Showing papers on "Coupled cluster published in 2013"
TL;DR: This work redesigns the LPNO-CCSD method with a new method based on the combination of the concepts of PNOs and projected atomic orbitals (PAOs), which is as accurate as the original method while leading to computational savings exceeding one order of magnitude for larger systems.
Abstract: In previous publications, it was shown that an efficient local coupled cluster method with single- and double excitations can be based on the concept of pair natural orbitals (PNOs) [F. Neese, A. Hansen, and D. G. Liakos, J. Chem. Phys. 131, 064103 (2009)]. The resulting local pair natural orbital-coupled-cluster single double (LPNO-CCSD) method has since been proven to be highly reliable and efficient. For large molecules, the number of amplitudes to be determined is reduced by a factor of 10(5)-10(6) relative to a canonical CCSD calculation on the same system with the same basis set. In the original method, the PNOs were expanded in the set of canonical virtual orbitals and single excitations were not truncated. This led to a number of fifth order scaling steps that eventually rendered the method computationally expensive for large molecules (e.g., >100 atoms). In the present work, these limitations are overcome by a complete redesign of the LPNO-CCSD method. The new method is based on the combination of the concepts of PNOs and projected atomic orbitals (PAOs). Thus, each PNO is expanded in a set of PAOs that in turn belong to a given electron pair specific domain. In this way, it is possible to fully exploit locality while maintaining the extremely high compactness of the original LPNO-CCSD wavefunction. No terms are dropped from the CCSD equations and domains are chosen conservatively. The correlation energy loss due to the domains remains below 8800 basis functions and >450 atoms. In all larger test calculations done so far, the LPNO-CCSD step took less time than the preceding Hartree-Fock calculation, provided no approximations have been introduced in the latter. Thus, based on the present development reliable CCSD calculations on large molecules with unprecedented efficiency and accuracy are realized.
1,207 citations
TL;DR: The extension of the previously developed domain based local pair-natural orbital (DLPNO) based singles- and doubles coupled cluster ( DLPNO-CCSD) method to perturbatively include connected triple excitations is reported and the first CCSD(T) level calculation on an entire protein, Crambin with 644 atoms, and more than 6400 basis functions is demonstrated.
Abstract: In this work, the extension of the previously developed domain based local pair-natural orbital (DLPNO) based singles- and doubles coupled cluster (DLPNO-CCSD) method to perturbatively include connected triple excitations is reported. The development is based on the concept of triples-natural orbitals that span the joint space of the three pair natural orbital (PNO) spaces of the three electron pairs that are involved in the calculation of a given triple-excitation contribution. The truncation error is very smooth and can be significantly reduced through extrapolation to the zero threshold. However, the extrapolation procedure does not improve relative energies. The overall computational effort of the method is asymptotically linear with the system size O(N). Actual linear scaling has been confirmed in test calculations on alkane chains. The accuracy of the DLPNO-CCSD(T) approximation relative to semicanonical CCSD(T0) is comparable to the previously developed DLPNO-CCSD method relative to canonical CCSD. Relative energies are predicted with an average error of approximately 0.5 kcal∕mol for a challenging test set of medium sized organic molecules. The triples correction typically adds 30%-50% to the overall computation time. Thus, very large systems can be treated on the basis of the current implementation. In addition to the linear C150H302 (452 atoms, >8800 basis functions) we demonstrate the first CCSD(T) level calculation on an entire protein, Crambin with 644 atoms, and more than 6400 basis functions.
1,151 citations
TL;DR: In the past decade, coupled-cluster theory has seen a renaissance in nuclear physics, with computations of neutron-rich and medium-mass nuclei as discussed by the authors, and it describes many aspects of weakly bound and unbound nuclei.
Abstract: In the past decade, coupled-cluster theory has seen a renaissance in nuclear physics, with computations of neutron-rich and medium-mass nuclei. The method is efficient for nuclei with product-state references, and it describes many aspects of weakly bound and unbound nuclei. This report reviews the technical and conceptual developments of this method in nuclear physics, and the results of coupled-cluster calculations for nucleonic matter, and for exotic isotopes of helium, oxygen, calcium, and some of their neighbors.
332 citations
TL;DR: The in-medium similarity renormalization group (IM-SRG) for open-shell nuclei is formed using a multireference formalism based on a generalized Wick theorem introduced in quantum chemistry, and is used to perform the first ab initio study of all even oxygen isotopes with chiral nucleon-n nucleon and three-nucleon interactions.
