbitals that would be involved in M-M bonding interact strongly with the carbonyls and show unusual shapes and occupations. The strongest electronic bands are caused by σ→σ* transitions in most of the molecules containing CpM(CO)3 groups, whereas in molecules such as Cp(CO)2M≡M(CO)2Cp the most intense bands are produced by π→π* transitions. The origin of other bands is now explained. The effect of the solvent on the electronic transitions and the use of EOM-CCSD method in some compounds were also checked.

Why does the presence of silicon atoms improve the emission properties of biphenyl derivatives? - Verification of various hypotheses by experiment and theory.

In the course of studying silicon modifications to improve emission properties of commonly used organic compounds, biphenyl with dimethylsilylvinyl groups in the para position (3-Si) was investigated. A comparative study was performed on the exact C-analogue (3-C) and expanded to biphenyl and dimethylbiphenyl to emphasize the general trend observed. Compound 3-Si displayed emission properties clearly different than all of the investigated hydrocarbon compounds, i.e. twice stronger fluorescence (Φf = 0.6) and a 3-times larger radiative rate constant as compared to 3-C in acetonitrile. Searching for the source of the unique emission of 3-Si, singlet and triplet processes were investigated for all of the compounds using steady-state and time-resolved methods, and their principal photophysical parameters are reported. Experimental work was supported by the theoretical predictions obtained using the EOM-CCSD method. The results led to the conclusion that the strong emission of 3-Si must be due to silicon's presence that enhanced intensity borrowing from the strongly allowed S0 → S2 transition and the larger S1 → S0 transition moment.

Calculations of electronic properties and vibrational parameters of alkaline-earth lithides: MgLi+ and CaLi+

ABSTRACTThe electronic ground states of MgLi and CaLi molecular ions are investigated for their spectroscopic constants and properties such as the dipole - and quadrupole moments, and static dipole polarisabilities. The quadrupole moments and the static dipole polarisabilities for these ions have been calculated and reported here, for the first time. The maximum possible error bars, arising due to the finite basis set and the exclusion of higher correlation effects beyond partial triples, are quoted for reliability. Further, the adiabatic effects such as diagonal Born-Oppenheimer corrections are also calculated for these molecules. The vibrational energies, the wavefunctions, and the relevant vibrational parameters are obtained by solving the vibrational Schrödinger equation using the potential energy curve and the permanent dipole moment curve of the molecular electronic ground state. Thereafter, spontaneous and black-body radiation induced transition rates are calculated to obtain the lifetimes of the vibrational states. The lifetime of rovibronic ground state for MgLi, at room temperature, is found to be and for CaLi it is . It has been observed that the lifetime of the highly excited vibrational state is several times larger than (comparable to) that of the vibrational ground state of MgLi (CaLi). In addition, a few low-lying electronic excited states of Σ and Π symmetries have been investigated for their electronic and vibrational properties, using EOM-CCSD method together with the QZ basis sets.

Exploring the Accuracy of a Low Scaling Similarity Transformed Equation of Motion Method for Vertical Excitation Energies.

The newly developed back transformed pair natural orbital based similarity transformed equation of motion (bt-STEOM) method at the coupled cluster singles and doubles level (CCSD) is combined with an appropriate modification of our earlier active space selection scheme for STEOM. The resulting method is benchmarked for valence, Rydberg, and charge transfer excited states of Thiel's test set and other test systems. The bt-PNO-STEOM-CCSD method gives very similar results to canonical STEOM-CCSD for both singlet and triplet excited states. It performs in a balanced manner for all these types of excited states, while the EOM-CCSD method performs especially well for Rydberg excited states and the CC2 method excels at obtaining accurate results for valence excited states. Both EOM-CCSD and CC2 perform worse than bt-PNO-STEOM-CCSD for charge transfer states for the test cases studied.

Photodissociation of FONO: an excited state nonadiabatic dynamics study.

