Coupled-cluster Singles Doubles Research Articles

Accelerated coupled cluster calculations with Procrustes orbital interpolation.

The coupled cluster method is considered a gold standard in quantum chemistry, reliably giving energies that are exact within chemical accuracy (1.6 mhartree). However, even in the coupled cluster single-double (CCSD) approximation, where the cluster operator is truncated to include only single and double excitations, the method scales as O(N6) in the number of electrons, and the cluster operator needs to be solved for iteratively, increasing the computation time. Inspired by eigenvector continuation, we present here an algorithm making use of the Gaussian processes that provides an improved initial guess for the coupled cluster amplitudes. The cluster operator is written as a linear combination of sample cluster operators that are obtained at particular sample geometries. By reusing the cluster operators from previous calculations in that way, it is possible to obtain a start guess for the amplitudes that surpasses both MP2 guesses and "previous geometry"-guesses in terms of the number of necessary iterations. As this improved guess is very close to the exact cluster operator, it can be used directly to calculate the CCSD energy to chemical accuracy, giving approximate CCSD energies scaling as O(N5).

Magnetic circular dichroism within the algebraic diagrammatic construction scheme of the polarization propagator up to third order.

We present an implementation of the B term of Magnetic Circular Dichroism (MCD) within the Algebraic Diagrammatic Construction (ADC) scheme of the polarization propagator and its Intermediate State Representation. As illustrative results, the MCD spectra of the ADC variants ADC(2), ADC(2)-x, and ADC(3) of the molecular systems uracil, 2-thiouracil, 4-thiouracil, purine, hypoxanthine 1,4-naphthoquinone, 9,10-anthraquinone, and 1-naphthylamine are computed and compared with results obtained by using the Resolution-of-Identity Coupled-Cluster Singles and Approximate Doubles method, with literature Time-Dependent Density Functional Theory results, and with available experimental data.

Coupling Natural Orbital Functional Theory and Many-Body Perturbation Theory by Using Nondynamically Correlated Canonical Orbitals.

We develop a new family of electronic structure methods for capturing at the same time the dynamic and nondynamic correlation effects. We combine the natural orbital functional theory (NOFT) and many-body perturbation theory (MBPT) through a canonicalization procedure applied to the natural orbitals to gain access to any MBPT approximation. We study three different scenarios: corrections based on second-order Møller-Plesset (MP2), random-phase approximation (RPA), and coupled-cluster singles doubles (CCSD). Several chemical problems involving different types of electron correlation in singlet and multiplet spin states have been considered. Our numerical tests reveal that RPA-based and CCSD-based corrections provide similar relative errors in molecular dissociation energies (De) to the results obtained using a MP2 correction. With respect to the MP2 case, the CCSD-based correction improves the prediction, while the RPA-based correction reduces the computational cost.

PDG: A Composite Method Based on the Resolution of the Identity.

The Gaussian-3 (G3) composite approach for thermochemical properties is revisited in light of the enhanced computational efficiency and reduced memory costs by applying the resolution-of-the-identity (RI) approximation for two-electron repulsion integrals (ERIs) to the computationally demanding component methods in the G3 model: the energy and gradient computations via the second-order Møller-Plesset perturbation theory (MP2) and the energy computations using the coupled-cluster singles-doubles method augmented with noniterative triples corrections [CCSD(T)]. Efficient implementation of the RI-based methods is achieved by employing a hybrid distributed/shared memory model based on MPI and OpenMP. The new variant of the G3 composite approach based on the RI approximation is termed the RI-G3 scheme, or alternatively the PDG method. The accuracy of the new RI-G3/PDG scheme is compared to the "standard" G3 composite approach that employs the memory-expensive four-center ERIs in the MP2 and CCSD(T) calculations. Taking the computation of the heats of formation of the closed-shell molecules in the G3/99 test set as a test case, it is demonstrated that the RI approximation introduces negligible changes to the mean absolute errors relative to the standard G3 model (less than 0.1 kcal/mol), while the standard deviations remain unaltered. The efficiency and memory requirements for the RI-MP2 and RI-CCSD(T) methods are compared to the standard MP2 and CCSD(T) approaches, respectively. The hybrid MPI/OpenMP-based RI-MP2 energy plus gradient computation is found to attain a 7.5× speedup over the standard MP2 calculations. For the most demanding CCSD(T) calculations, the application of the RI approximation is found to nearly halve the memory demand, confer about a 4-5× speedup for the CCSD iterations, and reduce the computational time for the compute-intensive triples correction step by several hours.

