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Rodney J. Bartlett - One of the best experts on this subject based on the ideXlab platform.
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spin orbit splitted excited states using explicitly correlated Equation of Motion coupled cluster singles and doubles eigenvectors
Chemical Physics Letters, 2018Co-Authors: Denis Bokhan, Ajith Perera, D N Trubnikov, Rodney J. BartlettAbstract:Abstract An explicitly-correlated method of calculation of excited states with spin-orbit couplings, has been formulated and implemented. Developed approach utilizes left and right eigenvectors of Equation-of-Motion coupled-cluster model, which is based on the linearly approximated explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] method. The spin-orbit interactions are introduced by using the spin-orbit mean field (SOMF) approximation of the Breit-Pauli Hamiltonian. Numerical tests for several atoms and molecules show good agreement between explicitly-correlated results and the corresponding values, calculated in complete basis set limit (CBS); the highly-accurate excitation energies can be obtained already at triple- ζ level.
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explicitly correlated double ionization potentials and double electron attachment Equation of Motion coupled cluster methods
Chemical Physics Letters, 2018Co-Authors: Denis Bokhan, Ajith Perera, D N Trubnikov, Rodney J. BartlettAbstract:Abstract Double ionization and double electron attachment Equation-of-Motion methods, based on linearly approximated explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] are formulated and implemented. An extension of double electron attachment operator is introduced for proper account of short-range correlation effects in states with two additional electrons. Numerical tests for set of doubly ionized and doubly electron attached states of several molecules have shown a good agreement between obtained explicitly-correlated results and the corresponding complete basis set limit values already at double- ζ level.
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approximating electronically excited states with Equation of Motion linear coupled cluster theory
Journal of Chemical Physics, 2015Co-Authors: Jason N Byrd, Rodney J. Bartlett, Ajith Perera, Varun RishiAbstract:A new perturbative approach to canonical Equation-of-Motion coupled-cluster theory is presented using coupled-cluster perturbation theory. A second-order Moller-Plesset partitioning of the Hamiltonian is used to obtain the well known Equation-of-Motion many-body perturbation theory Equations and two new Equation-of-Motion methods based on the linear coupled-cluster doubles and linear coupled-cluster singles and doubles wavefunctions. These new methods are benchmarked against very accurate theoretical and experimental spectra from 25 small organic molecules. It is found that the proposed methods have excellent agreement with canonical Equation-of-Motion coupled-cluster singles and doubles state for state orderings and relative excited state energies as well as acceptable quantitative agreement for absolute excitation energies compared with the best estimate theory and experimental spectra.
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explicitly correlated similarity transformed Equation of Motion coupled cluster method
Journal of Chemical Physics, 2015Co-Authors: Denis Bokhan, D N Trubnikov, Rodney J. BartlettAbstract:Similarity transformed Equation-of-Motion method, based on linearly approximated explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] model, has been formulated and implemented. An extension of similarity transformation operator is introduced in order to treat short-range correlation effects for excited states. Additionally, effective reduction of the number of active virtuals can be obtained by such modification. Numerical tests for sets of valence and Rydberg excited states of several molecules are conducted. Statistical measures of errors in excitation energies show that explicitly correlated results are accurate up to 0.1 e.V already at a double-ζ level compared to those in the complete basis set limit, if the excitation energy is not too close to an ionization threshold. An example of long-range charge transfer excitation is also considered and highly accurate results are obtained.
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approximating electronically excited states with Equation of Motion linear coupled cluster theory
arXiv: Chemical Physics, 2015Co-Authors: Jason N Byrd, Rodney J. Bartlett, Ajith Perera, Varun RishiAbstract:A new perturbative approach to canonical Equation-of-Motion coupled-cluster theory is presented using coupled-cluster perturbation theory. A second-order M{\o}ller-Plesset partitioning of the Hamiltonian is used to obtain the well known Equation-of-Motion many-body perturbation theory (EOM-MBPT(2)) Equations and two new Equation-of-Motion methods based on the linear coupled-cluster doubles (EOM-LCCD) and linear coupled-cluster singles and doubles (EOM-LCCSD) wavefunctions. This is achieved by performing a short-circuiting procedure on the MBPT(2) similarity transformed Hamiltonian. These new methods are benchmarked against very accurate theoretical and experimental spectra from 25 small organic molecules. It is found that the proposed methods have excellent agreement with canonical EOM-CCSD state for state orderings and relative excited state energies as well as acceptable quantitative agreement for absolute excitation energies compared with the best estimate theory and experimental spectra.
Marcel Nooijen - One of the best experts on this subject based on the ideXlab platform.
