Spin Contamination Error Research Articles

Transition state optimization based on approximate spin-projection (AP) method

Approximate spin-projection (AP) method, which eliminates a spin contamination error from the broken-symmetry (BS) state, is extended to calculations of vibrational frequencies and optimizations of transition state structure. In the case of methylene, the BS solution overestimates the biradical character and gives worse results than the symmetry-adapted solution. The AP method gives proper corrections on the geometry and vibrational frequencies. As for the [2 + 2] reaction of singlet oxygen ( 1Δ g) with ethylene, the spin contamination error on transition state structures is corrected, and the new method can provide more accurate stationary points for the reactions.

Spin Contamination Error in Optimized Geometry of Singlet Carbene (1A1) by Broken-Symmetry Method

Spin contamination errors of a broken-symmetry (BS) method in optimized structural parameters of the singlet methylene ((1)A(1)) molecule are quantitatively estimated for the Hartree-Fock (HF) method, post-HF methods (CID, CCD, MP2, MP3, MP4(SDQ)), and a hybrid DFT (B3LYP) method. For the purpose, the optimized geometry by the BS method is compared with that of an approximate spin projection (AP) method. The difference between the BS and the AP methods is about 10-20 degrees in the HCH angle. In order to examine the basis set dependency of the spin contamination error, calculated results by STO-3G, 6-31G*, and 6-311++G** are compared. The error depends on the basis sets, but the tendencies of each method are classified into two types. Calculated energy splitting values between the triplet and the singlet states (ST gap) indicate that the contamination of the stable triplet state makes the BS singlet solution stable and the ST gap becomes small. The energy order of the spin contamination error in the ST gap is estimated to be 10(-1) eV.

Theoretical studies on chemical bonding between Cu(II) and oxygen molecule in type 3 copper proteins

AbstractWe discussed the most stable coordination of O2 binding in the Cu2O2 core of type 3 copper proteins from a viewpoint of broken‐symmetry (BS) DFT approach. This study put its focus on the active site of both oxy and deoxy form of hemocyanin as an example. We examined four conventional hybrid GGA functional sets that contain different proportion of exact exchange in a range of 20–50% within a BS way. To evaluate their net accuracy, the spin contamination errors caused by the triplet (S = 1) state on energy and energy gradient in the BS (S = 0) state were replaced by our approximate spin projection (AP) procedure. We also examined OO stretch vibrational frequencies and Gibbs free energies of O2 binding with the conductor‐like polarizable continuum model. From the results, UBHandHLYP outperform the other functional sets, indicating that the Cu2O2 core in oxyHc has significant diradical character under AP‐BS approximation. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Approximately spin‐projected Hessian for broken symmetry method and stretching frequencies of F2 and singlet O2

AbstractAn approximate spin projection (AP) method is applied to a second derivative of energy (Hessian) of the broken‐symmetry (BS) method in order to eliminate a spin contamination error. Stretching frequencies of F2 (X1 ∑) and singlet molecular oxygen (a1Δg) are calculated by using the spin‐projected Hessian (AP Hessian). In case of F2 molecule, a potential curve of an unrestricted Hartree‐Fock (UHF) method does not have an energy minimum but the stretching frequency can be calculated by the AP UHF method. The difference in the calculated stretching frequencies between a restricted HF (RHF) and the AP UHF methods is 650–700 cm−1, and indicates that a static correlation correction is a crucial to consider the frequency. On the other hand, we cannot find a significant difference in calculated frequencies of RHF and AP‐BS HF in case of 1O2 molecule within the HF method. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Extended Hartree–Fock theory of chemical reactions. IX. Diradical and perepoxide mechanisms for oxygenations of ethylene with molecular oxygen and iron‐oxo species are revisited

AbstractSymmetry and broken symmetry (BS) in molecular orbital description of transition structures and intermediates in oxygenation reactions have been revisited to elucidate states correlation diagrams and mechanisms for addition reactions of molecular oxygen and metal‐oxo MO (M = Mn(II) and Fe(II)) species to CC double bonds. Relative stabilities between diradical (DR) and perepoxide (PE) intermediates were thoroughly investigated by several BS hybrid DFT (HDFT) methods and BS CCSD(T) method with and without spin projection. It has been found that recovery of spin symmetry, namely eliminating spin contamination error from the BS solutions, is crucial for the elucidation of reasonable state correlation diagrams and energy differences of the key structures in the oxygenation reactions because the singlet‐triplet energy gap for molecular oxygen is large (22 kcal/mol). The BS HDFT followed by spin correction reproduced activation barriers for transition structures along both PE and DR reaction pathways by the use of the CASPT2 method. Basis set dependence on the relative stability between PE and DR intermediates were also examined thoroughly. Solvation effect for DR and PE intermediates was further examined with self‐consistent reaction field (SCRF) and SCIPCM methods. Both BS HDFT and CASPT2 have concluded that the DR mechanism is favorable for the addition reaction of singlet oxygen to ethylene, supporting our previous conclusions. The BS HDFT with spin correction was concluded to be useful enough for theoretical investigations of mechanisms of oxygenation reactions. Implications of the computational results were discussed in relation to the theoretical framework (four configuration model) for elucidation of possible mechanisms of epoxidation reactions with Fe(IV)O cores in metalloenzymes on the basis of isolobal analogies among O, OO, and Fe(IV)O. Correspondence between magnetic coupling mode and radical pathway in oxygenations with these species was clarified based on the BS MO interaction diagrams, leading to local singlet and triplet diradical mechanisms for epoxidations. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Theoretical investigation of the interaction between oxygen molecules and small Au clusters using approximately spin-projected geometry optimization (AP-opt) method

The effects of spin contamination errors in the optimized geometry of oxygen-adsorbed Au cluster model systems were examined by using broken symmetry geometry optimization (BS-opt) and an approximate spin-projected broken symmetry geometry optimization (AP-opt) method combined with the hybrid density functional (B3LYP) method. The AP-opt method effectively eliminated spin contamination errors from the BS-opt calculations of optimized geometry and energy of Au n –O 2 ( n = 1, 2 and 13) model systems.