Effects of perturbation order and basis set on alchemical predictions.

Alchemical perturbation density functional theory has been shown to be an efficient and computationally inexpensive way to explore chemical compound space. We investigate approximations made, in terms of atomic basis sets and the perturbation order, introduce an electron-density based estimate of errors of the alchemical prediction, and propose a correction for effects due to basis set incompleteness. Our numerical analysis of potential energy estimates, and resulting binding curves, is based on coupled-cluster single double (CCSD) reference results and is limited to all neutral diatomics with 14 electrons (AlH⋯NN). The method predicts binding energy, equilibrium distance, and vibrational frequencies of neighboring out-of-sample diatomics with near CCSD quality using perturbations up to the fifth order. We also discuss simultaneous alchemical mutations at multiple sites in benzene.

Transition-Dipole Moments for Electronic Excitations in Strong Magnetic Fields Using Equation-of-Motion and Linear Response Coupled-Cluster Theory.

An implementation of transition-dipole moments at the equation-of-motion coupled-cluster singles-doubles (EOM-CCSD) and CCSD linear response (LR) levels of theory for the treatment of atoms and molecules in strong magnetic fields is presented. The presence of a finite magnetic field leads, in general, to a complex wave function and a gauge-origin dependence, necessitating a complex computer code together with the use of gauge-including atomic orbitals. As in the field-free case, for EOM-CC, the evaluation of transition-dipole moments consists of setting up the one-electron transition-density matrix (TDM) which is then contracted with dipole-moment integrals. In the case of CC-LR, the evaluation proceeds with a modified TDM but additionally requires a second contribution accounting for the amplitude response which is missing in EOM-CC theory for properties. We present a selected set of transitions for the sodium atom and investigate the LiH molecule in both a parallel as well as a perpendicular magnetic field. The dependence of excited-state energies and transition moments on the magnetic-field strength is discussed with a focus on magnetic-field-induced avoided crossings. Additionally, the differences between field-dependent EOM-CCSD and CCSD-LR transition moments are investigated.

The competitive formation mechanism of N-nitrosodimethylamine and formaldehyde dimethylhydrazone from 1,1-dimethylhydrazine during ozonation in air: A combined theoretical and experimental study

In order to controlling the yields of N-nitrosodimethylamine (NDMA), a highly human carcinogen, the competitive formation mechanism of NDMA and formaldehyde dimethylhydrazone (FDMH) from 1,1-dimethylhydrazine (UDMH) ozonation have been explored experimentally using gas chromatography-mass spectroscopy (GC–MS). Further, the results have been explained computationally using density functional theory (DFT) methods, as well as coupled cluster single-double (CCSD) methods, FDMH is not only an intermediate, but also a competitor for NDMA formation from UDMH. NDMA formation proceeds via H-abstraction from –NH2 moiety, while FDMH formation proceeds via H-abstraction from –CH3 moiety. The newly discovered NDMA formation mechanisms are: H-abstraction, diazene formation, O-addition. As ozone concentrations increases, the yields of NDMA rise accordingly. In addition, the theory results show that it is easier for NDMA to form from FDMH than that from UDMH. This study aims in providing a more detailed NDMA formation mechanism from UDMH than previous studies.

Modeling the hydrogen sulfide binding to heme

The binding of hydrogen sulfide to a model heme compound is investigated by coupled-cluster singles-doubles augmented by a perturbative triple excitations, CCSD(T), and density functional theory, DFT. The minimum energy path for the H2S addition to an isolated heme center of the heme protein is evaluated by adopting as a model the heme compound FeP(Im) (P = porphyrin; Im = imidazole). The FeP(Im)-H2S aduct is bound by 13.7 kcal/mol at the CCSD(T) level of theory. Relaxed potential energy curves for the lowest lying spin states of the H2S to FeP(Im) binding using DFT reveal that the binding process is associated with a “double spin-crossover” reaction with the existence of long-distance van der Waals minima only 5–7 kcal/mol above the FeP(Im)-H2S ground state. The fact that the energy of the singlet ground state of FeP(Im)-H2S is so close in energy to the dissociation products FeP(Im) + H2S points towards the reversibility of the H2S adsorption/desorption process in biochemical reactions.

