Multistate Extension Research Articles

Photodissociation mechanism of methyl nitrate. A study with the multistate second-order multiconfigurational perturbation theory

The photodissociation reactions of methyl nitrate CH(3)ONO(2) starting at the 193 and 248 nm photolytic wavelengths have been studied with the second-order multiconfigurational perturbation theory (CASPT2) by computation of numerical energy gradients for stationary points. In addition, energy profiles of reaction paths and vertical excitations have been investigated with the multistate extension of the multiconfigurational second-order perturbation theory (MS-CASPT2). It is found that excitation at 193 nm yields three reaction paths: (i) the so-called slow channel CH(3)ONO(2)--> CH(3)O + NO(2)--> CH(3)O + NO + O; (ii) the fast channel CH(3)ONO(2)--> CH(3)O + NO(2); and (iii) CH(3)ONO(2)--> CH(3)ONO + O. The slow channel starts at the S(4) surface, in contrast, the population of the S(3) state can lead to the fast channel or to direct atomic oxygen extrusion. The rather high relative yield of the channel leading to oxygen extrusion from methyl nitrate is explained on the basis of an S(3)/S(2) conical intersection that transfers the initial excitation localized in the npi* S(3) state to the sigmapi* S(2) state with a consequent weakening of the N-O bond. With respect to photolysis at 248 nm, it was not possible to unambiguously distinguish between S(1) and S(2) as the populated state, however, the S(2) state is suggested as mainly responsible for dissociation at this excitation energy.

Theoretical study on the excited states and photodissociation mechanism of dimethyldisulfide

The photophysics and photochemistry of dimethyldisulfide (DMDS) provide important clues for the photo-induced reactions between the cysteine residues in proteins. In this Letter, the state-average complete active space self-consistent field (SA-CASSCF) and multi-state extension of multiconfigurational second-order perturbation (MS-CASPT2) approaches are applied to investigate both the vertical excitation energies and the photodissociation mechanism of DMDS. The two lowest singlet excited states are predicted to be pure valence states, while the four higher states apparently have Rydberg characters. In either the S 1 or S 2 state, the S−S fission is the major channel compared with the S−C cleavage.

The photophysics of isolated protein chromophores

Gas-phase absorption properties of chromophores of several photoactive proteins have been studied experimentally at the electrostatic heavy-ion storage ring ELISA in Aarhus. The absorption wavelength has been calculated using an augmented effective Hamiltonian technique based on the multiconfigurational quasi-degenerate perturbation theory. The results have been compared to those of widely used state-specific second-order perturbation theory formalisms and their multistate extensions and also to ground-state linear response methods. It would appear that ab initio theory is now at a stage where the intrinsic properties of the chromophore molecules may be predicted with reasonable precision. There is evidence that in terms of absorption there is almost vacuum-like conditions in the hydrophobic interior of some proteins like the green fluorescent protein (GFP). In others, like for example the visual opsins, some significant perturbations are responsible for colour tuning.

Explaining the Effect of Gender on Functional Transitions in Older Persons

Background: Women live longer but experience greater disability than men. The reasons for this gender difference in disability are not well understood. Objective: Our objectives were to determine if the higher prevalence of disability in women is due to greater incidence of disability, longer duration of disability, or both, and to identify factors that potentially explain these gender differences. Methods: 754 community-living persons aged 70 and older who were non-disabled (required no personal assistance) in four essential activities of daily living (ADLs) were assessed monthly for disability for up to 6 years. A multi-state extension of the proportional hazards model was used to determine the effects of gender on transitions between states of no disability, mild disability, severe disability, and death, and to evaluate potential mediators of these effects. Results: Women were more likely to make the transition from no disability to mild disability and less likely to make the transitions from mild to no disability and from both mild and severe disability to death. The gender difference in the transitions between no disability and mild disability was largely explained by differences in gait speed and physical activity, but gender difference in transitions to death persisted despite adjustment for multiple potential mediators. Conclusion: The higher prevalence of disability in women versus men is due to a combination of higher incidence and longer duration, resulting from lower rates of recovery and mortality among disabled women.