Theoretical studies on the structure and effective exchange integral (Jab) of an active site in oxyhemocyanin (oxyHc) by using approximately spin-projected geometry optimization (AP-opt) method

The effect of a spin contamination error in an optimized geometry of Cu2O2 in the active site of oxyHc is examined by using broken-symmetry (BS) and AP-opt methods with hybrid density functional methods. The error was 3–5° on the Cu–O–Cu angle and 0.07–0.13 Å on the reaction coordinate R. The error in the optimized structure strongly affects the calculated Jab values such as 196 and 553 cm−1 for UBHandHLYP and UB3LYP methods, respectively. The underestimated Jab value of UB3LYP becomes close to the experimental one by the correction of the structure with the AP-opt method.

Extensive ab initio study of the OH+HCN reaction: Low lying electronic states of the stationary points on the 2A′ surface

We found many stationary points (minima and transition states) for the title reaction on the 2A′ surface at unrestricted Hartree–Fock self-consistent field (UHF-SCF) level with two different basis sets. Stable adducts, as suggested by previous experimental works, have been ascertained and several reaction paths are obtained through intrinsic reaction coordinate (IRC) calculations. A link to the HNC+OH reaction is possible. Multiconfiguration SCF (MC-SCF) calculations have been carried out for the addition reaction with the lowest energy barrier in order to eliminate the spin contamination error on these geometries. Correlation energy at the stationary points was estimated via a perturbative scheme, Mo/ller–Plesset at fourth order (MP4) which does not seem adequate for such a system, and via multireference double configuration interaction (MR-DCI) with extrapolation to full CI values for ground and first excited states. Electronic excitations may open some reaction channels.

EHF theory of chemical reactions Part 4. UNO CASSCF, UNO CASPT2 and R(U)HF coupled-cluster (CC) wavefunctions

Spin-restricted and spin-unrestricted post-Hartree-Fock methods are compared by depicting potential energy curves of several hydrogen clusters (H 2-H 6), hydrogen fluoride and fluorine molecules. In the former approach, RHF, RMP, RHF coupled-cluster (CC), UNO CASSCF and UNO CASPT2 are utilized, whereas the latter approach includes UHF MP n (UMP n) and UHF coupled-cluster (UCC), approximate spin-projected UMP n and UCC (APUMP n and APUCC) and Löwdin-type full spin-projected UMP n (PMP n). Characteristics (shapes in particular) of the potential curves are discussed in relation to the roles of electron correlation corrections revealed by both methods. The UNO CASSCF followed by PT2 provides reasonable potential curves in the whole region. The spin contamination error is remarkable in the case of the UMP n wavefunction, leading to the necessity of spin projection. The resulting PMP2 and APUMP2 can be used for larger clusters and are regarded as alternatives to UNO CASPT2. The spin contamination error is not so serious for UCCSD(T), at least in the weak and intermediate correlation regime, whereas it is important in the magnetic (dissociation) region where APUCCSD(T) works well in depicting the potential energy curves. It is regarded as an approximate version of UNO CASSCF CC SD(T). Implications of the calculated results are discussed in order to clarify the applicabilities of the post-HF methods to chemical reactions in the ground and lower-excited states.

EHF theory of chemical reactions Part 4. UNO CASSCF, UNO CASPT2 and R(U)HF coupled-cluster (CC) wavefunctions

Spin-restricted and spin-unrestricted post-Hartree-Fock methods are compared by depicting potential energy curves of several hydrogen clusters (H 2−H 6), hydrogen fluoride and fluorine molecules. In the former approach, RHF, RMP, RHF coupled-cluster (CC), UNO CASSCF and UNO CASPT2 are utilized, whereas the latter approach includes UHF MP n (UMP n) and UHF coupled-cluster (UCC), approximate spin-projected UMP n and UCC (APUMP n and APUCC) and Lowdin-type full spin-projected UMP n (PMP n). Characteristics (shapes in particular) of the potential curves are discussed in relation to the roles of electron correlation corrections revealed by both methods. The UNO CASSCF followed by PT2 provides reasonable potential curves in the whole region. The spin contamination error is remarkable in the case of the UMP n wavefunction, leading to the necessity of spin projection. The resulting PMP2 and APUMP2 can be used for larger clusters and are regarded as alternatives to UNO CASPT2. The spin contamination error is not so serious for UCCSD(T), at least in the weak and intermediate correlation regime, whereas it is important in the magnetic (dissociation) region where APUCCSD(T) works well in depicting the potential energy curves. It is regarded as an approximate version of UNO CASSCF CC SD(T). Implications of the calculated results are discussed in order to clarify the applicabilities of the post-HF methods to chemical reactions in the ground and lower-excited states.