Inclusion of orbital relaxation and correlation through the unitary group adapted open shell coupled cluster theory using non-relativistic and scalar relativistic Hamiltonians to study the core ionization potential of molecules containing light to medium-heavy elements.

The orbital relaxation attendant on ionization is particularly important for the core electron ionization potential (core IP) of molecules. The Unitary Group Adapted State Universal Coupled Cluster (UGA-SUMRCC) theory, recently formulated and implemented by Sen et al. [J. Chem. Phys. 137, 074104 (2012)], is very effective in capturing orbital relaxation accompanying ionization or excitation of both the core and the valence electrons [S. Sen et al., Mol. Phys. 111, 2625 (2013); A. Shee et al., J. Chem. Theory Comput. 9, 2573 (2013)] while preserving the spin-symmetry of the target states and using the neutral closed-shell spatial orbitals of the ground state. Our Ansatz invokes a normal-ordered exponential representation of spin-free cluster-operators. The orbital relaxation induced by a specific set of cluster operators in our Ansatz is good enough to eliminate the need for different sets of orbitals for the ground and the core-ionized states. We call the single configuration state function (CSF) limit of this theory the Unitary Group Adapted Open-Shell Coupled Cluster (UGA-OSCC) theory. The aim of this paper is to comprehensively explore the efficacy of our Ansatz to describe orbital relaxation, using both theoretical analysis and numerical performance. Whenever warranted, we also make appropriate comparisons with other coupled-cluster theories. A physically motivated truncation of the chains of spin-free T-operators is also made possible by the normal-ordering, and the operational resemblance to single reference coupled-cluster theory allows easy implementation. Our test case is the prediction of the 1s core IP of molecules containing a single light- to medium-heavy nucleus and thus, in addition to demonstrating the orbital relaxation, we have addressed the scalar relativistic effects on the accuracy of the IPs by using a hierarchy of spin-free Hamiltonians in conjunction with our theory. Additionally, the contribution of the spin-free component of the two-electron Gaunt term, not usually taken into consideration, has been estimated at the Self-Consistent Field (ΔSCF) level and is found to become increasingly important and eventually quite prominent for molecules with third period atoms and below. The accuracies of the IPs computed using UGA-OSCC are found to be of the same order as the Coupled Cluster Singles Doubles (ΔCCSD) values while being free from spin contamination. Since the UGA-OSCC uses a common set of orbitals for the ground state and the ion, it obviates the need of two N5 AO to MO transformation in contrast to the ΔCCSD method.

Similarity transformed equation of motion coupled-cluster theory based on an unrestricted Hartree-Fock reference for applications to high-spin open-shell systems.

The similarity transformed equation of motion coupled-cluster approach is extended for applications to high-spin open-shell systems, within the unrestricted Hartree-Fock (UHF) formalism. An automatic active space selection scheme has also been implemented such that calculations can be performed in a black-box fashion. It is observed that both the canonical and automatic active space selecting similarity transformed equation of motion (STEOM) approaches perform about as well as the more expensive equation of motion coupled-cluster singles doubles (EOM-CCSD) method for the calculation of the excitation energies of doublet radicals. The automatic active space selecting UHF STEOM approach can therefore be employed as a viable, lower scaling alternative to UHF EOM-CCSD for the calculation of excited states in high-spin open-shell systems.

First principles electron-correlated calculations of optical absorption in magnesium clusters

In this paper, we report large-scale configuration interaction (CI) calculations of linear optical absorption spectra of various isomers of magnesium clusters Mg$_{n}$ (n=2--5), corresponding to valence transitions. Geometry optimization of several low-lying isomers of each cluster was carried out using coupled-cluster singles doubles (CCSD) approach, and these geometries were subsequently employed to perform ground and excited state calculations using either the full-CI (FCI) or the multi-reference singles-doubles configuration interaction (MRSDCI) approach, within the frozen-core approximation. Our calculated photoabsorption spectrum of magnesium dimer (Mg$_{2}$) isomer is in excellent agreement with the experiments both for peak positions, and intensities. Owing to the sufficiently inclusive electron-correlation effects, these results can serve as benchmarks against which future experiments, as well as calculations performed using other theoretical approaches, can be tested.