A Bayesian Approach to the Multistate Jolly–Seber Capture–Recapture Model

This article considers a Bayesian approach to the multistate extension of the Jolly-Seber model commonly used to estimate population abundance in capture-recapture studies. It extends the work of George and Robert (1992, Biometrika79, 677-683), which dealt with the Bayesian estimation of a closed population with only a single state for all animals. A super-population is introduced to model new entrants in the population. Bayesian estimates of abundance are obtained by implementing a Gibbs sampling algorithm based on data augmentation of the missing data in the capture histories when the state of the animal is unknown. Moreover, a partitioning of the missing data is adopted to ensure the convergence of the Gibbs sampling algorithm even in the presence of impossible transitions between some states. Lastly, we apply our methodology to a population of fish to estimate abundance and movement.

New perspectives in multireference perturbation theory: the n-electron valence state approach

The n-electron valence state perturbation theory (NEVPT) is a form of multireference perturbation theory which is based on a zero order reference wavefunction of CAS-CI type (complete active space configuration interaction) and which is characterized by the utilization of correction functions (zero order wavefunctions external to the CAS) of multireference nature, obtained through the diagonalization of a suitable two-electron model Hamiltonian (Dyall’s Hamiltonian) in some well defined determinant spaces. A review of the NEVPT approach is presented, starting from the original second order state-specific formulation, going through the quasidegenerate multi-state extension and arriving at the recent implementations of the third order in the energy and of the internally contracted configuration interaction. The chief properties of NEVPT—size consistence and absence of intruder states—are analyzed. Finally, an application concerning the calculation of the vertical spectrum of the biologically important free base porphin molecule, is presented.

The Effect of Prior Disability History on Subsequent Functional Transitions

Many older persons experience multiple transitions between states of disability and independence, but little is known about the effect of prior disability history on subsequent functional transitions. Our objective was to determine the effect of prior disability on subsequent transitions between no disability, mild disability, severe disability, and death. For 60 months, 754 persons aged 70 or older underwent monthly assessments of disability in basic activities of daily living. We used a multistate extension of the proportional hazards model to determine the effects of amount, defined as cumulative duration, and distribution, defined as number of episodes, of prior disability on subsequent functional transitions, adjusted for age, gender, cognitive status, timed gait, and habitual physical activity. For each additional month of prior disability, participants were more likely to make transitions representing new or worsening disability and were less likely to make transitions from disability to independence or from severe disability to death. Adjusting for the cumulative duration of prior disability, more episodes of prior disability were associated with a higher likelihood of most transitions, representing both increasing and decreasing disability, but had no effect on transitions to death. Both the amount and distribution of prior disability are important determinants of the likelihood of subsequent functional transitions. Analytic methods that account for prior disability history should be used in studies of functional transitions, and new measures of disability burden are needed that incorporate distribution as well as amount of disability.

Multiconfigurational second-order perturbation study of the decomposition of the radical anion of nitromethane

The doublet potential energy surfaces involved in the decomposition of the nitromethane radical anion (CH(3)NO(2) (-)) have been studied by using the multistate extension of the multiconfigurational second-order perturbation method (MS-CASPT2) in conjunction with large atomic natural orbital-type basis sets. A very low energy barrier is found for the decomposition reaction: CH(3)NO(2) (-)-->[CH(3)NO(2)](-)-->CH(3)+NO(2) (-). No evidence has been obtained on the existence of an isomerization channel leading to the initial formation of the methylnitrite anion (CH(3)ONO(-)) which, in a subsequent reaction, would yield nitric oxide (NO). In contrast, it is suggested that NO is formed through the bimolecular reaction: CH(3)+NO(2) (-)-->[CH(3)O-N-O](-)-->CH(3)O(-)+NO. In particular, the CASSCF/MS-CASPT2 results indicate that the methylnitrite radical anion CH(3)ONO(-) does not represent a minimum energy structure, as concluded by using density functional theory (DFT) methodologies. The inverse symmetry breaking effect present in DFT is demonstrated to be responsible for such erroneous prediction.

