Coupled-cluster theory in quantum chemistry
TL;DR: In this article, the essential aspects of coupled-cluster theory are explained and illustrated with informative numerical results, showing that the theory offers the most accurate results among the practical ab initio electronic-structure theories applicable to moderate-sized molecules.
Abstract: Today, coupled-cluster theory offers the most accurate results among the practical ab initio electronic-structure theories applicable to moderate-sized molecules. Though it was originally proposed for problems in physics, it has seen its greatest development in chemistry, enabling an extensive range of applications to molecular structure, excited states, properties, and all kinds of spectroscopy. In this review, the essential aspects of the theory are explained and illustrated with informative numerical results.
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TL;DR: An overview of NWChem is provided focusing primarily on the core theoretical modules provided by the code and their parallel performance, as well as Scalable parallel implementations and modular software design enable efficient utilization of current computational architectures.
4,666 citations
TL;DR: A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided in this paper, covering approximately the last seven years, including developments in density functional theory and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces.
Abstract: A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Moller–Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr_2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.
2,396 citations
01 Jan 2015
TL;DR: Detailed benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Møller–Plesset methods for intermolecular interactions, and tests of the accuracy of implicit solvation models are provided.
Abstract: A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Møller–Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.
1,919 citations
TL;DR: The Cholesky decomposition method applied to some quantum chemical methods is described, and the ElectroStatic Potential Fitted scheme, a version of a quantum mechanics/molecular mechanics hybrid method implemented in MOLCAS, is described and discussed.
Abstract: Some of the new unique features of the MOLCAS quantum chemistry package version 7 are presented inthis report. In particular, the Cholesky decomposition method applied to some quantum chemical methods is described. This approach is used both in the context of a straight forward approximation of the two-electron integrals and in the generation of so-called auxiliary basis sets. The article describes how the method is implemented for most known wave functions models: self-consistent field, density functional theory, 2nd order perturbation theory, complete-active space self-consistent field multiconfigurational reference 2nd order perturbation theory, and coupled-cluster methods. The report further elaborates on the implementation of a restricted-active space self-consistent field reference function in conjunction with 2nd order perturbation theory. The average atomic natural orbital basis for relativistic calculations, covering the whole periodic table, are described and associated unique properties are demonstrated. Furthermore, the use of the arbitrary order Douglas-Kroll-Hess transformation for one-component relativistic calculations and its implementation are discussed. This section especially focuses on the implementation of the so-called picture-change-free atomic orbital property integrals. Moreover, the ElectroStatic Potential Fitted scheme, a version of a quantum mechanics/molecular mechanics hybrid method implemented in MOLCAS, is described and discussed. Finally, the report discusses the use of the MOLCAS package for advanced studies of photo chemical phenomena and the usefulness of the algorithms for constrained geometry optimization in MOLCAS in association with such studies. (c) 2009 Wiley Periodicals, Inc. J Corn put Chem 31: 224-247, 2010
1,492 citations
TL;DR: Peruzzo et al. as mentioned in this paper developed a variational adiabatic ansatz and explored unitary coupled cluster where they established a connection from second order unitary cluster to universal gate sets through a relaxation of exponential operator splitting.
Abstract: Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as 'the quantum variational eigensolver' was developed (Peruzzo et al 2014 Nat. Commun. 5 4213) with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through a relaxation of exponential operator splitting. We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we show how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.
1,490 citations
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TL;DR: In this paper, the Hartree and Hartree-Fock equations are applied to a uniform electron gas, where the exchange and correlation portions of the chemical potential of the gas are used as additional effective potentials.
Abstract: From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high density. For the ground state, they lead to self-consistent equations analogous to the Hartree and Hartree-Fock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as additional effective potentials. (The exchange portion of our effective potential differs from that due to Slater by a factor of $\frac{2}{3}$.) Electronic systems at finite temperatures and in magnetic fields are also treated by similar methods. An appendix deals with a further correction for systems with short-wavelength density oscillations.
47,477 citations
"Coupled-cluster theory in quantum c..." refers background in this paper
...For any other choice of orbitals and reference determinant, such as Kohn-Sham where the density is given by a single determinant Kohn and Sham, 1965 , natural Löwdin, 1955 where the first natural determinant gives the best single determinant approximation to the density matrix , and Brueckner…...
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TL;DR: In this paper, a detailed study of correlation effects in the oxygen atom was conducted, and it was shown that primitive basis sets of primitive Gaussian functions effectively and efficiently describe correlation effects.
