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Stefan Grimme - One of the best experts on this subject based on the ideXlab platform.
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Spin Component scaled electron correlation methods
Wiley Interdisciplinary Reviews: Computational Molecular Science, 2012Co-Authors: Stefan Grimme, Lars Goerigk, Reinhold F FinkAbstract:Spin-Component-scaled (SCS) electron correlation methods for electronic structure theory are reviewed. The methods can be derived theoretically by applying special conditions to the underlying wave functions in perturbation theory. They are based on the insight that low-order wave function expansions treat the correlation effects of electron pairs with opposite Spin (OS) and same Spin (SS) differently because of their different treatment at the underlying Hartree–Fock level. Physically, this is related to the different average inter-electronic distances in the SS and OS electron pairs. The overview starts with the original SCS-MP2 method and discusses its strengths and weaknesses and various ways to parameterize the scaling factors. Extensions to coupled-cluster and excited state methods as well the connection to virtual-orbital dependent density functional approaches are highlighted. The performance of various SCS methods in large thermochemical benchmarks and for excitation energies is discussed in comparison with other common electronic structure methods.
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assessment of orbital optimized Spin Component scaled second order many body perturbation theory for thermochemistry and kinetics
Journal of Chemical Theory and Computation, 2009Co-Authors: Frank Neese, Simone Kossmann, Tobias Schwabe, Birgitta Schirmer, Stefan GrimmeAbstract:An efficient implementation of the orbital-optimized second-order Moller−Plesset perturbation theory (OO-MP2) within the resolution of the identity (RI) approximation is reported. Both conventional MP2 and Spin-Component scaled (SCS-MP2) variants are considered, and an extensive numerical investigation of the accuracy of these approaches is presented. This work is closely related to earlier work of Lochan, R. C.; Head-Gordon, M. J. Chem. Phys. 2007, 126. Orbital optimization is achieved by making the Hylleraas functional together with the energy of the reference determinant stationary with respect to variations of the double excitation amplitudes and the molecular orbital rotation parameters. A simple iterative scheme is proposed that usually leads to convergence within 5−15 iterations. The applicability of the method to larger molecules (up to ∼1000−2000 basis functions) is demonstrated. The numerical results show that OO-SCS-MP2 is a major improvement in electronically complicated situations, such as re...
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is Spin Component scaled second order moller plesset perturbation theory an appropriate method for the study of noncovalent interactions in molecules
Journal of Physical Chemistry A, 2007Co-Authors: Jens Antony, Stefan GrimmeAbstract:Testing of the Spin-Component scaled second-order Moller−Plesset (SCS-MP2) method for the computation of noncovalent interaction energies is done with a database of 165 biologically relevant complexes. The effects of the Spin-scaling procedure (i.e., MP2 vs SCS-MP2), the basis set size, and the corrections for basis set superposition error (BSSE) are systematically examined. When using two-point basis set extrapolations for the correlation energy, augmentation of the atomic orbital basis with computationally costly diffuse functions is found to be obsolete. In general, SCS-MP2 also improves results for noncovalent interactions statistically on MP2, and significant outliers are removed. Moreover, it is shown that effects of BSSE and one-particle basis set incompleteness almost cancel each other in the case of triple-ζ sets (SCS-MP2/TZVPP or SCS-MP2/cc-pVTZ without counterpoise correction), which opens a practical route to efficient computations for large systems. We recommend SCS-MP2 as the preferred quant...