Equation-of-motion coupled-cluster methods for atoms and molecules in strong magnetic fields.

A program for the direct calculation of excitation energies of atoms and molecules in strong magnetic fields is presented. The implementation includes the equation-of-motion coupled-cluster singles-doubles (EOM-CCSD) method for electronically excited states as well as its spin-flip variant. Differences to regular EOM-CCSD implementations are due to the appearance of the canonical angular-momentum operator in the Hamiltonian causing the wave function to become complex. The gauge-origin problem is treated by the use of gauge-including atomic orbitals. Therefore, a modified Davidson method for diagonalizing complex non-Hermitian matrices is used. Excitation energies for selected atoms and molecules that are of importance in the astrochemical context are presented and their dependence on the magnetic field is discussed.

Ultrafast excited-state relaxation of a binuclear Ag(i) phosphine complex in gas phase and solution.

The binuclear complex [Ag2(dcpm)2](PF6)2 (dcpm = bis(dicyclohexylphosphino)methane) exhibits a structure with a close silver-silver contact mediated by the bridging ligand and thus a weak argentophilic interaction. Upon electronic excitation this cooperative effect is strongly increased and determines the optical and luminescence properties of the compound. We have studied here the ultrafast electronic dynamics in parallel in gas phase by transient photodissociation and in solution by transient absorption. In particular, we report the diverse photofragmentation pathways of isolated [Ag2(dcpm)2]2+ in an ion trap and its gas phase UV photodissociation spectrum. By pump-probe fragmentation action spectroscopy (λex = 260 nm) in the gas phase, we have obtained fragment-specific transients which exhibit a common ultrafast multiexponential decay. This is fitted to four time constants (0.6/5.8/100/>1000 ps), highlighting complex intrinsic photophysical processes. Remarkably, multiexponential dynamics (0.9/8.5/73/604 ps) are as well found for the relaxation dynamics in acetonitrile solution. Ab initio calculations at the level of approximate coupled-cluster singles-doubles (CC2) theory of ground and electronically excited states of the reduced model system [Ag2(dmpm)2]2+ (dmpm = bis(dimethylphosphino)methane) indicate a shortening of the Ag-Ag distance upon excitation by 0.3-0.4 Å. In C2 geometry two close-lying singlet states S1 (1MC(dσ*-pπ), 1B, 4.13 eV) and S2 (1MC(dσ*-pσ), 1A, 4.45 eV) are found. The nearly dark S1 state has not been reported so far. The excitation of the S2 state carries a large oscillator strength for the calculated vertical transition (266 nm). Two related triplets are calculated at T1 (3.87 eV) and T2 (3.90 eV). From these findings we suggest possible relaxation pathways with the two short time constants ascribed to ISC/IVR and propose from the obtained similar values in gas phase that the fast solution dynamics is dominated by intramolecular processes. A further relaxation by IC/IVR in the triplet manifold is likely to account for the observed intermediate time constants. For the acetonitrile relaxation dynamics additional modifications are invoked based on solvent-induced shifts of the energy levels and the possible formation of solvent and counterion exciplexes on a longer timescale.

Benchmarking Quantum Chemical Methods for Optical Absorption in Boron Wheels.

We benchmark various quantum chemical methods for calculating the optical absorption in planar boron wheel clusters. The geometries of neutral planar boron wheels B7, B8, and B9 clusters are optimized at the coupled-cluster singles doubles level of theory. The optical absorption spectra of these clusters are calculated using three wave-function-based methods, namely, configuration interaction singles, random phase approximation, and equation-of-motion coupled-cluster singles doubles (EOM-CCSD) as well as using a time-dependent density-functional-theory-based method using various hybrid and long-range-corrected exchange and correlation functionals. There is an ample variation in the optical absorption spectra computed using different density functionals. When compared to the EOM-CCSD spectrum, an excellent agreement is provided by CAM-B3LYP functional, followed by ωB97xD functional. PBE0, B3LYP, and B3PW91 functionals agree among each other. However, their spectra are red-shifted with respect to the EOM-CCSD counterpart. On the basis of the natural transition orbital analysis, the nature of optical excitation is also discussed.

