FN ISI Export Format VR 1.0 PT J AU Theophilou, I Thanos, S Theophilou, AK AF Theophilou, Iris Thanos, S. Theophilou, A. K. TI Spin contamination for Hartree-Fock, optimized effective potential, and density functional approximations SO JOURNAL OF CHEMICAL PHYSICS AB In an earlier paper [S. Thanos and A. K. Theophilou J. Chem. Phys. 124, 204109 (2006)], we found an explicit formula for the expansion of a Slater determinant vertical bar Phi(M)> in terms of eigenstates of S-2. In this paper, we use the same formula to determine the spin contamination S-con of the unrestricted single determinant approximations, i.e., Hartree-Fock, optimized effective potential, and density functional theory. We derived an expression which gives S-con in terms of the overlap of the spatial parts of the spin up and spin down "corresponding" orbitals. It was found that S-con does not depend on M, the eigenvalue of S-z, at least for the lower order approximations, i.e., when vertical bar vertical bar is large. In this case, the predominant coefficient of the expansion assumes its maximum value when S=M. However, for the class of solutions that vertical bar vertical bar is small, the spin L of the largest coefficient increases with the number of unpaired electrons. We also derived the explicit form of the expansion states. SN 0021-9606 PD DEC 21 PY 2007 VL 127 IS 23 AR 234103 DI 10.1063/1.2805367 UT ISI:000251908500004 ER PT J AU Wood, GPF Radom, L Petersson, GA Barnes, EC Frisch, MJ Montgomery, JA AF Wood, Geoffrey P. F. Radom, Leo Petersson, George A. Barnes, Ericka C. Frisch, Michael J. Montgomery, John A., Jr. TI A restricted-open-shell complete-basis-set model chemistry SO JOURNAL OF CHEMICAL PHYSICS AB A restricted-open-shell model chemistry based on the complete basis set-quadratic Becke3 (CBS-QB3) model is formulated and denoted ROCBS-QB3. As the name implies, this method uses spin-restricted wave functions, both for the direct calculations of the various components of the electronic energy and for extrapolating the correlation energy to the complete-basis-set limit. These modifications eliminate the need for empirical corrections that are incorporated in standard CBS-QB3 to compensate for spin contamination when spin-unrestricted wave functions are used. We employ an initial test set of 19 severely spin-contaminated species including doublet radicals and both singlet and triplet biradicals. The mean absolute deviation (MAD) from experiment for the new ROCBS-QB3 model (3.6 +/- 1.5 kJ mol(-1)) is slightly smaller than that of the standard unrestricted CBS-QB3 version (4.8 +/- 1.5 kJ mol(-1)) and substantially smaller than the MAD for the unrestricted CBS-QB3 before inclusion of the spin correction (16.1 +/- 1.5 kJ mol(-1)). However, when applied to calculate the heats of formation at 298 K for the moderately spin-contaminated radicals in the G2/97 test set, ROCBS-QB3 does not perform quite as well as the standard unrestricted CBS-QB3, with a MAD from experiment of 3.8 +/- 1.6 kJ mol(-1) (compared with 2.9 +/- 1.6 kJ mol(-1) for standard CBS-QB3). ROCBS-QB3 performs marginally better than standard CBS-QB3 for the G2/97 set of ionization energies with a MAD of 4.1 +/- 0.1 kJ mol(-1) (compared with 4.4 +/- 0.1 kJ mol(-1)) and electron affinities with a MAD of 3.9 +/- 0.2 kJ mol(-1) (compared with 4.3 +/- 0.2 kJ mol(-1)), but the differences in MAD values are comparable to the experimental uncertainties. Our overall conclusion is that ROCBS-QB3 eliminates the spin correction in standard CBS-QB3 with no loss in accuracy. (c) 2006 American Institute of Physics. SN 0021-9606 PD SEP 7 PY 2006 VL 125 IS 9 AR 094106 DI 10.1063/1.2335438 UT ISI:000240351500009 ER PT J AU Oprea, CI Telyatnyk, L Rinkevicius, Z Vahtras, O Agren, H TI Time-dependent density functional theory with the generalized restricted-unrestricted approach SO JOURNAL OF CHEMICAL PHYSICS AB This work presents the derivation, implementation, and first applications of the generalized restricted-unrestricted method based on the density functional Kohn-Sham formalism. By using a spin-restricted Kohn-Sham representation for the reference state the well-known