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accurate calculation of the heats of formation for large main group compounds with Spin Component scaled mp2 methods
Journal of Physical Chemistry A, 2005Co-Authors: Stefan GrimmeAbstract:Three MP2-type electron correlation treatments and standard density functional theory (DFT) approaches are used to predict the heats of formation for a wide variety of different molecules. The SCF and MP2 calculations are performed efficiently using the resolution-of-the-identity (RI) approximation such that large basis set (i.e., polarized valence quadruple-ζ quality) treatments become routinely possible for systems with 50−100 atoms. An atom equivalent scheme that corrects the calculated atomic energies is applied to extract the “real” accuracy of the methods for chemically relevant problems. It is found that the Spin-Component-scaled MP2 method (SCS-MP2, J. Chem. Phys, 2003, 118, 9095) performs best and provides chemical accuracy (MAD of 1.18 kcal/mol) for a G2/97 test set of molecules. The computationally more economical SOS-MP2 variant, which retains only the opposite-Spin part of the correlation energy, is slightly less accurate (MAD of 1.36 kcal/mol) than SCS-MP2. Both Spin-Component-scaled MP2 tre...
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improved reaction and activation energies of 4 2 cycloadditions 3 3 sigmatropic rearrangements and electrocyclizations with the Spin Component scaled mp2 method
Chemistry: A European Journal, 2004Co-Authors: T. P. M. Goumans, Andreas W. Ehlers, Koop Lammertsma, Ernst-ulrich Würthwein, Stefan GrimmeAbstract:A new quantum mechanical scheme to calculate electronic correlation energies, Spin-Component-scaled MP2, was tested as a tool to predict reaction energies and barriers in computational organic chemistry. Three common pericyclic reactions with known unsatisfactory MP2 descriptions were reinvestigated with the modified MP2 approach, in which the parallel and anti-parallel Spin Components of the correlation energy are scaled separately. The SCS-MP2 calculated reaction and activation energies of nine Diels–Alder reactions, four [3,3] sigmatropic rearrangements, and ten electrocyclization reactions are compared to those of the MP2, B3 LYP, QCISD(T), and G3 methods. For each, the SCS-MP2 results are in excellent agreement with the experimental data and compare far more favorably to G3 than both MP2 and B3 LYP. Careful evaluation of the effect of the size of the atomic orbital (AO) basis set shows that the larger expansions improve the agreement with experiment for the SCS-MP2 method, while they get worse for both MP2 and B3 LYP.
Reinhold F Fink - One of the best experts on this subject based on the ideXlab platform.
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Spin Component scaled electron correlation methods
Wiley Interdisciplinary Reviews: Computational Molecular Science, 2012Co-Authors: Stefan Grimme, Lars Goerigk, Reinhold F FinkAbstract:Spin-Component-scaled (SCS) electron correlation methods for electronic structure theory are reviewed. The methods can be derived theoretically by applying special conditions to the underlying wave functions in perturbation theory. They are based on the insight that low-order wave function expansions treat the correlation effects of electron pairs with opposite Spin (OS) and same Spin (SS) differently because of their different treatment at the underlying Hartree–Fock level. Physically, this is related to the different average inter-electronic distances in the SS and OS electron pairs. The overview starts with the original SCS-MP2 method and discusses its strengths and weaknesses and various ways to parameterize the scaling factors. Extensions to coupled-cluster and excited state methods as well the connection to virtual-orbital dependent density functional approaches are highlighted. The performance of various SCS methods in large thermochemical benchmarks and for excitation energies is discussed in comparison with other common electronic structure methods.
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Spin-Component-scaled Møller–Plesset (SCS-MP) perturbation theory: A generalization of the MP approach with improved properties
Journal of Chemical Physics, 2010Co-Authors: Reinhold F FinkAbstract:A rigorous perturbation theory is proposed, which has the same second order energy as the Spin-Component-scaled Moller–Plesset second order (SCS-MP2) method of Grimme [J. Chem. Phys. 118, 9095 (2003)]. This upgrades SCS-MP2 to a systematically improvable, true wave-function-based method. The perturbation theory is defined by an unperturbed Hamiltonian, H(0), that contains the ordinary Fock operator and Spin operators S2 that act either on the occupied or the virtual orbital spaces. Two choices for H(0) are discussed and the importance of a Spin-pure H(0) is underlined. Like the SCS-MP2 approach, the theory contains two parameters (cos and css) that scale the opposite-Spin and the same-Spin contributions to the second order perturbation energy. It is shown that these parameters can be determined from theoretical considerations by a Feenberg scaling approach or a fit of the wave functions from the perturbation theory to the exact one from a full configuration interaction calculation. The parameters cos=...