UV fragmentation and ultrafast dynamics of trinuclear silver/1-methylthymine and silver/1-methyluracil metal-base pairs in an ion trap

We report on gas phase UV action spectroscopy and photodynamics of [Ag3(1MT-H/1MU-H)2]+ comprised of a linear silver string and two deprotonated 1-methyl-thymine/uracil (1MT/1MU) ligands. We applied pump–probe femtosecond laser photofragmentation in an electrospray ion trap mass spectrometer and high-level ab initio calculations at the level of approximate coupled-cluster singles-doubles theory. The experimental UV band at 283/275nm is assigned to a red shifted 1ππ∗ nucleobase located transition. Relaxation of the 1ππ∗ state occurs with time constants of 0.2/1.1ps and 0.2/4.2ps for the 1MT and 1MU complexes, respectively, on a similar ultrafast time scale as non-metalated uracil derivatives.

Optical Rotation from Coupled Cluster and Density Functional Theory: The Role of Basis Set Convergence.

We have calculated the electronic optical rotation of seven molecules using coupled cluster singles-doubles (CCSD) and the second-order approximation (CC2) employing the aug-cc-pVXZ (X = D, T, or Q) basis sets. We have also compared to time-dependent density functional theory (TDDFT) by utilizing two functionals B3LYP and CAM-B3LYP and the same basis sets. Using relative and absolute error schemes, our calculations demonstrate that the CAM-B3LYP functional predicts optical rotation with the minimum deviations compared to CCSD at λ = 355 and 589.3 nm. Furthermore, our results illustrate that the aug-cc-pVDZ basis set provides the optical rotation in good agreement with the larger basis sets for molecules not possessing small-angle optical rotation at λ = 589.3 nm. We have also performed several two-point inverse power extrapolations for the basis set convergence, i.e., OR(∞) + AX(-n), using the CC2 model at λ = 355 and 589.3 nm. Our results reveal that a two-point inverse power extrapolation with the aug-cc-pVTZ and aug-cc-pVQZ basis sets at n = 5 provides optical rotation deviations similar to those of aug-cc-pV5Z with respect to the basis limit.

Hydrogen storage on metal oxide model clusters using density-functional methods and reliable van der Waals corrections

We investigate the capability of low-coordinated sites on small model clusters to act as active centers for hydrogen storage. A set of small magic clusters with the formula (XY)6 (X = Mg, Ba, Be, Zn, Cd, Na, Li, B and Y = O, Se, S, F, I, N) and a "drumlike" hexagonal shape showing a low coordination number of three was screened. Oxide clusters turned out to be the most promising candidates for hydrogen storage. For these ionic compounds we explored the suitability of different van der Waals (vdW) corrections to density-functional calculations by comparing the respective H2 physisorption profile to highly accurate CCSD(T) (Coupled Cluster Singles Doubles with perturbative Triples) calculations. The Grimme D3 vdW correction in combination with the Perdew-Burke-Ernzerhof exchange-correlation functional was found to be the best approach compared to CCSD(T) hydrogen physisorption profiles and is, therefore, suited to study these and other light metal oxide systems. H2 adsorption on sites of oxide model clusters is found to meet the adsorption energy criteria for H2 storage, with bond strengths ranging from 0.15 to 0.21 eV. Energy profiles and estimates of kinetic constants for the H2 splitting reaction reveal that H2 is likely to be adsorbed molecularly on sites of (MgO)6, (BaO)6, and (BeO)6 clusters, suggesting a rapid H2 uptake/release at operating temperatures and moderate pressures. The small mass of beryllium and magnesium makes such systems appealing for meeting the gravimetric criterion for H2 storage.

Large-scale first principles configuration interaction calculations of optical absorption in aluminum clusters.

