Complete Active-space Second-order Perturbation Theory Research Articles

Photophysical Deactivation Mechanisms of the Pyrimidine Analogue 1-Cyclohexyluracil.

The photophysical relaxation mechanisms of 1-cyclohexyluracil, in vacuum and water, were investigated by employing the Multi-State CASPT2 (MS-CASPT2, Multi-State Complete Active-Space Second-Order Perturbation Theory) quantum chemical method and Dunning’s cc-pVDZ basis sets. In both environments, our results suggest that the primary photophysical event is the population of the bright state. Afterwards, two likely deactivation pathways can take place, which is sustained by linear interpolation in internal coordinates defined via Z-Matrix scans connecting the most important characteristic points. The first one (Route 1) is the same relaxation mechanism observed for uracil, its canonical analogue, i.e., internal conversion to the ground state through an ethylenic-like conical intersection. The other route (Route 2) is the direct population transfer from the bright state to the triplet state via an intersystem crossing process involving the (/) singlet-triplet crossing point. As the spin-orbit coupling is not too large in either environment, we propose that most of the electronic population initially on the state returns to the ground following the same ultrafast deactivation mechanism observed in uracil (Route 1), while a smaller percentage goes to the triplet manifold. The presence of a minimum on the potential energy hypersurface in water can help to understand why experimentally it is noticed suppression of the triplet states population in polar protic solvent.

Mechanisms of the photodissociations of single isolated methanol

The mechanisms of the photodissociation of single isolated methanol (CH3OH) molecules in the lowest singlet-excited (S1) state were systematically studied using the complete active-space second-order perturbation theory (CASPT2) and transition state theory (TST). This theoretical study focused on the nonradiative relaxation processes that transform the S0 → S1 vertically excited molecule to the products in their respective electronic ground states. The results confirmed that O–H dissociation is the predominant exothermic process and that the formation of formaldehyde (CH2O), in which the O–H dissociated species are the precursors for the reaction in the S0 state, is the second most favorable process. For C–O dissociation, the theoretical results suggested a thermally excited precursor in a different Franck–Condon region in the S0 state, from which vertical excitation leads to a transition structure in the S1 state and spontaneously to the [CH3]· and [OH]· products in their electronic ground states. The CASPT2 and TST results also revealed the possibility of [CH3OH] → [CH2OH2] isomerization dissociation, in which another thermally excited precursor is vertically excited, and C–O dissociation and intermolecular proton transfer lead to the singlet and triplet [CH2]–[H2O] H-bond complexes in their electronic ground states. Although sufficient thermal energy to generate the precursors in the S0 state is available and the reactions are kinetically feasible at high temperatures, the strongly kinetically controlled O–H dissociation predominates the C–O and [CH3OH] → [CH2OH2] isomerization dissociations. The present results verified and confirmed the reported theoretical and experimental findings and provided insights into the thermal selectivity and interplay between thermal excitation and photoexcitation.

Extended separated-pair approximation for transition metal potential energy curves.

Developing a computational method that is both affordable and accurate for transition-metal chemistry is a major challenge. The bond dissociation energies and the potential energy curves are two important targets for theoretical prediction. Here, we investigate the performance of multiconfiguration pair-density functional theory (MC-PDFT) based on wave functions calculated by the complete-active-space (CAS) and generalized active space (GAS) self-consistent-field (SCF) methods for three transition-metal diatomics (TiC, TiSi, and WCl) for which accurate bond energies are available from recent experiments. We compare the results to those obtained by CAS second-order perturbation theory (CASPT2) and Kohn-Sham DFT (KS-DFT). We use six systematic methods to choose the active spaces: (1) we put the bonding orbitals, antibonding orbitals, and singly occupied nonbonding orbitals into the active space in the first method; (2) we also put s and p valence orbitals into the active space; we tried two levels of correlated participating orbitals (CPO) active spaces: (3) nominal CPO (nom-CPO) and (4) extended CPO (ext-CPO); and we used (5) the separated-pair (SP) approximation and (6) a new method presented here called extended separate pairs (ESP) approximation to divide the nom-CPO active space into subspaces. Schemes 1-4 are carried out within the CAS framework, and schemes 5 and 6 are carried out in the GAS framework to eliminate deadwood configurations. For TiC and TiSi, we used all six kinds of active spaces. For WCl, we used three active spaces (nom-CPO, SP, and ESP). We found that MC-PDFT performs better than both CASPT2 and KS-DFT. We also found that the SP (for TiSi) and ESP (for TiC and WCl) approximations are particularly appealing because they make the potential curves smoother and significantly decrease the computational cost of CASSCF calculations. Furthermore, ESP-PDFT can be as accurate as CAS-PDFT.