Abstract: We formulate the in-medium similarity renormalization group (IM-SRG) for open-shell nuclei using a multireference formalism based on a generalized Wick theorem introduced in quantum chemistry. The resulting multireference IM-SRG (MR-IM-SRG) is used to perform the first ab initio study of all even oxygen isotopes with chiral nucleon-nucleon and three-nucleon interactions, from the proton to the neutron drip lines. We obtain an excellent reproduction of experimental ground-state energies with quantified uncertainties, which is validated by results from the importance-truncated no-core shell model and the coupled cluster method. The agreement between conceptually different many-body approaches and experiment highlights the predictive power of current chiral two- and three-nucleon interactions, and establishes the MR-IM-SRG as a promising new tool for ab initio calculations of medium-mass nuclei far from shell closures.
155 citations
TL;DR: In this article, the Moller-Plesset perturbation theory of the second order (MP2) was employed to compute the polycyclic aromatic hydrocarbon (PAH)-water interaction energies, with proper size of basis sets and energy component analysis to extrapolate to infinite-sized graphene limit.
Abstract: In this study, we develop graphitic carbon-water nonbonded interaction parameters entirely from ab initio calculation data of interaction energies between graphene and a single water molecule. First, we employ the Moller-Plesset perturbation theory of the second order (MP2) method to compute the polycyclic aromatic hydrocarbon (PAH)-water interaction energies, with proper size of basis sets and energy component analysis to extrapolate to infinite-sized graphene limit. Then, we develop graphitic carbon-water interaction parameters based on the MP2 data from this work and the ab initio data available in the literature from other methods such as random-phase approximation (RPA), density functional theory-symmetry-adapted perturbation theory (DFT-SAPT), and coupled cluster treatment with single and double excitations and perturbative triples (CCSD(T)). The accuracy of the interaction parameters is evaluated by predicting water contact angle on graphite and carbon nanotube (CNT) radial breathing mode (RBM) frequency shift and comparing them with experimental data. The interaction parameters obtained from MP2 data predict the CNT RBM frequency shift that is in good agreement with experiments. The interaction parameters obtained from RPA and DFT-SAPT data predict the contact angles and the CNT RBM frequency shift that agree well with experiments. The interaction parameters obtained from CCSD(T) data underestimate the contact angles and overestimate the CNT RBM frequency shift probably due to the use of small basis sets in CCSD(T) calculations.
149 citations
TL;DR: The most recent innovations in the EFP model have been to make the computationally expensive charge transfer term much more efficient and to interface the general EFP dispersion and exchange repulsion interactions with QM methods.
Abstract: The general effective fragment potential (EFP) method provides model potentials for any molecule that is derived from first principles, with no empirically fitted parameters. The EFP method has been interfaced with most currently used ab initio single-reference and multireference quantum mechanics (QM) methods, ranging from Hartree-Fock and coupled cluster theory to multireference perturbation theory. The most recent innovations in the EFP model have been to make the computationally expensive charge transfer term much more efficient and to interface the general EFP dispersion and exchange repulsion interactions with QM methods. Following a summary of the method and its implementation in generally available computer programs, these most recent new developments are discussed.
148 citations
TL;DR: An algorithm for coupled-cluster through perturbative triples based on a t1-dressed Hamiltonian and the use of density fitting or Cholesky decomposition approximations for the construction and contraction of all electron repulsion integrals (ERIs) is presented.
Abstract: We present an algorithm for coupled-cluster through perturbative triples [CCSD(T)] based on a t1-dressed Hamiltonian and the use of density fitting (DF) or Cholesky decomposition (CD) approximations for the construction and contraction of all electron repulsion integrals (ERIs). An efficient implementation of this algorithm is then used to explore whether preoptimized density fitting basis sets [specifically, the (aug-)cc-pVXZ-RI series designed for DF-MP2 computations] are suitable for DF-CCSD(T) computations and how they compare to the CD representation of the integrals. The code is also used to systematically explore the accuracy and efficiency of DF/CD combined with frozen natural orbitals (FNOs) to reduce computational costs. The mean absolute errors due to DF/CD in the CCSD(T)/aug-cc-pVDZ interaction energies of 11 van der Waals dimers are only 0.001 kcal mol(-1) for the preoptimized RI basis set and only 0.002 and 0.001 kcal mol(-1) for CD with cutoffs of 10(-4) and 10(-5), respectively. The very similar performance of the aug-cc-pVDZ-RI auxiliary set is a bit surprising considering that the numbers of CD vectors using these thresholds are, on average, 28% and 73% larger than the dimension of the RI set. When FNOs are coupled with DF/CD, the DF/CD error is roughly an order of magnitude less than the FNO truncation error (at a conservative FNO occupation cutoff of 10(-5)). Utilizing t1-dressed three-index integrals, which remove the explicit dependence of the doubles residual equations on the t1-amplitudes, results in a moderate performance acceleration for the CCSD portion of the algorithm. Moreover, the t1-dressing results in a simpler code which will be more amenable to parallelization. Utilizing both CD and FNO techniques, we observe a speedup of four times for the evaluation of the three-body contribution to the interaction energy for the benzene trimer described by an aug-cc-pVDZ basis set; the error incurred by the CD and FNO approximations in the three-body contribution is only 0.002 kcal mol(-1).