Abstract: In the past, basis sets for use in correlated molecular calculations have largely been taken from single configuration calculations. Recently, Almlof, Taylor, and co‐workers have found that basis sets of natural orbitals derived from correlated atomic calculations (ANOs) provide an excellent description of molecular correlation effects. We report here a careful study of correlation effects in the oxygen atom, establishing that compact sets of primitive Gaussian functions effectively and efficiently describe correlation effects i f the exponents of the functions are optimized in atomic correlated calculations, although the primitive (s p) functions for describing correlation effects can be taken from atomic Hartree–Fock calculations i f the appropriate primitive set is used. Test calculations on oxygen‐containing molecules indicate that these primitive basis sets describe molecular correlation effects as well as the ANO sets of Almlof and Taylor. Guided by the calculations on oxygen, basis sets for use in correlated atomic and molecular calculations were developed for all of the first row atoms from boron through neon and for hydrogen. As in the oxygen atom calculations, it was found that the incremental energy lowerings due to the addition of correlating functions fall into distinct groups. This leads to the concept of c o r r e l a t i o n c o n s i s t e n t b a s i s s e t s, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation consistent sets are given for all of the atoms considered. The most accurate sets determined in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding ANO sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estimated that this set yields 94%–97% of the total (HF+1+2) correlation energy for the atoms neon through boron.
26,705 citations
"Coupled-cluster theory in quantum c..." refers background in this paper
...High-level calculations will typically use a converging series of Gaussian basis functions such as the cc-pVXZ sets Dunning, 1989; Kendall et al., 1992; Woon and Dunning, 1993 or atomic natural orbital sets Almlöf and Taylor, 1987 , where cc means “correlation consistent,” the pV indicates…...
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TL;DR: In this paper, a reliable procedure for calculating the electron affinity of an atom and present results for hydrogen, boron, carbon, oxygen, and fluorine (hydrogen is included for completeness).
Abstract: The calculation of accurate electron affinities (EAs) of atomic or molecular species is one of the most challenging tasks in quantum chemistry. We describe a reliable procedure for calculating the electron affinity of an atom and present results for hydrogen, boron, carbon, oxygen, and fluorine (hydrogen is included for completeness). This procedure involves the use of the recently proposed correlation‐consistent basis sets augmented with functions to describe the more diffuse character of the atomic anion coupled with a straightforward, uniform expansion of the reference space for multireference singles and doubles configuration‐interaction (MRSD‐CI) calculations. Comparison with previous results and with corresponding full CI calculations are given. The most accurate EAs obtained from the MRSD‐CI calculations are (with experimental values in parentheses) hydrogen 0.740 eV (0.754), boron 0.258 (0.277), carbon 1.245 (1.263), oxygen 1.384 (1.461), and fluorine 3.337 (3.401). The EAs obtained from the MR‐SD...
12,969 citations
"Coupled-cluster theory in quantum c..." refers background in this paper
...High-level calculations will typically use a converging series of Gaussian basis functions such as the cc-pVXZ sets Dunning, 1989; Kendall et al., 1992; Woon and Dunning, 1993 or atomic natural orbital sets Almlöf and Taylor, 1987 , where cc means “correlation consistent,” the pV indicates…...
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TL;DR: In this paper, a new augmented version of coupled-cluster theory, denoted as CCSD(T), is proposed to remedy some of the deficiencies of previous augmented coupledcluster models.
7,249 citations
TL;DR: The coupled cluster singles and doubles model (CCSD) as discussed by the authors is derived algebraically, presenting the full set of equations for a general reference function explicitly in spin-orbital form, and the computational implementation of the CCSD model, which involves cubic and quartic terms, is discussed and results are compared with full CI calculations for H2O and BeH2.
Abstract: The coupled‐cluster singles and doubles model (CCSD) is derived algebraically, presenting the full set of equations for a general reference function explicitly in spin–orbital form. The computational implementation of the CCSD model, which involves cubic and quartic terms, is discussed and results are reported and compared with full CI calculations for H2O and BeH2. We demonstrate that the CCSD exponential ansatz sums higher‐order correlation effects efficiently even for BeH2, near its transition state geometry where quasidegeneracy efforts are quite large, recovering 98% of the full CI correlation energy. For H2O, CCSD plus the fourth‐order triple excitation correction agrees with the full CI energy to 0.5 kcal/mol. Comparisons with low‐order models provide estimates of the effect of the higher‐order terms T1T2, T21T2, T31, and T41 on the correlation energy.
5,603 citations
"Coupled-cluster theory in quantum c..." refers background or methods in this paper
...Yet, today, CCSD Purvis and Bartlett, 1982 , CCSDT-1 Lee et al., 1984 , CCSDT-3 Noga et al., 1987 , CCSD T Urban et al., 1985 , and CCSD T Ragavachari et al., 1989; Bartlett et al., 1990 calculations are done with 300 basis functions and have used 600....
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...Starting in 1978 general purpose programs and applications of CC theory were developed Bartlett and Purvis, 1978, 1980; Pople et al., 1978; Purvis and Bartlett, 1982 ....
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...The role of single excitations in CCSD Purvis and Bartlett, 1982 theory, CCSD=exp T1+T2 0 , is quite important....
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...CCSD was first formulated and implemented in 1982 Purvis and Bartlett, 1982 ....
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