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a perturbative approach to multireference Equation of Motion coupled cluster
Molecular Physics, 2021Co-Authors: Marvin H Lechner, Robert Izsak, Marcel Nooijen, Frank NeeseAbstract:We introduce a variant of the multireference Equation-of-Motion coupled-cluster (MR-EOMCC) method where the amplitudes used for the similarity transformations are estimated from perturbation theory...
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similarity transformed Equation of Motion vibrational coupled cluster theory
Journal of Chemical Physics, 2018Co-Authors: Jacob A Faucheaux, Marcel Nooijen, So HirataAbstract:A similarity-transformed Equation-of-Motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the Equation-of-Motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working Equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore el...
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Benchmark Applications of Variations of Multireference Equation of Motion Coupled-Cluster Theory
2016Co-Authors: Lee M J Huntington, Ondřej Demel, Marcel NooijenAbstract:In this work, several variations of the multireference Equation of Motion (MR-EOM) methodology are investigated for the calculation of excitation spectra. These variants of MR-EOM are characterized by the following aspects: (1) the operators included in the sequence of similarity transformations of the molecular electronic Hamiltonian, (2) whether permutational symmetries (i.e., hermitization, vertex symmetry) are imposed on the final elements of the similarity-transformed Hamiltonian, (3) the size of the manifold over which the similarity-transformed Hamiltonian is diagonalized, (4) whether the two-body cumulant is included in the expressions defining the amplitudes and the elements of the transformed Hamiltonian. The MR-EOM methods are benchmarked for the calculation of the excitation energies of a test set of organic molecules. With the availability of reliable benchmark data for this test set, it is possible to gauge the relative accuracy of these approaches. We also further examine a subset of the MR-EOM methods for the calculation of the excitation energies of some transition-metal complexes. These systems prove to be particularly difficult for single-reference coupled-cluster methods
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application of the multireference Equation of Motion coupled cluster method including spin orbit coupling to the atomic spectra of cr mn fe and co
Molecular Physics, 2015Co-Authors: Zhebing Liu, Lee M J Huntington, Marcel NooijenAbstract:The recently introduced multireference Equation of Motion (MR-EOM) approach is combined with a simple treatment of spin–orbit coupling, as implemented in the ORCA program. The resulting multireference Equation of Motion spin–orbit coupling (MR-EOM-SOC) approach is applied to the first-row transition metal atoms Cr, Mn, Fe and Co, for which experimental data are readily available. Using the MR-EOM-SOC approach, the splittings in each L-S multiplet can be accurately assessed (root mean square (RMS) errors of about 70 cm−1). The RMS errors for J-specific excitation energies range from 414 to 783 cm−1 and are comparable to previously reported J-averaged MR-EOM results using the ACESII program. The MR-EOM approach is highly efficient. A typical MR-EOM calculation of a full spin–orbit spectrum takes about 2 CPU hours on a single processor of a 12-core node, consisting of Intel XEON 2.93 GHz CPUs with 12.3 MB of shared cache memory.
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analytical energy gradients for excited state coupled cluster methods automated algebraic derivation of first derivatives for Equation of Motion coupled cluster and similarity transformed Equation of Motion coupled cluster theories
AdQC, 2005Co-Authors: Mark Wladyslawski, Marcel NooijenAbstract:Abstract The Equation-of-Motion coupled-cluster (EOM-CC) and similarity transformed Equation-of-Motion coupled-cluster (STEOM-CC) methods have been firmly established as accurate and routinely applicable extensions of single-reference coupled-cluster theory to describe electronically excited states. An overview of these methods is provided, with emphasis on the many-body similarity transform concept that is the key to a rationalization of their accuracy. The main topic of the paper is the derivation of analytical energy gradients for such non-variational electronic structure approaches, with an ultimate focus on obtaining their detailed algebraic working Equations. A general theoretical framework using Lagrange's method of undetermined multipliers is presented, and the method is applied to formulate the EOM-CC and STEOM-CC gradients in abstract operator terms, following the previous work in [P.G. Szalay, Int. J. Quantum Chem. 55 (1995) 151] and [S.R. Gwaltney, R.J. Bartlett, M. Nooijen, J. Chem. Phys. 111 (1999) 58]. Moreover, the systematics of the Lagrange multiplier approach is suitable for automation by computer, enabling the derivation of the detailed derivative Equations through a standardized and direct procedure. To this end, we have developed the SMART (Symbolic Manipulation and Regrouping of Tensors) package of automated symbolic algebra routines, written in the Mathematica programming language. The SMART toolkit provides the means to expand, differentiate, and simplify Equations by manipulation of the detailed algebraic tensor expressions directly. The Lagrangian multiplier formulation establishes