We report the linear optical absorption spectra of aluminum clusters Aln (n = 2-5) involving valence transitions, computed using the large-scale all-electron configuration interaction (CI) methodology. Several low-lying isomers of each cluster were considered, and their geometries were optimized at the coupled-cluster singles-doubles (CCSD) level of theory. With these optimized ground-state geometries, excited states of different clusters were computed using the multi-reference singles-doubles configuration-interaction (MRSDCI) approach, which includes electron correlation effects at a sophisticated level. These CI wave functions were used to compute the transition dipole matrix elements connecting the ground and various excited states of different clusters, and thus their photoabsorption spectra. The convergence of our results with respect to the basis sets, and the size of the CI expansion, was carefully examined. Our results were found to be significantly different as compared to those obtained using time-dependent density functional theory (TDDFT) [Deshpande et al. Phys. Rev. B: Condens. Matter Mater. Phys., 2003, 68, 035428]. When compared to the available experimental data for the isomers of Al2 and Al3, our results are in very good agreement as far as important peak positions are concerned. The contribution of configurations to many body wave functions of various excited states suggests that in most cases optical excitations involved are collective, and plasmonic in nature.

Coupled-cluster single-double theory study on the analytic potential energy function of the SeN2 radicals

The coupled-cluster single-double (CCSD) theory in combination with the quadruple correlation-consistent basis set (cc-pVQZ) of Dunning and co-workers is employed to estimate the equilibrium geometry, dissociation energy and vibrational frequencies of the SeN2 radical. The computational results show that the ground state of SeN2 has C2v symmetry and its ground electronic state is X1A1. The equilibrium parameters of the structure are RSe-N=0.1691 nm, RN-N=0.1970 nm, αN-Se-N =71.289°, and the dissociation energy is De=4.78 eV. The vibrational frequencies are ν1=326.9288 cm-1, ν2=808.0161 cm-1, and ν3=948.3430 cm-1, respectively. The whole potential curves for the ground electronic states of SeN and N2 are further scanned using the above method, the potential energy functions and relevant spectroscopic constants are then obtained by least square fitting to the Murrell-Sorbie function. Compared with other theoretical results and the experimental values, our computational results are very accurate. Then the analytic potential energy function of SeN2 is derived by many-body expansion theory. The potential curves correctly describe the configurations and the dissociation energy for the SeN2 radical.

Density functional theory study of the interaction of vinyl radical, ethyne, and ethene with benzene, aimed to define an affordable computational level to investigate stability trends in large van der Waals complexes

Our purpose is to identify a computational level sufficiently dependable and affordable to assess trends in the interaction of a variety of radical or closed shell unsaturated hydro-carbons A adsorbed on soot platelet models B. These systems, of environmental interest, would unavoidably have rather large sizes, thus prompting to explore in this paper the performances of relatively low-level computational methods and compare them with higher-level reference results. To this end, the interaction of three complexes between non-polar species, vinyl radical, ethyne, or ethene (A) with benzene (B) is studied, since these species, involved themselves in growth processes of polycyclic aromatic hydrocarbons (PAHs) and soot particles, are small enough to allow high-level reference calculations of the interaction energy ΔEAB. Counterpoise-corrected interaction energies ΔEAB are used at all stages. (1) Density Functional Theory (DFT) unconstrained optimizations of the A-B complexes are carried out, using the B3LYP-D, ωB97X-D, and M06-2X functionals, with six basis sets: 6-31G(d), 6-311 (2d,p), and 6-311++G(3df,3pd); aug-cc-pVDZ and aug-cc-pVTZ; N07T. (2) Then, unconstrained optimizations by Møller-Plesset second order Perturbation Theory (MP2), with each basis set, allow subsequent single point Coupled Cluster Singles Doubles and perturbative estimate of the Triples energy computations with the same basis sets [CCSD(T)//MP2]. (3) Based on an additivity assumption of (i) the estimated MP2 energy at the complete basis set limit [EMP2/CBS] and (ii) the higher-order correlation energy effects in passing from MP2 to CCSD(T) at the aug-cc-pVTZ basis set, ΔECC-MP, a CCSD(T)/CBS estimate is obtained and taken as a computational energy reference. At DFT, variations in ΔEAB with basis set are not large for the title molecules, and the three functionals perform rather satisfactorily even with rather small basis sets [6-31G(d) and N07T], exhibiting deviation from the computational reference of less than 1 kcal mol(-1). The zero-point vibrational energy corrected estimates Δ(EAB+ZPE), obtained with the three functionals and the 6-31G(d) and N07T basis sets, are compared with experimental D0 measures, when available. In particular, this comparison is finally extended to the naphthalene and coronene dimers and to three π-π associations of different PAHs (R, made by 10, 16, or 24 C atoms) and P (80 C atoms).