A multireference coupled-electron pair approximation combined with complete-active space perturbation theory in local pair-natural orbital framework.

The Complete-Active Space Second-order Perturbation Theory (CASPT2) has been one of the most widely-used methods for reliably calculating electronic structures of multireference systems. Because of its lowest level treatment of dynamic correlation, it has a high computational feasibility; however, its accuracy in some cases falls short of needs. Here, as a simple yet higher-order alternative, we introduce a hybrid theory of the CASPT2 and a multireference variant of the Coupled-Electron Pair Approximation (CEPA), which is a class of high level correlation theory. A central feature of our theory (CEPT2) is to use the two underlying theories for describing different divisions of correlation components based on the full internal contraction framework. The external components, which usually give a major contribution to the dynamic correlation, are intensively described using the CEPA Ansatz, while the rests are treated at the CASPT2 level. Furthermore, to drastically reduce the computational demands, we have incorporated the pair-natural orbital (PNO) method into our multireference implementations. This development, thus, requires highly complex derivations and coding, while it has been largely facilitated with an automatic expression and code generation technique. To highlight the accuracy of the CEPT2 approach and to assess the errors caused by the PNO truncation, benchmark calculations are shown on small- to medium-size molecules, illustrating the high accuracy of the present CEPT2 model. By tightening the truncation thresholds, the PNO-CEPT2 energy converges toward the canonical counterpart and is more accurate than that of PNO-CASPT2 as long as the same truncation thresholds are used.

Nature of the 11Bu and 21Ag Excited States of Butadiene and the Goldilocks Principle of Basis Set Diffuseness.

Butadiene, being the simplest conjugated organic molecule, has been studied extensively by experiments and various high-level theoretical methods. Previous studies conclude that the complete active space (CAS) self-consistent field (SCF) method was unable to obtain the correct 11Bu and 21Ag state ordering and that it introduces artificial valence-Rydberg mixing into the 11Bu state because of the lack of external correlation. Basis sets and initial guesses specifically constructed for this problem were able to improve the vertical excitation energy of the 11Bu state but did not resolve the controversy of the nature of the 11Bu state. In the present work, we demonstrate that, using standard intermediately diffuse basis sets such as jul-cc-pVTZ and ma-TZVP, CASSCF is able to obtain the 11Bu and 21Ag states of trans-butadiene with much improved vertical excitation energy and reasonable wave function characteristics, and it provides a good reference wave function (capable of yielding quantitative excitation energies for excited states) for three methods that treat electron correlation in different ways, namely, multiconfiguration pair-density functional theory (MC-PDFT), CAS second-order perturbation theory (PT2), and multistate (MS) CASPT2. We demonstrate that a combined analysis of the orbital second moments, state second moments, and MC-PDFT energy components is a very useful approach in determining excited-state characteristics and assigning states, and we show that basis sets without diffuse functions or with very diffuse basis functions are not stable or accurate in predicting the excited states of butadiene. We show that the 21Ag state is valence-like and has an atypical double/single excitation character and the 11Bu state has a certain degree of Rydberg character that is not artificial, settling the decades of controversy of the characters of these states.

Wavefunction in density functional theory embedding for excited states: which wavefunctions, which densities?

We present a detailed analysis of our recently proposed wavefunction in density functional theory method to include differential polarization effects through state-specific embedding potentials. We study methylenecyclopropene and acrolein in water by using several wavefunction approaches to validate the supermolecular reference and to assess their response to embedding. We find that quantum Monte Carlo, complete-active space second-order perturbation theory, and coupled cluster methods give very consistent solvatochromic shifts and a similar response to embedding. Our scheme corrects the excitation energies produced with a frozen environment, but the values are often overshot. To ameliorate the problem, one needs to use wavefunction densities to polarize the environment. The choice of the exchange-correlation functional in the construction of the potential has little effect on the excitation, whereas the approximate kinetic-energy functional appears to be the largest source of error.