a uniform strategy to perform the automated derivation in a standardized manner: A Lagrange multiplier functional is constructed from the explicit algebraic Equations that define the energy in the electronic method; the energy functional is then made fully variational with respect to all of its parameters, and the symbolic differentiations directly yield the explicit Equations for the wavefunction amplitudes, the Lagrange multipliers, and the analytical gradient via the perturbation-independent generalized Hellmann–Feynman effective density matrix. This systematic automated derivation procedure is applied to obtain the detailed gradient Equations for the excitation energy (EE-), double ionization potential (DIP-), and double electron affinity (DEA-) similarity transformed Equation-of-Motion coupled-cluster singles-and-doubles (STEOM-CCSD) methods. In addition, the derivatives of the closed-shell-reference excitation energy (EE-), ionization potential (IP-), and electron affinity (EA-) Equation-of-Motion coupled-cluster singles-and-doubles (EOM-CCSD) methods are derived. Furthermore, the perturbative EOM-PT and STEOM-PT gradients are obtained. The algebraic derivative expressions for these dozen methods are all derived here uniformly through the automated Lagrange multiplier process and are expressed compactly in a chain-rule/intermediate-density formulation, which facilitates a unified modular implementation of analytic energy gradients for CCSD/PT-based electronic methods. The working Equations for these analytical gradients are presented in full detail, and their factorization and implementation into an efficient computer code are discussed.
Y Itoh - One of the best experts on this subject based on the ideXlab platform.
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Equation of Motion for relativistic compact binaries with the strong field point particle limit third post newtonian order
Physical Review D, 2004Co-Authors: Y ItohAbstract:An Equation of Motion for relativistic compact binaries is derived through the third post-Newtonian (3PN) approximation of general relativity. The strong field point-particle limit and multipole expansion of the stars are used to solve iteratively the harmonically relaxed Einstein Equations. We take into account the Lorentz contraction on the multipole moments defined in our previous works. We then derive a 3PN acceleration of the binary orbital Motion of the two spherical compact stars based on a surface integral approach which is a direct consequence of local energy momentum conservation. Our resulting Equation of Motion admits a conserved energy (neglecting the 2.5PN radiation reaction effect), is Lorentz invariant, and is unambiguous: there exist no undetermined parameters reported in the previous works. We shall show that our 3PN Equation of Motion agrees physically with the Blanchet-Faye 3PN Equation of Motion if $\ensuremath{\lambda}=\ensuremath{-}1987/3080,$ where $\ensuremath{\lambda}$ is the parameter which is undetermined within their framework. This value of $\ensuremath{\lambda}$ is consistent with the result of Damour, Jaranowski, and Sch\"afer, who first completed a 3PN iteration of the ADM Hamiltonian in the ADMTT gauge using dimensional regularization.
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Equation of Motion for relativistic compact binaries with the strong field point particle limit the second and half post newtonian order
Physical Review D, 2001Co-Authors: Y Itoh, Toshifumi Futamase, Hideki AsadaAbstract:We study the Equation of Motion appropriate to an inspiraling binary star system whose constituent stars have strong internal gravity. We use the post-Newtonian approximation with the strong field point particle limit by which we can introduce into general relativity a notion of a pointlike particle with strong internal gravity without using the Dirac delta distribution. In addition to this limit, to deal with strong internal gravity we express the Equation of Motion in surface integral forms and calculate these integrals explicitly. As a result we obtain the Equation of Motion for a binary of compact bodies accurate through the second and half post-Newtonian (2.5 PN) order. This Equation is derived in the harmonic coordinate. Our resulting Equation perfectly agrees with the Damour-Deruelle 2.5 PN Equation of Motion. Hence it is found that the 2.5 PN Equation of Motion is applicable to a relativistic compact binary.
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Equation of Motion for relativistic compact binaries with the strong field point particle limit formulation the first post newtonian order and multipole terms
Physical Review D, 2000Co-Authors: Y Itoh, Toshifumi Futamase, Hideki AsadaAbstract:We derive the Equation of Motion for the relativistic compact binaries in the post-Newtonian approximation taking explicitly their strong internal gravity into account. For this purpose we adopt the method of the point particle limit where the Equation of Motion is expressed in terms of the surface integrals. We examine carefully the behavior of the surface integrals in the derivation. As a result, we obtain the Einstein-Infeld-Hoffman Equation of Motion at the first post-Newtonian (1PN) order, and a part of the 2PN order which depends on the quadrupole moments and the spins of component stars. Hence, it is found that the Equation of Motion in the post-Newtonian approximation is valid for compact binaries by a suitable definition of the mass, spin, and quadrupole moment.