141 citations
TL;DR: The utility of this benchmark data set is demonstrated by examining a wide variety of Kohn-Sham exchange-correlation functionals for the calculation of these properties, none of the existing approximate functionals provide an accuracy competitive with that provided by CCSD or CCST(T) theory.
Abstract: Accurate sets of benchmark nuclear-magnetic-resonance shielding constants and spin–rotation constants are calculated using coupled-cluster singles–doubles (CCSD) theory and coupled-cluster singles–doubles–perturbative-triples [CCSD(T)] theory, in a variety of basis sets consisting of (rotational) London atomic orbitals. The accuracy of the calculated coupled-cluster constants is established by a careful comparison with experimental data, taking into account zero-point vibrational corrections. Coupled-cluster basis-set convergence is analyzed and extrapolation techniques are employed to estimate basis-set-limit quantities, thereby establishing an accurate benchmark data set. Together with the set provided for rotational g-tensors and magnetizabilities in our previous work [O. B. Lutnaes, A. M. Teale, T. Helgaker, D. J. Tozer, K. Ruud, and J. Gauss, J. Chem. Phys. 131, 144104 (2009)]10.1063/1.3242081, it provides a substantial source of consistently calculated high-accuracy data on second-order magnetic resp...
139 citations
TL;DR: For the first time excellent agreement between theoretically predicted and experimentally measured vanadium L-edge NEXAFS spectra of V2O5 was achieved, indicating that the covalency of the metal-ligand bonds is correctly described by the calculations.
Abstract: A detailed study of the electronic and geometric structure of V2O5 and its X-ray spectroscopic properties is presented. Cluster models of increasing size were constructed in order to represent the surface and the bulk environment of V2O5. The models were terminated with hydrogen atoms at the edges or embedded in a Madelung field. The structure and interlayer binding energies were studied with dispersion-corrected local, hybrid and double hybrid density functional theory as well as the local pair natural orbital coupled cluster method (LPNO-CCSD). Convergence of the results with respect to cluster size was achieved by extending the model to up to 20 vanadium centers. The O K-edge and the V L2,3-edge NEXAFS spectra of V2O5 were calculated on the basis of the newly developed Restricted Open shell Configuration Interaction with Singles (DFT-ROCIS) method. In this study the applicability of the method is extended to the field of solid-state catalysis. For the first time excellent agreement between theoretically predicted and experimentally measured vanadium L-edge NEXAFS spectra of V2O5 was achieved. At the same time the agreement between experimental and theoretical oxygen K-edge spectra is also excellent. Importantly, the intensity distribution between the oxygen K-edge and vanadium L-edge spectra is correctly reproduced, thus indicating that the covalency of the metal–ligand bonds is correctly described by the calculations. The origin of the spectral features is discussed in terms of the electronic structure using both quasi-atomic jj coupling and molecular LS coupling schemes. The effects of the bulk environment driven by weak interlayer interactions were also studied, demonstrating that large clusters are important in order to correctly calculate core level absorption spectra in solids.
126 citations
TL;DR: The ωB97X-D functional gives the best estimate of the binding energies with a mean absolute error as low as 2.12 kcal mol(-1) over the large test set of clusters.
Abstract: This work assesses the binding energies of atmospherically relevant clusters containing H2SO4, H2O, NH3 and (CH3)2NH using density functional theory. The performance of seven DFT functionals (B3LYP, CAM-B3LYP, M06-2X, PW91, LC-PW91, PBE0 and ωB97X-D) is evaluated against high level explicitly correlated coupled cluster methods using a test set of 107 atmospherically relevant clusters. Our studies show that all the tested functionals correlate well with the coupled cluster results, but with highly varying mean absolute errors. The PBE0, CAM-B3LYP, PW91 and M06-2X functionals are found to perform similarly with errors in the range of 2.53–3.46 kcal mol−1, while the B3LYP and LC-PW91 functionals yield higher errors of 6.95 kcal mol−1 and 10.66 kcal mol−1, respectively. The ωB97X-D functional gives the best estimate of the binding energies with a mean absolute error as low as 2.12 kcal mol−1 over the large test set of clusters.