Thermodynamics of Titanium and Vanadium Reduction in Non-Aqueous Environment Calculated at Various Levels of Theory

Reduction of titanium and vanadium compounds is a process accompanying the activation of coordinative olefin polymerization catalysts. Four density functional theory (DFT) functionals, coupled cluster with single, double, and perturbative triple excitations method CCSD(T) as well as complete active-space second-order perturbation theory method CASPT2 with a complete active-space self-consistent field CASSCF reference wave function were applied to investigate the thermodynamics of titanium and vanadium reduction. The performance of these theoretical methods was assessed and compared with experimental values. The calculations indicate that vanadium(IV) chloride is more easily reduced by trimethylaluminum than the corresponding titanium compound; the energies of reaction calculated at the CCSD(T) level are equal -57.21 and -33.10 kcal/mol, respectively. The calculations deal with the redox reactions of metal chlorides in the gas phase, rather than solvated ions in the aqueous solution. This approach may be more appropriate for olefin polymerization, usually carried out in nonpolar solvents.

A New Route towards Redox Bistability through the Inspection of Manganese-Porphyrin Complexes

The redox and spin versatilities of manganese-porphyrin complexes [Mn(II)P] are examined to construct a redox-switchable device. The electronic structure of [Mn(III)P](+) was analyzed by using wavefunction-based calculations (complete active spaces plus single excitations on top of the active spaces, that is, CAS+singles). A non-negligible σ-type electron-transfer configuration is present in the [Mn(III)P](+) S=2 ground state. By contrast, the [Mn(II)P(.)](+) valence tautomer is a purely π-type intramolecular charge transfer, thus reflecting an S=3 spin state as a result of the strong ferromagnetic interaction (J=30 meV) between the S=5/2 Mn(II) ion and the S=1/2 porphyrin radical cation P(.+). The change of the redox-sensitive site in the valence tautomer leads to a 'triangular scheme' that involves a critical step in which a simultaneous electron transfer and spin change are expected to induce bistability. From the wavefunction inspection, a meso-substituted porphyrin candidate was designed to support this scenario. The complete active-space second-order perturbation theory (CASPT2) adiabatic energy difference between the S=2 and the S=3 spin states was reduced down to 0.15 eV, thereby giving rise to a metastable S=3 state characterized by a 0.10 Å extension of the porphyrin cavity radius. These results not only confirm the rather versatile nature of these inorganic systems but also demonstrate that redox and spin changes are intermingled in this class of compounds and can be used for applied devices.

Testing the parametric two-electron reduced-density-matrix method with improved functionals: Application to the conversion of hydrogen peroxide to oxywater

Parametrization of the two-electron reduced density matrix (2-RDM) has recently enabled the direct calculation of electronic energies and 2-RDMs at the computational cost of configuration interaction with single and double excitations. While the original Kollmar energy functional yields energies slightly better than those from coupled cluster with single-double excitations, a general family of energy functionals has recently been developed whose energies approach those from coupled cluster with triple excitations [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. In this paper we test the parametric 2-RDM method with one of these improved functionals through its application to the conversion of hydrogen peroxide to oxywater. Previous work has predicted the barrier from oxywater to hydrogen peroxide with zero-point energy correction to be 3.3-to-3.9 kcal/mol from coupled cluster with perturbative triple excitations [CCSD(T)] and -2.3 kcal/mol from complete active-space second-order perturbation theory (CASPT2) in augmented polarized triple-zeta basis sets. Using a larger basis set than previously employed for this reaction-an augmented polarized quadruple-zeta basis set (aug-cc-pVQZ)-with extrapolation to the complete basis-set limit, we examined the barrier with two parametric 2-RDM methods and three coupled cluster methods. In the basis-set limit the M parametric 2-RDM method predicts an activation energy of 2.1 kcal/mol while the CCSD(T) barrier becomes 4.2 kcal/mol. The dissociation energy of hydrogen peroxide to hydroxyl radicals is also compared to the activation energy for oxywater formation. We report energies, optimal geometries, dipole moments, and natural occupation numbers. Computed 2-RDMs nearly satisfy necessary N-representability conditions.

