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Rodney J Bartlett - One of the best experts on this subject based on the ideXlab platform.
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vertical valence ionization potential benchmarks from equation of motion Coupled Cluster Theory and qtp functionals
Journal of Chemical Physics, 2019Co-Authors: Duminda S Ranasinghe, Johannes T Margraf, Ajith Perera, Rodney J BartlettAbstract:The ionization potential (IP) of a molecule quantifies the energy required to remove an electron from the system. As such, it is a fundamental quantity in the context of redox chemistry, charge transfer, and molecular electronics. The accurate theoretical prediction of this property is therefore highly desirable for virtual materials design. Furthermore, vertical IPs are of interest in the development of many-body Green’s function methods like the GW formalism, as well as density functionals and semiempirical methods. In this contribution, we report over 1468 vertical valence IPs calculated with the IP variant of equation-of-motion Coupled Cluster Theory with singles and doubles (IP-EOM-CCSD) covering 155 molecules. The purpose of this is two-fold: First, the quality of the predicted IPs is compared with respect to experiments and higher-order Coupled Cluster Theory. This confirms the overall high accuracy and robustness of this method, with some outliers which are discussed in detail. Second, a large set of consistent theoretical reference values for vertical valence IPs are generated. This addresses a lack of reliable reference data for lower-lying valence IPs, where experimental data are often unavailable or of dubious quality. The benchmark set is then used to assess the quality of the eigenvalues predicted by different density functional approximations (via Bartlett’s IP-eigenvalue theorem) and the extended Koopmans’ theorem approach. The QTP family of functionals are found to be remarkably accurate, low-cost alternatives to IP-EOM-CCSD.The ionization potential (IP) of a molecule quantifies the energy required to remove an electron from the system. As such, it is a fundamental quantity in the context of redox chemistry, charge transfer, and molecular electronics. The accurate theoretical prediction of this property is therefore highly desirable for virtual materials design. Furthermore, vertical IPs are of interest in the development of many-body Green’s function methods like the GW formalism, as well as density functionals and semiempirical methods. In this contribution, we report over 1468 vertical valence IPs calculated with the IP variant of equation-of-motion Coupled Cluster Theory with singles and doubles (IP-EOM-CCSD) covering 155 molecules. The purpose of this is two-fold: First, the quality of the predicted IPs is compared with respect to experiments and higher-order Coupled Cluster Theory. This confirms the overall high accuracy and robustness of this method, with some outliers which are discussed in detail. Second, a large set...
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explicitly correlated Coupled Cluster Theory for static polarizabilities
Journal of Chemical Physics, 2016Co-Authors: Denis Bokhan, Ajith Perera, D N Trubnikov, Rodney J BartlettAbstract:A method of calculation of static polarizabilities with wavefunctions, corresponding to linearly approximated explicitly correlated Coupled-Cluster singles and doubles [CCSD(F12)] model, has been formulated and implemented. For the proper description of the response of system on applied electric field, modified ansatz is introduced for geminal part of Cluster operators. Such extension of CCSD(F12) model provides balanced description of both perturbed and unperturbed wave functions, what leads to the increase of the accuracy of target polarizabilities. As a part of algorithm, explicitly correlated version of Coupled-perturbed CCSD equations has also been derived and implemented. Numerical tests conducted for the set of eight molecules show good agreement between static polarizabilities, calculated with developed explicitly correlated approach and corresponding complete basis set results in regular CCSD already at triple-ζ level.
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gas phase rdx decomposition pathways using Coupled Cluster Theory
Physical Chemistry Chemical Physics, 2016Co-Authors: Rodney J Bartlett, Robert W Molt, Thomas Watson, Alexandre P Bazante, Nigel G J RichardsAbstract:Electronic and free energy barriers for a series of gas-phase RDX decomposition mechanisms have been obtain using Coupled Cluster singles, doubles, and perturbative triples with complete basis set (CCSD(T)/CBS) electronic energies for MBPT(2)/cc-pVTZ structures. Importantly, we have located a well-defined transition state for NN homolysis, in the initial RDX decomposition step, thereby obtaining a true barrier for this reaction. These calculations support the view that HONO elimination is preferred at STP over other proposed mechanisms, including NN homolysis, “triple whammy” and NONO isomerization. Indeed, our calculated values of Arrhenius parameters are in agreement with experimental findings for gas phase RDX decomposition. We also investigate a number of new pathways leading to breakdown of the intermediate formed by the initial HONO elimination, and find that NN homolysis in this intermediate has an activation energy barrier comparable with that computed for HONO elimination.