spin contamination problem is avoided, while the unrestricted representation of the perturbation response retains a proper description of spin polarization. The formulation is a generalization of our previous implementation of the restricted-unrestricted method [Z. Rinkevicius , J. Chem. Phys. 121, 7614 (2004)], as it accounts for the full unrestricted response instead of describing the spin polarization in terms of triplet operators only. The purpose of this paper is to investigate the role of the generalization employed and demonstrate its numerical performance. For this purpose we focus on isotropic hyperfine coupling constants of a set of organic radicals and transition metal compounds. For both classes of molecules we observe that the effect of neglecting singlet excitation operators in the response part of restricted-unrestricted formalism changes the calculated hyperfine coupling parameters by a few MHz. The obtained results confirm the validity of the approximation used in the simplified restricted-unrestricted approach, i.e. spin polarization can, in most cases, be adequately described by an account of only triplet operators in the response term. (c) 2006 American Institute of Physics. SN 0021-9606 PD MAY 7 PY 2006 VL 124 IS 17 AR 174103 DI 10.1063/1.2191501 UT ISI:000237321700005 ER PT J AU Cronstrand, P Rinkevicius, Z Luo, Y Agren, H TI Time-dependent density-functional theory calculations of triplet-triplet absorption SO JOURNAL OF CHEMICAL PHYSICS AB We present density-functional theory calculations of triplet-triplet absorption by three different approaches based on time-dependent density-functional theory (DFT): unrestricted DFT linear response, open-shell restricted DFT linear response applied to the triplet state, and quadratic response with triplet excitations applied to the ground state. Comparison is also made with corresponding results obtained by Hartree-Fock and multiconfiguration self-consistent-field response theory. Two main conclusions concerning triplet-triplet transitions are drawn in this study: First, the very good agreement between unrestricted and restricted DFT results indicates that spin contamination of the triplet state is not a serious problem when computing triplet-triplet spectra of common organic molecules. Second, DFT response calculations of triplet-triplet transitions can be affected by triplet instability problems, especially for the combination of DFT quadratic response with functionals containing fractional exact Hartree-Fock exchange. SN 0021-9606 PD JUN 8 PY 2005 VL 122 IS 22 AR 224104 DI 10.1063/1.1914772 UT ISI:000229858500006 ER PT J AU Rinkevicius, Z Telyatnyk, L Salek, P Vahtras, O Agren, H TI Restricted density-functional linear response theory calculations of electronic g-tensors SO JOURNAL OF CHEMICAL PHYSICS AB A method for calculations of electronic g-tensors based on a spin-restricted open-shell Kohn-Sham formalism and linear response theory is described. Test calculations for main group organic radicals and transition metal compounds have been carried out using two different spin-orbit approximations: Scaled spin-orbit and atomic mean-field spin-orbit operators. The results indicate slightly better performance of the proposed spin-restricted approach compared to previous methods based on the unrestricted Kohn-Sham formalism. An exception to this general improvement are the anions, as they show considerable spin-polarization. The results also show the superiority of the atomic mean field spin-orbit approximation of the spin-orbit operator with respect to the scaled approximation. For main group radicals, quantitative agreement with high level ab initio as well as experimental data are achieved, whereas for transition metal compounds the results systematically underestimate experimental values, showing also a considerable dependency on the employed exchange correlation functional, similarly to previous reports on calculations using unrestricted density functional theory. From this work we conclude that these problems are not primarily associated with the spin-contamination problem, and that they must be referred to the current