Reductive cleavage of the O–O bond in multicopper oxidases: a QM/MM and QM study

The key step in the reaction mechanism of multicopper oxidases (MCOs)--the cleavage of the O-O bond in O2--has been investigated using combined quantum mechanical and molecular mechanical (QM/MM) methods. This process represents a reaction pathway from the peroxy intermediate after it accepts one electron from the nearby type-1 Cu site to the experimentally-observed native intermediate, which is the only fully oxidised catalytically relevant state in MCOs. Scans of the QM(DFT)/MM potential energy surface have allowed us to obtain estimates of the activation energies. Furthermore, vacuum calculations on a smaller model of the active site have allowed us to estimate the entropy contributions to the barrier height and to obtain further insight into the reaction by comparing the small cluster model with the QM/MM model, which includes the entire protein. Owing to the complicated electronic structure of these low-spin exchange coupled systems, multireference quantum chemical calculations at the complete-active space second-order perturbation theory (CASPT2) were used in an attempt to benchmark the barrier heights obtained at the DFT(B3LYP) level. Our best estimate of the activation barrier is deltaG = 60-65 kJ mol(-1), in good agreement with the experimental barrier of approximately 55 kJ mol(-1), which can be inferred from the experimental rate constant of k > 350 s(-1). It has also been shown that the reaction involves protonation of the O2 moiety before bond cleavage. The proton likely comes from a nearby carboxylate residue which was recently suggested by the experiments.

The relativistic complete active-space second-order perturbation theory with the four-component Dirac Hamiltonian

The relativistic complete active-space second-order perturbation theory (CASPT2) is developed for the four-component relativistic Hamiltonian. The present method can describe the near-degenerated and dissociated electronic states of molecules involving atoms of heavy elements. The present approach is less expensive than the relativistic multireference configuration interaction method. The ground and low-lying excited states of TlH, Tl(2), and PtH molecules are calculated with the Dirac-Coulomb (DC) CASPT2 method and their spectroscopic constants are obtained. These spectroscopic constants are compared with experimental findings and previous theoretical work. For all the molecules, the spectroscopic constants of DC-CASPT2 show good agreement with the experimental or previous theoretical spectroscopic constants. The present theory provides accurate descriptions of bonding or dissociation states and of ground and excited states in a well-balanced way.

On the S 1→S 0 internal conversion in the photodissociation of HNCO: the role of the NC stretch as a promoting mode

A possible pathway for the S 1/S 0 internal conversion in the photodissociation of HNCO in the first absorption band is discussed on the basis of electronic structure calculations for the two relevant potential energy surfaces. The ab initio calculations are performed at two levels of theory: multi-reference configuration interaction (MRCI) and complete-active space second-order perturbation theory (CASPT2). The NCO bending angle and the NC stretch coordinate are varied. It is concluded that the combined motion of both modes is most efficient in promoting the transition from S 1 to S 0, which is in qualitative accordance with the recent experimental findings.

Comparison of methods for calculating the properties of intramolecular hydrogen bonds. Excited state proton transfer

A series of molecules related to malonaldehyde, containing an intramolecular H-bond, are used as the testbed for a variety of levels of ab initio calculation. Of particular interest are the excitation energies of the first set of valence excited states, nπ* and ππ*, both singlet and triplet, as well as the energetics of proton transfer in each state. Taking coupled cluster results as a point of reference, configuration interaction-singles–second-order Møller–Plesset (CIS–MP2) excitation energies are too large, as are CIS to a lesser extent, although these approaches successfully reproduce the order of the various states. The same may be said of complete active space self-consistent-field (CASSCF), which is surprisingly sensitive to the particular choice of orbitals included in the active space. Complete active space–second-order perturbation theory (CASPT2) excitation energies are rather close to coupled cluster singles and doubles (CCSD), as are density functional theory (DFT) values. CASSCF proton transfer barriers are large overestimates; the same is true of CIS to a lesser extent. MP2, CASPT2, and DFT barriers are closer to coupled cluster results, although yielding slight underestimates.