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Coupled Cluster Theory and its equation of motion extensions
Wiley Interdisciplinary Reviews: Computational Molecular Science, 2012Co-Authors: Rodney J BartlettAbstract:Coupled-Cluster Theory offers today's reference quantum chemical method for most of the problems encountered in electronic structure Theory. It has been instrumental in establishing the now well-known paradigm of converging, many-body methods, Many-body perturbation Theory (MBPT) for second, MBPT2, and fourth-order MBPT4; and Coupled-Cluster (CC) Theory for different categories of excitations, singles, doubles, triples, quadruples (SDTQ). Although built on the same basic concept as configuration interaction (CI), many-body methods fundamentally improve upon CI approximations by introducing the property of size extensivity, meaning that contrary to any truncated CI all terms properly scale with the number of electrons in the problem. This fundamental aspect of many-electron methods leads to the exceptional performance of CC Theory and its finite-order MBPT approximations plus its equation-of-motion extensions for excited, ionized, and electron attached states. This brief overview will describe formal aspects of the Theory which should be understood by perspective users of CC methods. We will also comment on some current developments that are improving the Theory's accuracy or applicability. © 2011 John Wiley & Sons, Ltd.
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many body methods in chemistry and physics mbpt and Coupled Cluster Theory
2009Co-Authors: Isaiah Shavitt, Rodney J BartlettAbstract:Written by two leading experts in the field, this book explores the 'many-body' methods that have become the dominant approach in determining molecular structure, properties and interactions. With a tight focus on the highly popular Many-Body Perturbation Theory (MBPT) and Coupled-Cluster theories (CC), the authors present a simple, clear, unified approach to describe the mathematical tools and diagrammatic techniques employed. Using this book the reader will be able to understand, derive and confidently implement relevant algebraic equations for current and even new multi-reference CC methods. Hundreds of diagrams throughout the book enhance reader understanding through visualization of computational procedures and extensive referencing allows further exploration of this evolving area. With an extensive bibliography and detailed index, this book will be suitable for graduates and researchers within quantum chemistry, chemical physics and atomic, molecular and solid-state physics.
Frank Neese - One of the best experts on this subject based on the ideXlab platform.
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sparse maps a systematic infrastructure for reduced scaling electronic structure methods ii linear scaling domain based pair natural orbital Coupled Cluster Theory
Journal of Chemical Physics, 2016Co-Authors: Christoph Riplinger, Peter Pinski, Ute Becker, Edward F Valeev, Frank NeeseAbstract:Domain based local pair natural orbital Coupled Cluster Theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain Coupled Cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the Coupled Cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate previous implementation.
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sparse maps a systematic infrastructure for reduced scaling electronic structure methods ii linear scaling domain based pair natural orbital Coupled Cluster Theory
Journal of Chemical Physics, 2016Co-Authors: Christoph Riplinger, Peter Pinski, Ute Becker, Edward F Valeev, Frank NeeseAbstract:Domain based local pair natural orbital Coupled Cluster Theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain Coupled Cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital con...
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exploring the accuracy limits of local pair natural orbital Coupled Cluster Theory
Journal of Chemical Theory and Computation, 2015Co-Authors: Dimitrios G Liakos, Manuel Sparta, Manoj K Kesharwani, Jan M L Martin, Frank NeeseAbstract:The domain based local pair natural orbital Coupled Cluster method with single-, double-, and perturbative triple excitations (DLPNO–CCSD(T)) is an efficient quantum chemical method that allows for Coupled Cluster calculations on molecules with hundreds of atoms. Because Coupled-Cluster Theory is the method of choice if high-accuracy is needed, DLPNO–CCSD(T) is very promising for large-scale chemical application. However, the various approximations that have to be introduced in order to reach near linear scaling also introduce limited deviations from the canonical results. In the present work, we investigate how far the accuracy of the DLPNO–CCSD(T) method can be pushed for chemical applications. We also address the question at which additional computational cost improvements, relative to the previously established default scheme, come. To answer these questions, a series of benchmark sets covering a broad range of quantum chemical applications including reaction energies, hydrogen bonds, and other noncov...