121 citations
TL;DR: Neutral silver clusters, Ag(n), were studied using density functional theory (DFT) followed by high level coupled cluster CCSD(T) calculations to determine the low energy isomers for each cluster size for small clusters to predict that the normalized atomization energies start to converge slowly to the bulk at n = 55.
Abstract: Neutral silver clusters, Ag(n), were studied using density functional theory (DFT) followed by high level coupled cluster CCSD(T) calculations to determine the low energy isomers for each cluster size for small clusters. The normalized atomization energy, heats of formation, and average bond lengths were calculated for each of the different isomeric forms of the silver clusters. For n = 2-6, the preferred geometry is planar, and the larger n = 7-8 clusters prefer higher symmetry, three-dimensional geometries. The low spin state is predicted to be the ground state for every cluster size. A number of new low energy isomers for the heptamer and octamer were found. Additional larger Ag(n) structures, n < 100, were initially optimized using a tree growth-hybrid genetic algorithm with an embedded atom method (EAM) potential. For n ≤ 20, DFT was used to optimize the geometries. DFT with benchmarked functionals were used to predict that the normalized atomization energies ((AE)s) for Ag(n) start to converge slowly to the bulk at n = 55. The (AE) for Ag99 is predicted to be ~50 kcal/mol.
TL;DR: Analysis has shown that deficiencies in the zeroth-order wave functions, in particular for the subset of π → π* singlet excitations, are responsible for the largest deviations from CC3.
Abstract: The multireference n-electron Valence State Perturbation Theory is applied to a benchmark set of 28 organic molecules compiled by Schreiber et al. J. Chem. Phys. (2008) 128, 13. Different types of low-lying vertical excitation energies are computed using the same geometries and TZVP basis set as in the original work. The previously published coupled cluster CC3 results are used as a reference. The complete active space second order perturbation theory (CASPT2) results, as well as the results of second order N-electron valence perturbation theory (NEVPT2) (both in their single-state variants) are evaluated against this reference set, which includes 153 singlet and 72 triplet vertical transition energies. NEVPT2 calculations are carried out in two variants: the partially contracted (PC) and the strongly contracted (SC) scheme. The statistical evaluation with respect to CC3 is found to be similar for both: the mean unsigned deviations is 0.28 eV for singlets and 0.16 eV for triplets for PC-NEVPT2, while it is 0.23 and 0.17 eV for SC-NEVPT2, respectively. Further analysis has shown that deficiencies in the zeroth-order wave functions, in particular for the subset of π → π* singlet excitations, are responsible for the largest deviations from CC3. Those states have either a charge transfer or an ionic character. For the remaining singlet and all triplet excitations the general trend was established that NEVPT2 tends to slightly overestimate excitation energies while CASPT2 slightly underestimates them. However, overall, both methods are of very similar accuracy provided that the IPEA shift is used in the CASPT2 method. Interestingly, the conclusions reached in this study are independent of the orbital canonicalization scheme used in the NEVPT2 calculation.
TL;DR: A method that accurately describes strongly correlated states and captures dynamical correlation is presented, called the distinguishable cluster approximation, which smoothly dissociates difficult cases such as the nitrogen molecule, with the modest N(6) computational cost of CCSD.
Abstract: We present a method that accurately describes strongly correlated states and captures dynamical correlation. It is derived as a modification of coupled-cluster theory with single and double excitations (CCSD) through consideration of particle distinguishability between dissociated fragments, whilst retaining the key desirable properties of particle-hole symmetry, size extensivity, invariance to rotations within the occupied and virtual spaces, and exactness for two-electron subsystems. The resulting method, called the distinguishable cluster approximation, smoothly dissociates difficult cases such as the nitrogen molecule, with the modest N(6) computational cost of CCSD. Even for molecules near their equilibrium geometries, the new model outperforms CCSD. It also accurately describes the massively correlated states encountered when dissociating hydrogen lattices, a proxy for the metal-insulator transition, and the fully dissociated system is treated exactly.
TL;DR: This work demonstrates how to extend the pair natural orbital (PNO) methodology for excited states, presented in a previous work for the perturbative doubles correction to configuration interaction singles (CIS(D), to iterative coupled cluster methods such as the approximate singles and doubles model CC2.
Abstract: We demonstrate how to extend the pair natural orbital (PNO) methodology for excited states, presented in a previous work for the perturbative doubles correction to configuration interaction singles (CIS(D)), to iterative coupled cluster methods such as the approximate singles and doubles model CC2. The original O(N5) scaling of the PNO construction is reduced by using orbital-specific virtuals (OSVs) as an intermediate step without spoiling the initial accuracy of the PNO method. Furthermore, a slower error convergence for charge-transfer states is analyzed and resolved by a numerical Laplace transformation during the PNO construction, so that an equally accurate treatment of local and charge-transfer excitations is achieved. With state-specific truncated PNO expansions, the eigenvalue problem is solved by combining the Davidson algorithm with deflation to project out roots that have already been determined and an automated refresh with a generation of new PNOs to achieve self-consistency of the PNO space...