The photo dissociation of nitrosyl fluorite, FONO, a potential source of atmospheric fluorine, underlies its active role in ozone depletion and other activities in the troposphere. In the present work, the electronic structure of FONO is revisited at high level of ab initio and density functional theory (DFT) theoretical levels. Several different post SCF methods were used to compute excited states, vertical excitation energies and intensities, namely configuration interaction with single excitations (CIS), equation of motion coupled cluster with single and double excitations (EOM-CCSD), and symmetry adopted cluster configuration interaction (SAC-CI) methods. The potential energy functions along two internal coordinates, namely the F-ONO bond and the FONO dihedral angle, have been computed on the ground state relaxed potential energy surface (PES) for the ground, 5A' and 5A″ excited states using the EOM-CCSD method. In the gas phase, the decay of the excited states of FONO was examined closely by calculating the UV photoabsorption cross-section spectrum and by nonadiabatic dynamics simulations. Nonadiabatic dynamics were simulated by sampling 300 trajectories in two spectral windows at 3.0 ± 0.25 and 4.5 ± 0.25eV using the surface hopping method. Two different photodissociation reaction pathways with two main products, including multifragmentation (FO+NO) and atomic elimination (F) mechanisms were identified. For the cis-isomer, the main photochemical channel is F+NO2, representing 67% of all processes. For the trans-isomer, however, the main dissociation pathway is (FO+NO). Graphical Abstract Photodisscociation of nitrosyl fluorite (FONO) seems to underlie its active role in ozone depletion and other activities in the troposphere. The present research revisits the electronic structure of FONO at high level of ab initio and DFT theoretical levels. Cis-trans isomerization and dissociation in the ground and low lying excited states were examined. Photoabsorption cross-section spectra were computed and nonadiabatic dynamics were launched for both cis and trans FONO isomers.

Perturbative approximation to hybrid equation of motion coupled cluster/effective fragment potential method

Hybrid quantum mechanics/molecular mechanics (QM/MM) methods provide an attractive way to closely retain the accuracy of the QM method with the favorable computational scaling of the MM method. Therefore, it is not surprising that QM/MM methods are being increasingly used for large chemical/biological systems. Hybrid equation of motion coupled cluster singles doubles/effective fragment potential (EOM-CCSD/EFP) methods have been developed over the last few years to understand the effect of solvents and other condensed phases on the electronic spectra of chromophores. However, the computational cost of this approach is still dominated by the steep scaling of the EOM-CCSD method. In this work, we propose and implement perturbative approximations to the EOM-CCSD method in this hybrid scheme to reduce the cost of EOM-CCSD/EFP. The timings and accuracy of this hybrid approach is tested for calculation of ionization energies, excitation energies, and electron affinities of microsolvated nucleic acid bases (thymine and cytosine), phenol, and phenolate.

TD-CI Simulation of the Electronic Optical Response of Molecules in Intense Fields II: Comparison of DFT Functionals and EOM-CCSD

Time-dependent configuration interaction (TD-CI) simulations can be used to simulate molecules in intense laser fields. TD-CI calculations use the excitation energies and transition dipoles calculated in the absence of a field. The EOM-CCSD method provides a good estimate of the field-free excited states but is rather expensive. Linear-response time-dependent density functional theory (TD-DFT) is an inexpensive alternative for computing the field-free excitation energies and transition dipoles needed for TD-CI simulations. Linear-response TD-DFT calculations were carried out with standard functionals (B3LYP, BH&HLYP, HSE2PBE (HSE03), BLYP, PBE, PW91, and TPSS) and long-range corrected functionals (LC-ωPBE, ωB97XD, CAM-B3LYP, LC-BLYP, LC-PBE, LC-PW91, and LC-TPSS). These calculations used the 6-31G(d,p) basis set augmented with three sets of diffuse sp functions on each heavy atom. Butadiene was employed as a test case, and 500 excited states were calculated with each functional. Standard functionals yield average excitation energies that are significantly lower than the EOM-CC, while long-range corrected functionals tend to produce average excitation energies slightly higher. Long-range corrected functionals also yield transition dipoles that are somewhat larger than EOM-CC on average. The TD-CI 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. The nonlinear response as indicated by the residual populations of the excited states after the pulse is far too large with standard functionals, primarily because the excitation energies are too low. The LC-ωPBE, LC-PBE, LC-PW91, and LC-TPSS long-range corrected functionals produce responses comparable to EOM-CC.