Gustavo E Scuseria - One of the best experts on this subject based on the ideXlab platform.
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exact parameterization of fermionic wave functions via unitary Coupled Cluster Theory
Journal of Chemical Physics, 2019Co-Authors: Francesco A Evangelista, Garnet Kin-lic Chan, Gustavo E ScuseriaAbstract:A formal analysis is conducted on the exactness of various forms of unitary Coupled Cluster (UCC) Theory based on particle-hole excitation and de-excitation operators. Both the conventional single exponential UCC parameterization and a factorized (referred to here as “disentangled”) version are considered. We formulate a differential Cluster analysis to determine the UCC amplitudes corresponding to a general quantum state. The exactness of conventional UCC (ability to represent any state) is explored numerically, and it is formally shown to be determined by the structure of the critical points of the UCC exponential mapping. A family of disentangled UCC wave functions is proven to exactly parameterize any state, thus showing how to construct Trotter-error-free parameterizations of UCC for applications in quantum computing. From these results, we construct an exact disentangled UCC parameterization that employs an infinite sequence of particle-hole or general one- and two-body substitution operators.
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exact parameterization of fermionic wave functions via unitary Coupled Cluster Theory
arXiv: Chemical Physics, 2019Co-Authors: Francesco A Evangelista, Garnet Kin-lic Chan, Gustavo E ScuseriaAbstract:A formal analysis is conducted on the exactness of various forms of unitary Coupled Cluster (UCC) Theory based on particle-hole excitation and de-excitation operators. Both the conventional single exponential UCC parameterization and a disentangled (factorized) version are considered. We formulate a differential Cluster analysis to determine the UCC amplitudes corresponding to a general quantum state. The exactness of conventional UCC (ability to represent any state) is explored numerically and it is formally shown to be determined by the structure of the critical points of the UCC exponential mapping. A family of disentangled UCC wave functions are shown to exactly parameterize any state, thus showing how to construct Trotter-error-free parameterizations of UCC for applications in quantum computing. From these results, we derive an exact disentangled UCC parameterization that employs an infinite sequence of particle-hole or general one- and two-body substitution operators.
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projected Coupled Cluster Theory optimization of Cluster amplitudes in the presence of symmetry projection
Journal of Chemical Physics, 2018Co-Authors: Yiheng Qiu, Thomas M Henderson, Jinmo Zhao, Gustavo E ScuseriaAbstract:Methods which aim at universal applicability must be able to describe both weak and strong electronic correlation with equal facility. Such methods are in short supply. The combination of symmetry projection for strong correlation and Coupled Cluster Theory for weak correlation offers tantalizing promise to account for both on an equal footing. In order to do so, however, the Coupled Cluster portion of the wave function must be optimized in the presence of the symmetry projection. This paper discusses how this may be accomplished, and shows the importance of doing so for both the Hubbard model Hamiltonian and the molecular Hamiltonian, all with a computational scaling comparable to that of traditional Coupled Cluster Theory.
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projected hartree fock Theory as a polynomial of particle hole excitations and its combination with variational Coupled Cluster Theory
Journal of Chemical Physics, 2017Co-Authors: Yiheng Qiu, Thomas M Henderson, Gustavo E ScuseriaAbstract:Projected Hartree-Fock Theory provides an accurate description of many kinds of strong correlations but does not properly describe weakly correlated systems. Coupled Cluster Theory, in contrast, does the opposite. It therefore seems natural to combine the two so as to describe both strong and weak correlations with high accuracy in a relatively black-box manner. Combining the two approaches, however, is made more difficult by the fact that the two techniques are formulated very differently. In earlier work, we showed how to write spin-projected Hartree-Fock in a Coupled-Cluster-like language. Here, we fill in the gaps in that earlier work. Further, we combine projected Hartree-Fock and Coupled Cluster Theory in a variational formulation and show how the combination performs for the description of the Hubbard Hamiltonian and for several small molecular systems.