TL;DR: Overall, it is found that the effect of including excitations beyond CCSD(T) is smaller than inclusion of core-valence correlation and comparable to scalar-relativistic and adiabatic effects.
Abstract: The equilibrium geometry of the lowest energy structure of water dimer [(H2O)2] has been investigated using coupled cluster theory. A hierarchy of conventional coupled cluster methods is utilized up to singles doubles triples and quadruples excitations (CCSDTQ). The geometry of (H2O)2 is also optimized using the explicitly correlated coupled cluster singles doubles and perturbative triples [CCSD(T)-F12b] method. Overall, we find that the effect of including excitations beyond CCSD(T) is smaller than inclusion of core–valence correlation and comparable to scalar-relativistic and adiabatic effects.
TL;DR: In this paper, an ab initio electric dipole moment surfaces (DMSs) of methane in its ground electronic state are presented using an explicitly correlated coupled cluster CCSD(T)-F12 method in conjunction with an F12-optimized correlation consistent basis set of the TZ-family.
TL;DR: The ideas and connections discussed in this paper may help design improved ways of incorporating RPA correlation into density functionals based on a CC perspective.
Abstract: We establish a formal connection between the particle-particle (pp) random phase approximation (RPA) and the ladder channel of the coupled cluster doubles (CCD) equations. The relationship between RPA and CCD is best understood within a Bogoliubov quasiparticle (qp) RPA formalism. This work is a follow-up to our previous formal proof on the connection between particle-hole (ph) RPA and ring-CCD. Whereas RPA is a quasibosonic approximation, CC theory is a “correct bosonization” in the sense that the wavefunction and Hilbert space are exactly fermionic, yet the amplitude equations can be interpreted as adding different quasibosonic RPA channels together. Coupled cluster theory achieves this goal by interacting the ph (ring) and pp (ladder) diagrams via a third channel that we here call “crossed-ring” whose presence allows for full fermionic antisymmetry. Additionally, coupled cluster incorporates what we call “mosaic” terms which can be absorbed into defining a new effective one-body Hamiltonian. The inclusion of these mosaic terms seems to be quite important. The pp-RPA and qp-RPA equations are textbook material in nuclear structure physics but are largely unknown in quantum chemistry, where particle number fluctuations and Bogoliubov determinants are rarely used. We believe that the ideas and connections discussed in this paper may help design improved ways of incorporating RPA correlation into density functionals based on a CC perspective.
TL;DR: In this paper, a self-consistent Kohn-Sham (KS) method is presented that treats correlation on the basis of the adiabatic-connection dissipationfluctuation theorem employing the direct random phase approximation (dRPA), i.e., taking into account only the Coulomb kernel while neglecting the exchange-correlation kernel in the calculation of the Kohn Sham correlation energy and potential.
Abstract: A self-consistent Kohn-Sham (KS) method is presented that treats correlation on the basis of the adiabatic-connection dissipation-fluctuation theorem employing the direct random phase approximation (dRPA), i.e., taking into account only the Coulomb kernel while neglecting the exchange-correlation kernel in the calculation of the Kohn-Sham correlation energy and potential. The method, denoted self-consistent dRPA method, furthermore treats exactly the exchange energy and the local multiplicative KS exchange potential. It uses Gaussian basis sets, is reasonably efficient, exhibiting a scaling of the computational effort with the forth power of the system size, and thus is generally applicable to molecules. The resulting dRPA correlation potentials in contrast to common approximate correlation potentials are in good agreement with exact reference potentials. The negatives of the eigenvalues of the highest occupied molecular orbitals are found to be in good agreement with experimental ionization potentials. Total energies from self-consistent dRPA calculations, as expected, are even poorer than non-self-consistent dRPA total energies and dRPA reaction and non-covalent binding energies do not significantly benefit from self-consistency. On the other hand, energies obtained with a recently introduced adiabatic-connection dissipation-fluctuation approach (EXXRPA+, exact-exchange random phase approximation) that takes into account, besides the Coulomb kernel, also the exact frequency-dependent exchange kernel are significantly improved if evaluated with orbitals obtained from a self-consistent dRPA calculation instead of an exact exchange-only calculation. Total energies, reaction energies, and noncovalent binding energies obtained in this way are of the same quality as those of high-level quantum chemistry methods, like the coupled cluster singles doubles method which is computationally more demanding.