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Spin Component scaled moller plesset scs mp perturbation theory a generalization of the mp approach with improved properties
Journal of Chemical Physics, 2010Co-Authors: Reinhold F FinkAbstract:A rigorous perturbation theory is proposed, which has the same second order energy as the Spin-Component-scaled Moller–Plesset second order (SCS-MP2) method of Grimme [J. Chem. Phys. 118, 9095 (2003)]. This upgrades SCS-MP2 to a systematically improvable, true wave-function-based method. The perturbation theory is defined by an unperturbed Hamiltonian, H(0), that contains the ordinary Fock operator and Spin operators S2 that act either on the occupied or the virtual orbital spaces. Two choices for H(0) are discussed and the importance of a Spin-pure H(0) is underlined. Like the SCS-MP2 approach, the theory contains two parameters (cos and css) that scale the opposite-Spin and the same-Spin contributions to the second order perturbation energy. It is shown that these parameters can be determined from theoretical considerations by a Feenberg scaling approach or a fit of the wave functions from the perturbation theory to the exact one from a full configuration interaction calculation. The parameters cos=...
Martin Headgordon - One of the best experts on this subject based on the ideXlab platform.
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separate electronic attenuation allowing a Spin Component scaled second order moller plesset theory to be effective for both thermochemistry and noncovalent interactions
Journal of Physical Chemistry B, 2014Co-Authors: Matthew Goldey, Martin HeadgordonAbstract:Spin-Component-scaled (SCS) second-order Moller–Plesset perturbation theory (MP2) improves the treatment of thermochemistry and noncovalent interactions relative to MP2, although the optimal scaling coefficients are quite different for thermochemistry versus noncovalent interactions. This work reconciles these two different scaling regimes for SCS-MP2 by using two different length scales for electronic attenuation of the two Spin Components. The attenuation parameters and scaling coefficients are optimized in the aug-cc-pVTZ (aTZ) basis using the S66 database of intermolecular interactions and the W4-11 database of thermochemistry. Transferability tests are performed for atomization energies and barrier heights, as well as on further test sets for inter- and intramolecular interactions. SCS dual-attenuated MP2 in the aTZ basis, SCS-MP2(2terfc, aTZ), performs similarly to SCS-MP2/aTZ for thermochemistry while frequently outperforming MP2 at the complete basis set limit (CBS) for nonbonded interactions.
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optimized Spin Component scaled second order moller plesset perturbation theory for intermolecular interaction energies
Molecular Physics, 2007Co-Authors: A Robert J R Distasio, Martin HeadgordonAbstract:The optimal set of scaling parameters that minimize the error between Spin-Component scaled (SCS-MP2) and scaled opposite Spin (SOS-MP2) theories and CCSD(T) in computing intermolecular binding energies were determined using multivariate linear least squares analysis. Counterpoise corrected intermolecular binding energies among a diverse test set of hydrogen bonded, dispersion, and mixed complexes (S22 training set) were obtained using RI-MP2 theory and the cc-pVXZ (X = D, T, and Q) and the extrapolated cc-pV(XY)Z (XY = D → T, T → Q) atomic orbital basis set series. Optimization of the opposite Spin-Component scaling parameter yielded the SOS(MI)-MP2 model, with the ability to outperform RI-MP2 theory in obtaining accurate intermolecular binding energies among dispersion complexes with only fourth-order computational effort. At the extrapolated cc-pV(DT)Z and cc-pV(TQ)Z levels, for example, intermolecular binding energies among dispersion complexes were computed with RMS errors of 1.00 kcal/mol and 0.87 k...