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projected hartree fock as a polynomial of particle hole excitations and its combination with variational Coupled Cluster Theory
arXiv: Strongly Correlated Electrons, 2017Co-Authors: Ethan Qiu, Thomas M Henderson, Gustavo E ScuseriaAbstract:Projected Hartree-Fock Theory provides an accurate description of many kinds of strong correlation but does not properly describe weakly correlated systems. Coupled Cluster Theory, in contrast, does the opposite. It therefore seems natural to combine the two so as to describe both strong and weak correlations with high accuracy in a relatively black-box manner. Combining the two approaches, however, is made more difficult by the fact that the two techniques are formulated very differently. In earlier work, we showed how to write spin-projected Hartree-Fock in a Coupled-Cluster-like language. Here, we fill in the gaps in that earlier work. Further, we combine projected Hartree-Fock and Coupled Cluster Theory in a variational formulation and show how the combination performs for the description of the Hubbard Hamiltonian and for several small molecular systems.
Hansjoachim Werner - One of the best experts on this subject based on the ideXlab platform.
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Perturbation Expansion of Internally Contracted Coupled-Cluster Theory up to Third Order
2019Co-Authors: Yuri Alexandre Aoto, Hansjoachim Werner, Daniel Kats, Arne Bargholz, Andreas KöhnAbstract:The internally contracted multireference Coupled-Cluster (icMRCC) method is analyzed through third order in perturbation Theory. Up to second order, the icMRCC perturbation expansion is equivalent to that of the standard Rayleigh–Schrödinger perturbation Theory, which is based on a linear ansatz for the wave function, and the resulting Theory is, depending on the employed zeroth-order Hamiltonian, equivalent to either second-order complete active space perturbation Theory (CASPT2), N-electron valence perturbation Theory (NEVPT2), or Fink’s retention of the excitation degree perturbation Theory (REPT2). At third order, the icMRCC perturbation expansion features additional terms in comparison to the Rayleigh–Schrödinger perturbation Theory, but these are shown to be nearly negligibly small by both analytic arguments and numerical examples. Considering these systematic cancellations, however, may be important in future work on approximations to icMRCC Theory. In addition, we provide an extensive set of tests of the second and third-order perturbation theories based on three different zeroth-order Hamiltonians, namely, the projected effective Fock operator as used for CASPT, the Dyall Hamiltonian as used for NEVPT, and the Fink Hamiltonian used for REPT. While the third-order variant of REPT often gives absolute energies that are rather close to values from higher level calculations, the results for relative energies and spectroscopic constants such as harmonic frequencies, give a less clear picture and a general conclusion about any best zeroth-order Hamiltonian does not emerge from our data. For small active spaces, REPT is rather prone to intruder state problems
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Embedded Multireference Coupled Cluster Theory
2018Co-Authors: David J. Coughtrie, Hansjoachim Werner, Robin Giereth, Daniel Kats, Andreas KöhnAbstract:Internally contracted multireference Coupled Cluster (icMRCC) Theory is embedded within multireference perturbation Theory (MRPT) to calculate energy differences in large strongly correlated systems. The embedding scheme is based on partitioning the orbital spaces of a complete active space self-consistent field (CASSCF) wave function, with a truncated virtual space constructed by transforming selected projected atomic orbitals (PAOs). MRPT is applied to the environment using a subtractive embedding approach that also allows for multilayer embedding. Benchmark calculations are presented for biradical bond dissociation, spin splitting in a heterocyclic carbene and hydrated Fe(II), and for the super-exchange coupling constant in solid nickel oxide. The method is further applied to two large transition metal complexes with a triple-ζ basis set: an iron complex with 175 atoms and 2939 basis functions, and a nickel complex with 231 atoms, and 4175 basis functions
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accurate calculation of vibrational frequencies using explicitly correlated Coupled Cluster Theory
Journal of Chemical Physics, 2009Co-Authors: Guntram Rauhut, Gerald Knizia, Hansjoachim WernerAbstract:The recently proposed explicitly correlated CCSD(T)-F12x (x=a,b) approximations [T. B. Adler, G. Knizia, and H.-J. Werner, J. Chem. Phys. 127, 221106 (2007)] are applied to compute equilibrium structures and harmonic as well as anharmonic vibrational frequencies for H2O, HCN, CO2, CH2O, H2O2, C2H2, CH2NH, C2H2O, and the trans-isomer of 1,2-C2H2F2. Using aug-cc-pVTZ basis sets, the CCSD(T)-F12a equilibrium geometries and harmonic vibrational frequencies are in very close agreement with CCSD(T)/aug-cc-pV5Z values. The anharmonic frequencies are evaluated using vibrational self-consistent field and vibrational configuration interaction methods based on automatically generated potential energy surfaces. The mean absolute deviation of the CCSD(T)-F12a/aug-cc-pVTZ anharmonic frequencies from experimental values amounts to only 4.0 cm−1.