TL;DR: This work proposes a simple modification to the widely used coupled cluster singles and doubles plus perturbative triples method that lifts the divergent behavior and is shown to give very accurate correlation energies for the homogeneous electron gas.
Abstract: We investigate the accuracy of a number of wave function based methods at the heart of quantum chemistry for metallic systems. Using the Hartree-Fock wave function as a reference, perturbative (Moller-Plesset) and coupled cluster theories are used to study the uniform electron gas model. Our findings suggest that nonperturbative coupled cluster theories are acceptable for modeling electronic interactions in metals while perturbative coupled cluster theories are not. Using screened interactions, we propose a simple modification to the widely used coupled cluster singles and doubles plus perturbative triples method that lifts the divergent behavior and is shown to give very accurate correlation energies for the homogeneous electron gas.
TL;DR: The interaction energies of the guanine-cytosine dimers in the Watson-Crick and stacked arrangements are investigated at the level of local coupled cluster theory with singles and doubles and perturbative triples and new complete-basis-set-limit estimates are proposed.
Abstract: A local method based on orbital specific virtuals (OSVs) for calculating the perturbative triples correction in local coupled cluster calculations is presented. In contrast to the previous approach based on projected atomic orbitals (PAOs), described by Schutz [J. Chem. Phys. 113, 9986 (2000)]10.1063/1.1323265, the new scheme works without any ad hoc truncations of the virtual space to domains. A single threshold defines the pair and triple specific virtual spaces completely and automatically. It is demonstrated that the computational cost of the method scales linearly with molecular size. Employing the recommended threshold a similar fraction of the correlation energy is recovered as with the original PAO method at a somewhat lower cost. A benchmark for 52 reactions demonstrates that for reaction energies the intrinsic accuracy of the coupled cluster with singles and doubles excitations and a perturbative treatment of triples excitations method can be reached by OSV-local coupled cluster theory with singles and doubles and perturbative triples, provided a MP2 correction is applied that accounts for basis set incompleteness errors as well as for remaining domain errors. As an application example the interaction energies of the guanine-cytosine dimers in the Watson-Crick and stacked arrangements are investigated at the level of local coupled cluster theory with singles and doubles and perturbative triples. Based on these calculations we propose new complete-basis-set-limit estimates for these interaction energies at this level of theory.
TL;DR: The penta-2,4-dieniminium (PSB3) cation is employed as a minimal model of the retinal chromophore of visual pigments and its excited state isomerization paths are compared at the CASSCF and CASPT2 levels of theory to provide benchmark values against which other ab initio methods are validated.
Abstract: The photoisomerization of the retinal chromophore of visual pigments proceeds along a complex reaction coordinate on a multidimensional surface that comprises a hydrogen-out-of-plane (HOOP) coordinate, a bond length alternation (BLA) coordinate, a single bond torsion and, finally, the reactive double bond torsion. These degrees of freedom are coupled with changes in the electronic structure of the chromophore and, therefore, the computational investigation of the photochemistry of such systems requires the use of a methodology capable of describing electronic structure changes along all those coordinates. Here, we employ the penta-2,4-dieniminium (PSB3) cation as a minimal model of the retinal chromophore of visual pigments and compare its excited state isomerization paths at the CASSCF and CASPT2 levels of theory. These paths connect the cis isomer and the trans isomer of PSB3 with two structurally and energetically distinct conical intersections (CIs) that belong to the same intersection space. MRCISD+Q energy profiles along these paths provide benchmark values against which other ab initio methods are validated. Accordingly, we compare the energy profiles of MRPT2 methods (CASPT2, QD-NEVPT2, and XMCQDPT2) and EOM-SF-CC methods (EOM-SF-CCSD and EOM-SF-CCSD(dT)) to the MRCISD+Q reference profiles. We find that the paths produced with CASSCF and CASPT2 are topologically and energetically different, partially due to the existence of a "locally excited" region on the CASPT2 excited state near the Franck-Condon point that is absent in CASSCF and that involves a single bond, rather than double bond, torsion. We also find that MRPT2 methods as well as EOM-SF-CCSD(dT) are capable of quantitatively describing the processes involved in the photoisomerization of systems like PSB3.