So Hirata - One of the best experts on this subject based on the ideXlab platform.
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similarity transformed Equation of Motion vibrational coupled cluster theory
Journal of Chemical Physics, 2018Co-Authors: Jacob A Faucheaux, Marcel Nooijen, So HirataAbstract:A similarity-transformed Equation-of-Motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the Equation-of-Motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working Equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore el...
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Higher-order Equation-of-Motion coupled-cluster methods for ionization processes
Journal of Chemical Physics, 2006Co-Authors: Muneaki Kamiya, So HirataAbstract:Compact algebraic Equations defining the Equation-of-Motion coupled-cluster (EOM-CC) methods for ionization potentials (IP-EOM-CC) have been derived and computer implemented by virtue of a symbolic algebra system largely automating these processes. Models with connected cluster excitation operators truncated after double, triple, or quadruple level and with linear ionization operators truncated after two-hole-one-particle (2h1p), three-hole-two-particle (3h2p), or four-hole-three-particle (4h3p) level (abbreviated as IP-EOM-CCSD, CCSDT, and CCSDTQ, respectively) have been realized into parallel algorithms taking advantage of spin, spatial, and permutation symmetries with optimal size dependence of the computational costs. They are based on spin-orbital formalisms and can describe both α and β ionizations from open-shell (doublet, triplet, etc.) reference states into ionized states with various spin magnetic quantum numbers. The application of these methods to Koopmans and satellite ionizations of N2 and C...
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Higher-order Equation-of-Motion coupled-cluster methods
Journal of Chemical Physics, 2004Co-Authors: So HirataAbstract:The Equation-of-Motion coupled-cluster (EOM-CC) methods truncated after double, triple, or quadruple cluster and linear excitation operators (EOM-CCSD, EOM-CCSDT, and EOM-CCSDTQ) have been derived and implemented into parallel execution programs. They compute excitation energies, excited-state dipole moments, and transition moments of closed- and open-shell systems, taking advantage of spin, spatial (real Abelian), and permutation symmetries simultaneously and fully (within the spin–orbital formalisms). The related Λ Equation solvers for coupled-cluster (CC) methods through and up to connected quadruple excitation (CCSD, CCSDT, and CCSDTQ) have also been developed. These developments have been achieved, by virtue of the algebraic and symbolic manipulation program that automated the formula derivation and implementation altogether. The EOM-CC methods and CC Λ Equations introduce a class of second quantized ansatz with a de-excitation operator (Ŷ), a number of excitation operators (X), and a physical (e.g....
Hideki Asada - One of the best experts on this subject based on the ideXlab platform.
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Equation of Motion for relativistic compact binaries with the strong field point particle limit the second and half post newtonian order
Physical Review D, 2001Co-Authors: Y Itoh, Toshifumi Futamase, Hideki AsadaAbstract:We study the Equation of Motion appropriate to an inspiraling binary star system whose constituent stars have strong internal gravity. We use the post-Newtonian approximation with the strong field point particle limit by which we can introduce into general relativity a notion of a pointlike particle with strong internal gravity without using the Dirac delta distribution. In addition to this limit, to deal with strong internal gravity we express the Equation of Motion in surface integral forms and calculate these integrals explicitly. As a result we obtain the Equation of Motion for a binary of compact bodies accurate through the second and half post-Newtonian (2.5 PN) order. This Equation is derived in the harmonic coordinate. Our resulting Equation perfectly agrees with the Damour-Deruelle 2.5 PN Equation of Motion. Hence it is found that the 2.5 PN Equation of Motion is applicable to a relativistic compact binary.
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Equation of Motion for relativistic compact binaries with the strong field point particle limit formulation the first post newtonian order and multipole terms
Physical Review D, 2000Co-Authors: Y Itoh, Toshifumi Futamase, Hideki AsadaAbstract:We derive the Equation of Motion for the relativistic compact binaries in the post-Newtonian approximation taking explicitly their strong internal gravity into account. For this purpose we adopt the method of the point particle limit where the Equation of Motion is expressed in terms of the surface integrals. We examine carefully the behavior of the surface integrals in the derivation. As a result, we obtain the Einstein-Infeld-Hoffman Equation of Motion at the first post-Newtonian (1PN) order, and a part of the 2PN order which depends on the quadrupole moments and the spins of component stars. Hence, it is found that the Equation of Motion in the post-Newtonian approximation is valid for compact binaries by a suitable definition of the mass, spin, and quadrupole moment.