time-dependent density functional theories as such. (C) 2003 American Institute of Physics. SN 0021-9606 PD NOV 22 PY 2003 VL 119 IS 20 BP 10489 EP 10496 DI 10.1063/1.1620497 UT ISI:000186554500004 ER PT J AU Krylov, AI TI Spin-contamination of coupled-cluster wave functions SO JOURNAL OF CHEMICAL PHYSICS AB The propensity of approximate solutions of the electronic Schrodinger equation to break spin-symmetry is directly related to the quality of the approximate wave function, and thus can be used as a diagnostic tool. The quasi-variational nature of the (valence) optimized orbitals coupled-cluster doubles methods, (V)OO-CCD, enables a discussion of the stability of coupled-cluster wave functions in terms of both spin-contamination and a corresponding energy lowering relative to the pure spin solutions. The spin-contamination of (V)OO-CCD models has been studied for bond-breaking processes and diradicals. The main findings are: (i) The OO-CCD method is stable for a relatively large range of nuclear distortions and is capable of eliminating even very large spin-contamination of the unrestricted Hartree-Fock solution given that the molecular electronic configuration remains essentially single-reference. When a spin-contaminated solution arises, the energy splitting rapidly becomes large and [(S) over cap(2)] approaches the Hartree-Fock value; (ii) The VOO-CCD method, which is designed to approximate a multi-reference model, remains stable over broader ranges; however, for pure diradicals it becomes unstable. In these cases, spin-contamination is also very large, but the energy lowering for the spin-unrestricted solutions is negligible; (iii) Higher order corrections described by perturbation theory lead to smaller energy splittings between restricted and unrestricted (V)OO-CCD energies. However, in case of spin-contaminated (V)OO-CCD solutions, these corrections may lead to unphysical shapes of the potential energy surfaces. Thus, in order to quantitatively characterize the quality of the wave functions, both spin-contamination and energy lowering due to the breaking of spin-symmetry must be considered. (C) 2000 American Institute of Physics. [S0021-9606(00)31439-8]. SN 0021-9606 PD OCT 15 PY 2000 VL 113 IS 15 BP 6052 EP 6062 UT ISI:000089635200006 ER PT J AU Wittbrodt, JM Schlegel, HB TI Some reasons not to use spin projected density functional theory SO JOURNAL OF CHEMICAL PHYSICS AB Spin unrestricted calculations using density functional theory can yield wave functions with spin contamination. In conventional post Hartree-Fock calculations (such as Moller-Plesset perturbation theory), spin projection can ameliorate some of the problems caused by spin contamination. However, spin projection can seriously degrade the quality of potential energy surfaces calculated by density functional methods, just as spin projection can yield poor results for Hartree-Fock potential energy surfaces. (C) 1996 American Institute of Physics. SN 0021-9606 PD OCT 15 PY 1996 VL 105 IS 15 BP 6574 EP 6577 UT ISI:A1996VM55400048 ER PT J AU BAKER, J SCHEINER, A ANDZELM, J TI SPIN CONTAMINATION IN DENSITY-FUNCTIONAL THEORY SO CHEMICAL PHYSICS LETTERS AB Local density functional calculations on a series of small, neutral radicals demonstrate that the unrestricted Kohn-Sham wavefunction is much less contaminated by higher spin states than its unrestricted Hartree-Fock counterpart, even for radicals which exhibit major contamination in their standard UHF wavefunction. A study of the dissociation curves for the OH and CN radicals shows that the UKS wavefunction remains essentially spin pure out to about 1.5 rimes the equilibrium bond length. Some general observations regarding spin contamination in unrestricted SCF wavefunctions are presented. SN 0009-2614 PD DEC 31 PY 1993 VL 216 IS 3-6 BP 380 EP 388 UT ISI:A1993MP57200024 ER PT J AU TOZER, DJ HANDY, NC AMOS, RD POPLE, JA NOBES, RH XIE, YM SCHAEFER, HF TI THEORY AND APPLICATIONS OF SPIN-RESTRICTED OPEN-SHELL MOLLER-PLESSET THEORY SO MOLECULAR PHYSICS AB Formulae in terms of integrals and orbital energies are presented for the evaluation of the second-, third- and fourth-order