TL;DR: In this article, the authors investigate the failure of time-dependent density functional theory (TDDFT) with the CAM-B3LYP exchange-correlation (xc) functional coupled to the polarisable embedding (PE) scheme (PE-CAM-B 3LYP) in reproducing the solvatochromic shift of the lowest intense charge-transfer excitation in para-nitroaniline (pNA) in water by comparing with results obtained with the coupled cluster singles and doubles (CCSD) model also coupled to polarizable embedding
Abstract: We investigate the failure of time-dependent density functional theory (TDDFT) with the CAM-B3LYP exchange-correlation (xc) functional coupled to the polarisable embedding (PE) scheme (PE-CAM-B3LYP) in reproducing the solvatochromic shift of the lowest intense charge-transfer excitation in para-nitroaniline (pNA) in water by comparing with results obtained with the coupled cluster singles and doubles (CCSD) model also coupled to the polarisable embedding scheme (PE-CCSD). We determine the amount of charge separation in the ground and excited charge-transfer state with both methods by calculating the electric dipole moments in the gas phase and for 100 solvent configurations. We find that CAM-B3LYP overestimates the amount of charge separation inherent in the ground state and TDDFT/CAM-B3LYP drastically underestimates this amount in the excited charge-transfer state. As the errors in the solvatochromatic shift are found to be inverse proportional to the change in dipole moment upon excitation, we conclude ...
TL;DR: It is demonstrated that the DEA- and DIP-EOMCC methods with an active-space treatment of 4p-2h and 4h-2p excitations reproduce the results of the analogous full calculations at the small fraction of the computer effort.
Abstract: The full and active-space doubly electron-attached (DEA) and doubly ionized (DIP) equation-of-motion coupled-cluster (EOMCC) methods with up to 4-particle–2-hole (4p-2h) and 4-hole–2-particle (4h-2p) excitations are developed. By examining bond breaking in F2 and low-lying singlet and triplet states in the methylene, (HFH)−, and trimethylenemethane biradicals, we demonstrate that the DEA- and DIP-EOMCC methods with an active-space treatment of 4p-2h and 4h-2p excitations reproduce the results of the analogous full calculations at the small fraction of the computer effort, while improving the DEA/DIP-EOMCC theories truncated at 3p-1h/3h-1p excitations.
TL;DR: This implementation of THC-CC2 uses a grid-based least-squares THC (LS-THC) approximation to the density-fitted electron repulsion integrals, and the accuracy of the CC2 correlation energy under these approximations is shown to be suitable for most practical applications.
Abstract: The second-order approximate coupled cluster singles and doubles method (CC2) is a valuable tool in electronic structure theory. Although the density fitting approximation has been successful in extending CC2 to larger molecules, it cannot address the steep O(N5) scaling with the number of basis functions, N. Here, we introduce the tensor hypercontraction (THC) approximation to CC2 (THC-CC2), which reduces the scaling to O(N4) and the storage requirements to O(N2). We present an algorithm to efficiently evaluate the THC-CC2 correlation energy and demonstrate its quartic scaling. This implementation of THC-CC2 uses a grid-based least-squares THC (LS-THC) approximation to the density-fitted electron repulsion integrals. The accuracy of the CC2 correlation energy under these approximations is shown to be suitable for most practical applications.
TL;DR: The complexes of a DNA base bound to graphitic systems are studied and the optB86b nonlocal functional and the Tkatchenko-Scheffler functional are used to study the binding energies of nucleobases on graphene.
Abstract: The complexes of a DNA base bound to graphitic systems are studied. Considering naphthalene as the simplest graphitic system, DNA base−naphthalene complexes are scrutinized at high levels of ab initio theory including coupled cluster theory with singles, doubles, and perturbative triples excitations (CCSD(T)) at the complete basis set (CBS) limit. The stacked configurations are the most stable, where the CCSD(T)/CBS binding energies of guanine, adenine, thymine, and cytosine are 9.31, 8.48, 8.53, 7.30 kcal/mol, respectively. The energy components are investigated using symmetry-adapted perturbation theory based on density functional theory including the dispersion energy. We compared the CCSD(T)/CBS results with several density functional methods applicable to periodic systems. Considering accuracy and availability, the optB86b nonlocal functional and the Tkatchenko−Scheffler functional are used to study the binding energies of nucleobases on graphene. The predicted values are 18−24 kcal/mol, though many-body effects on screening and energy need to be further considered.
TL;DR: In this article, a diatomic molecule in a spatially degenerate electronic state interacting with a non-resonant laser field and investigating its rovibrational structure in the presence of the field was investigated.
Abstract: We formulate the theory for a diatomic molecule in a spatially degenerate electronic state interacting with a non-resonant laser field and investigate its rovibrational structure in the presence of the field. We report on ab initio calculations employing the double electron attachment intermediate Hamiltonian Fock space coupled cluster method restricted to single and double excitations for all electronic states of the Rb2 molecule up to 5s+5d dissociation limit of about 26,000 cm−1. In order to correctly predict the spectroscopic behaviour of Rb2, we have also calculated the electric transition dipole moments, non-adiabatic coupling and spin-orbit coupling matrix elements, and static dipole polarisabilities, using the multireference configuration interaction method. When a molecule is exposed to strong non-resonant light, its rovibrational levels get hybridised. We study the spectroscopic signatures of this effect for transitions between the X1Σ+ g electronic ground state and the A1Σ+ u and b3Π u excited ...