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Local treatment of electron correlation in Coupled Cluster Theory
The Journal of Chemical Physics, 1996Co-Authors: Claudia Hampel, Hansjoachim WernerAbstract:The closed‐shell Coupled Cluster Theory restricted to single and double excitation operators (CCSD) is formulated in a basis of nonorthogonal local correlation functions. Excitations are made from localized molecular orbitals into subspaces (domains) of the local basis, which strongly reduces the number of amplitudes to be optimized. Furthermore, the correlation of distant electrons can be treated in a simplified way (e.g., by MP2) or entirely neglected. It is demonstrated for 20 molecules that the local correlation treatment recovers 98%–99% of the correlation energy obtained in the corresponding full CCSD calculation. Singles‐doubles configuration interac‐ tion (CISD), quadratic configuration interaction (QCISD), and Mo/ller–Plesset perturbation Theory [MP2, MP3, MP4(SDQ)] are treated as special cases.
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Coupled Cluster Theory for high spin open shell reference wave functions
Journal of Chemical Physics, 1993Co-Authors: Peter J Knowles, Claudia Hampel, Hansjoachim WernerAbstract:The Coupled Cluster method restricted to single and double excitations (CCSD) is considered for the case of a spin restricted Hartree–Fock open shell reference determinant. A spin–orbital based formulation, in which the Cluster operator spans exactly the minimal first order interacting space, is presented, and computationally optimal working equations are given. In the limit of a large number of closed shell orbitals, the cost is identical to that of an optimum treatment of an equivalent closed shell problem, which is obtained as a special case of the formulation presented. The Theory is applied to the calculation of a number of diatomic potential energy functions and compared with spin‐unrestricted Theory.
Debashis Mukherjee - One of the best experts on this subject based on the ideXlab platform.
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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
Journal of Chemical Physics, 2018Co-Authors: Sangita Sen, Avijit Shee, Debashis MukherjeeAbstract: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.