energies in open-shell spin-restricted Moller-Plesset (RMP) perturbation theory. The performance of RMP theory is evaluated by calculating equilibrium structures and harmonic vibrational frequencies of a large number of open-shell systems and by calculating energies of reactions which have been shown to be poorly described by spin-unrestricted Moller-Plesset (UMP) theory. RMP theory removes the spin contamination present in the unrestricted Hartree-Fock (UHF) reference of UMP theory. In cases where the spin contamination gives rise to large errors in UMP calculations, such as for the harmonic frequencies of NO, CN, CO+ and FO2 and the energies of reactions involving CN and FO2, RMP theory is shown to offer a substantial improvement. In cases where the Moller-Plesset series exhibits large oscillations, such as for O2, O2+ and F2+, RMP theory is shown to offer no improvement over UMP theory; in these cases good results are achieved with higher-order methods such as quadratic configuration interaction and coupled-cluster theory. SN 0026-8976 PD JUL PY 1993 VL 79 IS 4 BP 777 EP 793 UT ISI:A1993LQ09600009 ER PT J AU CASSAMCHENAI, P CHANDLER, GS TI SPIN-UNRESTRICTED CALCULATIONS IN QUANTUM-CHEMISTRY SO INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY AB The unrestricted complete active space self-consistent field (UCASSCF) function is defined, and a proof that a UCASSCF eigenfunction of the spin operator S2 is a CASSCF function is given. The spin-contamination for an unrestricted Hartree-Fock (UHF) function is evaluated by using Araki angle operators, and the UHF function is then projected on the restricted open-shell Hartree-Fock (ROHF) space. The present analysis has deep consequences since it implies that the only non-spin-contaminated UHF functions are the ROHF functions. This is illustrated in a calculation of the spin density of He2+. SN 0020-7608 PY 1993 VL 46 IS 5 BP 593 EP 607 UT ISI:A1993KZ33400001 ER PT J AU CARSKY, P HUBAC, I TI RESTRICTED HARTREE-FOCK AND UNRESTRICTED HARTREE-FOCK AS REFERENCE STATES IN MANY-BODY PERTURBATION-THEORY - A CRITICAL COMPARISON OF THE 2 APPROACHES SO THEORETICA CHIMICA ACTA AB The paper deals with two topics related to the problem which reference state is better for many-body perturbation theory: restricted Hartree-Fock (RHF) or unrestricted Hartree-Fock (UHF)? The first topic concerns the potential surfaces. Several examples are presented to show shortcomings of the two approaches and a simple way is presented which seems to give a useful potential curve in the whole range of interatomic distances by a composition of RHF and UHF potential curves. The second topic concerns the many-body perturbation theory for open-shell systems in the RHF formalism. The method is critically examined and compared with the ordinary many-body perturbation theory using UHF as the reference. This examination of many-body techniques provides also some insight into the problems inherent of the SCF theory: spin contamination from higher multiplets, localization of orbitals, and self-consistency effects. SN 0040-5744 PD OCT PY 1991 VL 80 IS 4-5 BP 407 EP 425 UT ISI:A1991GM73300010 ER PT J AU ANDREWS, JS JAYATILAKA, D BONE, RGA HANDY, NC AMOS, RD TI SPIN CONTAMINATION IN SINGLE-DETERMINANT WAVE-FUNCTIONS SO CHEMICAL PHYSICS LETTERS AB Spin contamination in single-determinant wavefunctions is examined by performing unrestricted Hartree-Fock (UHF) calculations which constrain the value using a Lagrange multiplier lambda. We call this method spin-constrained unrestricted Hartree-Fock (SUHF). It is shown that as lambda --> infinity, restricted open-shell Hartree-Fock (ROHF) solutions are obtained. Small values of lambda can significantly reduce the error, whilst changing the energy only slightly. Calculations are performed with SUHF and its Moller-Plesset counterpart SUMP2. SUMPn calculations with large values of lambda appear to be a way to carry out ROHF Moller-Plesset studies. Applications are presented for CN, NH2 and BH and are compared with UHF and annihilated UHF (AUHF) results. SN 0009-2614 PD SEP 6 PY 1991 VL 183 IS 5 BP 423 EP 431 UT ISI:A1991GF69500020 ER EF