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scaled second order perturbation corrections to configuration interaction singles efficient and reliable excitation energy methods
Journal of Physical Chemistry A, 2007Co-Authors: Young Min Rhee, Martin HeadgordonAbstract:Two modifications of the perturbative doubles correction to configuration interaction with single substitutions (CIS(D)) are suggested, which are excited state analogues of ground state scaled second-order Moller−Plesset (MP2) methods. The first approach employs two parameters to scale the two Spin Components of the direct term of CIS(D), starting from the two-parameter Spin-Component scaled (SCS) MP2 ground state, and is termed SCS−CIS(D). An efficient resolution-of-the-identity (RI) implementation of this approach is described. The second approach employs a single parameter to scale only the opposite-Spin direct term of CIS(D), starting from the one-parameter scaled opposite-Spin (SOS) MP2 ground state, and is called SOS−CIS(D). By utilizing auxiliary basis expansions and a Laplace transform, a fourth-order algorithm for SOS−CIS(D) is described and implemented. The parameters that describe SCS−CIS(D) and SOS−CIS(D) are optimized based on a training set that includes valence excitations of various organi...
Ugur Bozkaya - One of the best experts on this subject based on the ideXlab platform.
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Assessment of Orbital-Optimized Third-Order Møller−Plesset Perturbation Theory and Its Spin-Component and Spin-Opposite Scaled Variants for Thermochemistry and Kinetics
Journal of Chemical Theory and Computation, 2013Co-Authors: Emine Soydas, Ugur BozkayaAbstract:An assessment of the OMP3 method and its Spin-Component and Spin-scaled variants for thermochemistry and kinetics is presented. For reaction energies of closed-shell systems, the CCSD, SCS-MP3, and SCS-OMP3 methods show better performances than other considered methods, and no significant improvement is observed due to orbital optimization. For barrier heights, OMP3 and SCS-OMP3 provide the lowest mean absolute deviations. The MP3 method yields considerably higher errors, and the Spin scaling approaches do not help to improve upon MP3, but worsen it. For radical stabilization energies, the CCSD, OMP3, and SCS-OMP3 methods exhibit noticeably better performances than MP3 and its variants. Our results demonstrate that if the reference wave function suffers from a Spin-contamination, then the MP3 methods dramatically fail. On the other hand, the OMP3 method and its variants can tolerate the Spin-contamination in the reference wave function. For overall evaluation, we conclude that OMP3 is quite helpful, espec...
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assessment of orbital optimized third order moller plesset perturbation theory and its Spin Component and Spin opposite scaled variants for thermochemistry and kinetics
Journal of Chemical Theory and Computation, 2013Co-Authors: Emine Soydas, Ugur BozkayaAbstract:An assessment of the OMP3 method and its Spin-Component and Spin-scaled variants for thermochemistry and kinetics is presented. For reaction energies of closed-shell systems, the CCSD, SCS-MP3, and SCS-OMP3 methods show better performances than other considered methods, and no significant improvement is observed due to orbital optimization. For barrier heights, OMP3 and SCS-OMP3 provide the lowest mean absolute deviations. The MP3 method yields considerably higher errors, and the Spin scaling approaches do not help to improve upon MP3, but worsen it. For radical stabilization energies, the CCSD, OMP3, and SCS-OMP3 methods exhibit noticeably better performances than MP3 and its variants. Our results demonstrate that if the reference wave function suffers from a Spin-contamination, then the MP3 methods dramatically fail. On the other hand, the OMP3 method and its variants can tolerate the Spin-contamination in the reference wave function. For overall evaluation, we conclude that OMP3 is quite helpful, espec...