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inactive excitations in mukherjee s state specific multireference Coupled Cluster Theory treated with internal contraction development and applications
Journal of Chemical Physics, 2012Co-Authors: Sanghamitra Das, Dipayan Datta, Shubhrodeep Pathak, Debashis MukherjeeAbstract:One generic difficulty of most state-specific many-body formalisms using the Jeziorski-Monkhorst ansatz: ψ = Σ(μ)exp(T(μ))|φ(μ)>c(μ) for the wave-operators is the large number of redundant Cluster amplitudes. The number of Cluster amplitudes up to a given rank is many more in number compared to the dimension of the Hilbert Space spanned by the virtual functions of up to the same rank of excitations. At the same time, all inactive excitations--though linearly independent--are far too numerous. It is well known from the success of the contracted multi-reference configuration interaction (MRCI(SD)) that, at least for the inactive double excitations, their model space dependence (μ-dependence) is weak. Considerable simplifications can thus be obtained by using a partially internally contracted description, which uses the physically appealing approximation of taking the inactive excitations T(i) to be independent of the model space labels (μ-independent). We propose and implement in this paper such a formalism with internal contractions for inactive excitations (ICI) within Mukherjee's state-specific multi-reference Coupled Cluster Theory (SS-MRCC) framework (referred to from now on as the ICI-SS-MRCC). To the extent the μ-independence of T(i) is valid, we expect the ICI-SS-MRCC to retain the conceptual advantages of size-extensivity yet using a drastically reduced number of Cluster amplitudes without sacrificing accuracy. Moreover, greater coupling is achieved between the virtual functions reached by inactive excitations as a result of the internal contraction while retaining the original coupling term for the μ-dependent excitations akin to the parent Theory. Another major advantage of the ICI-SS-MRCC, unlike the other analogous internally contracted theories, such as IC-MRCISD, CASPT2, or MRMP2, is that it can use relaxed coefficients for the model functions. However, at the same time it employs projection manifolds for the virtuals obtained from inactive n hole-n particle (nh-np) excitations on the entire reference function containing relaxed model space coefficients. The performance of the method has been assessed by applying it to compute the potential energy surfaces of the prototypical H(4); to the torsional potential energy barrier for the cis-trans isomerism in C(2)H(4) as well as that of N(2)H(2), automerization of cyclobutadiene, single point energy calculation of CH(2), SiH(2), and comparing them against the SS-MRCC results, benchmark full CI results, wherever available and those from the allied MR formalisms. Our findings are very much reminiscent of the experience gained from the IC-MRCISD method.
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the spin free analogue of mukherjee s state specific multireference Coupled Cluster Theory
Journal of Chemical Physics, 2011Co-Authors: Dipayan Datta, Debashis MukherjeeAbstract:In this paper, we develop a rigorously spin-adapted version of Mukherjee's state-specific multireference Coupled Cluster Theory (SS-MRCC, also known as Mk-MRCC) [U. S. Mahapatra, B. Datta, and D. Mukherjee, J. Chem. Phys. 110, 6171 (1999)] for reference spaces comprising open-shell configurations. The principal features of our approach are as follows: (1) The wave operator Ω is written as Ω = ∑(μ)Ω(μ)|φ(μ)>c(μ), where {φ(μ)} is the set of configuration state functions spanning a complete active space. (2) In contrast to the Jeziorski-Monkhorst Ansatz in spin-orbital basis, we write Ω(μ) as a power series expansion of Cluster operators R(μ) defined in terms of spin-free unitary generators. (3) The operators R(μ) are either closed-shell-like n hole-n particle excitations (denoted as T(μ)) or they involve valence (active) destruction operators (denoted as S(μ)); these latter type of operators can have active-active scatterings, which can also carry the same active orbital labels (such S(μ)'s are called to have spectator excitations). (4) To simulate multiple excitations involving powers of Cluster operators, we allow the S(μ)'s carrying the same active orbital labels to contract among themselves. (5) We exclude S(μ)'s with direct spectator scatterings. (6) Most crucially, the factors associated with contracted composites are chosen as the inverse of the number of ways the S(μ)'s can be joined among one another leading to the same excitation. The factors introduced in (6) have been called the automorphic factors by us. One principal thrust of this paper is to show that the use of the automorphic factors imparts a remarkable simplicity to the final amplitude equations: the equations consist of terms that are at most quartic in Cluster amplitudes, barring only a few. In close analogy to the Mk-MRCC Theory, the inherent linear dependence of the Cluster amplitudes leading to redundancy is resolved by invoking sufficiency conditions, which are exact spin-free analogues of the spin-orbital based Mk-MRCC Theory. This leads to manifest size-extensivity and an intruder-free formulation. Our formalism provides a relaxed description of the nondynamical correlation in presence of dynamical correlation. Pilot numerical applications to doublet systems, e.g., potential energy surfaces for the first two excited (2)A' states of asymmetric H(2)S(+) ion and the ground (2)Σ(+)state of BeH radical are presented to assess the viability of our formalism over an wide range of nuclear geometries and the manifest avoidance of intruder state problem.