Multi-reference state-universal coupled-cluster approaches to electronically excited states

The multi-reference (MR), general model space (GMS), state-universal (SU), coupled-cluster (CC) method with singles and doubles (GMS-SU-CCSD), as well as its triple-corrected versions GMS-SU-CCSD(T), are employed to assess their ability to describe low-lying excited states of various molecules, with an emphasis on a simultaneous handling of several states of the same symmetry species. A special attention is given to the role of the so-called C-conditions that account for non-vanishing internal cluster amplitudes when relying on an incomplete GMS, as well as to the choice of suitable model spaces and a perturbative account of secondary triples. The ambiguities arising when using large basis sets are also pointed out. To achieve a general assessment of the potential of the GMS-type SU-CC approaches, the vertical excitation energies of several species, including the challenging BN diatomic as well as larger systems, namely formaldehyde, trans-butadiene, formamide, and benzene are considered. These results are compared with those provided by the equation-of-motion EOM-CCSD method and, whenever available, the density functional theory results and experimental data. These comparisons clearly demonstrate the usefulness of GMS-type MR-CC approaches.

ClClO2 Is the Most Stable Isomer of Cl2O2. Accurate Coupled Cluster Energetics and Electronic Spectra of Cl2O2 Isomers

High level ab initio electronic structure calculations at the coupled cluster level with a correction for triples (CCSD(T)) extrapolated to the complete basis set limit have been made for the thermodynamics of the Cl2O2 isomers: ClClO2, ClOOCl, and ClOClO. The ClClO2 isomer is predicted to be the most stable isomer and is more stable than ClOOCl by 3.1 kcal/mol at 298 K. The ClOClO isomer is less stable than ClOOCl by 8.3 kcal/mol at 298 K. The weakest bond in ClClO2 is the Cl-Cl bond with a bond dissociation energy (BDE) of 24.4 kcal/mol, and the smallest BDE in ClOOCl is the O-O bond with a value of 18.0 kcal/mol. The smallest BDE in ClOClO is for the central O-Cl bond with a BDE of 9.7 kcal/mol. Electronic transitions were calculated with the equations of motion EOM-CCSD method. The calculations clearly demonstrate that singlet states of ClClO2 absorb to longer wavelengths in the visible than do the singlet states of ClOOCl as does ClOClO.

Probing the proton‐transfer coordinate of complexes with FH…P hydrogen bonds using one‐ and two‐bond spin–spin coupling constants

Scalar coupling constants have been computed using the EOM-CCSD method for equilibrium structures of complexes stabilized by F--H...P hydrogen bonds, as well as structures along the proton-transfer coordinates of these complexes. Variations in the signs and absolute values of (1)J(F--H), (1h)J(H--P) and (2h)J(F--P) have been analyzed and interpreted in terms of changing hydrogen bond type. Of the three phosphorus bases (phosphine, trimethylphosphine and phosphinine) investigated in this study, trimethylphosphine forms the strongest complex with FH, and has the largest two-bond F--P coupling constant. Among the relatively simple phosphorus bases, it would appear to be a leading candidate for experimental NMR study. Similarities and differences are noted between the corresponding coupling constants (J) and the reduced coupling constants (K) across F--H...P and F--H...N hydrogen bonds.

Completely renormalized EOMCCSD(T) method employing independent optimization of the cluster product terms

In this Letter, we introduce a new variant of the completely renormalized equation-of-motion method with singles, doubles, and non-iterative triples (CR-EOMCCSD(T)) that employs a novel strategy of handling the cluster product terms that naturally appears in the EOMCC-type expansion for the trial wavefunction. The new parametrization, as shown on several examples, including the N 2, C 2, and the ozone molecule, assures the required flexibility of the CR-EOMCCSD(T) approach especially in dealing with the challenging excited states primarily dominated by double excitations.