TL;DR: In this paper, the authors combine both approaches to prove existence and uniqueness results, quasi-optimality estimates and energy estimates for the Coupled Cluster method with respect to the solution of the full, original Schrodinger equation.
Abstract: The Coupled Cluster (CC) method is a widely used and highly successful high precision method for the solution of the stationary electronic Schrodinger equation, with its practical convergence properties being similar to that of a corresponding Galerkin (CI) scheme. This behaviour has for the discrete CC method been analyzed with respect to the discrete Galerkin solution (the "full-CI-limit") in (Schneider, 2009). Recently, we globalized the CC formulation to the full continuous space, giving a root equation for an infinite dimensional, nonlinear Coupled Cluster operator that is equivalent the full electronic Schrodinger equation (Rohwedder, 2011). In this paper, we combine both approaches to prove existence and uniqueness results, quasi-optimality estimates and energy estimates for the CC method with respect to the solution of the full, original Schrodinger equation. The main property used is a local strong monotonicity result for the Coupled Cluster function, and we give two characterizations for situations in which this property holds.
TL;DR: These CBS limits can now be used as benchmarks to calibrate more approximate calculations using smaller basis sets, and the sequence of basis sets provides data on convergence patterns for each component of the correlation energy.
Abstract: We extrapolate to the coupled cluster single and double excitation and the perturbative triples (CCSD(T))/complete basis set (CBS) limit with a sequence of optimized n-tuple-ζ augmented polarization augmented (nZaPa) basis sets (n = 4, 5, 6, and 7) for 115 species representing the first two rows of the Periodic Table. The species include the entire set of atoms, positive and negative atomic ions, homonuclear diatomic molecules, and hydrides. The benchmark set also includes the rare gas dimers, polar molecules such as oxides and fluorides, and a few transition states for chemical reactions. The CCSD correlation energies agree with available CCSD-F12b/3C(FIX) values to within ±0.18 mEh root-mean-square (rms) deviation. The (T) components agree to within ±0.10 mEh and the total CCSD(T) correlation energies to within ±0.26 mEh or 0.1% rms deviation, which is probably the better measure, since the largest deviation is 0.43 mEh or 0.13%. These CBS limits can now be used as benchmarks to calibrate more approximate calculations using smaller basis sets. The sequence of basis sets provides data on convergence patterns for each component of the correlation energy.
TL;DR: In this article, a segmented all-electron contracted triple zeta valence plus polarization function (TZP) basis set for the elements from Rb to Xe was constructed to be used in conjunction with the non-relativistic and Douglas-Kroll-Hess (DKH) Hamiltonians.
Abstract: Segmented all-electron contracted triple zeta valence plus polarization function (TZP) basis sets for the elements from Rb to Xe were constructed to be used in conjunction with the non-relativistic and Douglas–Kroll–Hess (DKH) Hamiltonians. This extends earlier work on segmented contracted TZ basis set for the atoms H-Kr. At the coupled cluster level of theory, ionization energy of some atoms as well as spectroscopic constants of a sample of diatomics were calculated and compared with benchmark theoretical values. One verifies that the benchmark bond length, dissociation energy, and harmonic vibrational frequency can be reproduced well with the TZP-DKZ set.
TL;DR: Perturbative triples corrections to the equation of motion coupled cluster singles and doubles (EOM-CCSD) are rederived and implemented in a pilot parallel code, enabling the routine and accurate study of excited states for ever larger molecular systems.
Abstract: Perturbative triples corrections ((T) and (T)) to the equation of motion coupled cluster singles and doubles (EOM-CCSD) are rederived and implemented in a pilot parallel code. The vertical excitation energies of molecules in the test set of Sauer et al. [J. Chem. Theor. Comput. 2009, 5, 555] are reported and compared to the iterative EOM-CCSDT-3 method. The average absolute deviations of EOM-CCSD(T) and EOM-CCSD(T) from EOM-CCSDT-3 over this wide test set are 0.06 and 0.18 eV, respectively. The poor performance of the latter suggests misbalanced handling of the (T) terms. Scaling curves for EOM-CCSD(T) are also presented to demonstrate the performance across multiple compute nodes, thus enabling the routine and accurate study of excited states for ever larger molecular systems.