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orbital optimized third order moller plesset perturbation theory and its Spin Component and Spin opposite scaled variants application to symmetry breaking problems
Journal of Chemical Physics, 2011Co-Authors: Ugur BozkayaAbstract:In this research, orbital-optimized third-order Moller-Plesset perturbation theory (OMP3) and its Spin-Component and Spin-opposite scaled variants (SCS-OMP3 and SOS-OMP3) are introduced. Using a Lagrangian-based approach, an efficient, quadratically convergent algorithm for variational optimization of the molecular orbitals (MOs) for third-order Moller-Plesset perturbation theory (MP3) is presented. Explicit equations for response density matrices, the MO gradient, and Hessian are reported in Spin-orbital form. The OMP3, SCS-OMP3, and SOS-OMP3 approaches are compared with the second-order Moller-Plesset perturbation theory (MP2), MP3, coupled-cluster doubles (CCD), optimized-doubles (OD), and coupled-cluster singles and doubles (CCSD) methods. All these methods are applied to the O4+, O3, and seven diatomic molecules. Results demonstrate that the OMP3 and its variants provide significantly better vibrational frequencies than MP3, CCSD, and OD for the molecules where the symmetry-breaking problems are obse...
David C Sherrill - One of the best experts on this subject based on the ideXlab platform.
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appointing silver and bronze standards for noncovalent interactions a comparison of Spin Component scaled scs explicitly correlated f12 and specialized wavefunction approaches
Journal of Chemical Physics, 2014Co-Authors: Lori A Burns, Michael S Marshall, David C SherrillAbstract:A systematic examination of noncovalent interactions as modeled by wavefunction theory is presented in comparison to gold-standard quality benchmarks available for 345 interaction energies of 49 bimolecular complexes. Quantum chemical techniques examined include Spin-Component-scaling (SCS) variations on second-order perturbation theory (MP2) [SCS, SCS(N), SCS(MI)] and coupled cluster singles and doubles (CCSD) [SCS, SCS(MI)]; also, method combinations designed to improve dispersion contacts [DW-MP2, MP2C, MP2.5, DW-CCSD(T)-F12]; where available, explicitly correlated (F12) counterparts are also considered. Dunning basis sets augmented by diffuse functions are employed for all accessible ζ-levels; truncations of the diffuse space are also considered. After examination of both accuracy and performance for 394 model chemistries, SCS(MI)-MP2/cc-pVQZ can be recommended for general use, having good accuracy at low cost and no ill-effects such as imbalance between hydrogen-bonding and dispersion-dominated syste...
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performance of Spin Component scaled moller plesset theory scs mp2 for potential energy curves of noncovalent interactions
Physical Chemistry Chemical Physics, 2007Co-Authors: Tait Takatani, David C SherrillAbstract:An examination of the performance of density-fitted, Spin-Component-scaled, second-order Moller–Plesset theory (SCS-MP2), SCS-MP2 with parameters optimized for nucleic acids (SCSN-MP2), and their local-correlation variants, SCS-LMP2 and SCSN-LMP2, is presented for the sandwich and T-shaped benzene dimers, the methane–benzene and H2S–benzene complexes, and the methane dimer over entire potential energy curves. These are compared to benchmark-quality estimates of the complete-basis-set limit for coupled-cluster theory through perturbative triple excitations, CCSD(T)/CBS. With the exception of the methane dimer, SCSN-LMP2/CBS tends to outperform SCS-LMP2/CBS with maximum relative errors of 6 and 18%, respectively, at the optimal CCSD(T)/CBS intermolecular distances. For the methane dimer, errors for SCS(N)-(L)MP2/CBS remain in the 0.2–0.3 kcal mol−1 range, corresponding to a larger relative error of 40–50%. Although the local MP2 methods perform very similarly to their conventional counterparts when aug-cc-pVTZ or larger basis sets are used, in the absence of counterpoise correction the local approximation becomes significantly worse for the aug-cc-pVDZ basis set. The changes due to local correlation approximations for the aug-cc-pVDZ basis are reduced when diffuse functions are neglected for hydrogen atoms.