The ground and excited state potential energy surfaces of nitromethane related to its dissociation dynamics after excitation at 193 nm

The relevant low-lying singlet and triplet potential energy surfaces in the photolysis of nitromethane have been studied by using the multistate extension of the multiconfigurational second-order perturbation theory in conjunction with large atomic natural orbital-type basis sets. The proposed mechanism for the photolytic decomposition of CH3NO2 provides a consistent and reinterpreted picture of the available experimental results. Two reaction paths are found in the photolysis of nitromethane after excitation at 193 nm: (1) Major Channel, CH3NO2(1A′)+hν(193 nm)→CH3NO2(2A″)→ lim ICCH3NO2(2A′)→CH3(1A1′)+NO2(1 2B1)→ lim −hν′ICCH3(1A1′)+NO2(1 2A1)→ lim 193 nmhνCH3(1A1′)+NO(A 2Σ+)+αO(3P)+βO(1D). (2) Minor Channel, CH3NO2(1A′)+hν(193 nm)→CH3NO2(2A″)→CH3(1A1′)+NO2(1 2A2)→CH3(1A1′)+NO(X 2Π)+αO(3P)+βO(1D), being α and β fractional numbers. No ionic species are found in any dissociation path. Additionally, the respective low-lying Rydberg states of nitromethane and nitrogen dioxide have been studied too.

Zero-One Law for the Non-Availability of Multistate Repairable Systems

In a monotone system whose failure depends on a large number of independent components, the non-availability should increase abruptly over a relatively short interval of time. Our first step is a reliability interpretation of a result of Friedgut and Kalai.1 Then we prove a zero-one law which is more adapted in a reliability context. In the last section some multistate extensions of classical models are considered as examples.

The electronic spectra of aryl olefins: A theoretical study of phenylacetylene

The electronic absorption and emission spectra of phenylacetylene have been studied by means of a multiconfigurational second-order perturbation method and its multistate extension. The low-lying valence singlet and triplet π→π* excited states together with 3s3p3d members of the two lowest Rydberg series have been computed in the vertical spectrum. By optimization of the geometries of the ground and low-lying excited states and the calculation of transition energies and properties, the obtained results lead to a detailed analysis and assignment of the available experimental absorption spectrum and to the description of the basic features of the emission processes in phenylacetylene. Vibrational frequencies for the two lowest singlet and triplet excited states have also been computed. The spectroscopy of phenylacetylene is finally related to that of other aryl olefins such as styrene and benzaldehyde. Differences and similarities of their excited state structures are discussed.

Theoretical characterization of the lowest-energy absorption band of pyrrole

The lowest-energy band of the electronic spectrum of pyrrole has been studied with vibrational resolution by using multiconfigurational second-order perturbation theory (CASPT2) and its multistate extension (MS–CASPT2) in conjunction with large atomic natural orbital-type basis sets including Rydberg functions. The obtained results provide a consistent picture of the recorded spectrum in the energy region 5.5–6.5 eV and confirm that the bulk of the intensity of the band arises from a ππ* intravalence transition, in contradiction to recent theoretical claims. Computed band origins for the 3s,3p Rydberg electronic transitions are in agreement with the available experimental data, although new assignments are suggested. As illustrated in the paper, the proper treatment of the valence–Rydberg mixing is particularly challenging for ab initio methodologies and can be seen as the main source of deviation among the recent theoretical results as regards the position of the low-lying valence excited states of pyrrole.

Electronic Transitions in Tetrathiafulvalene and Its Radical Cation: A Theoretical Contribution

The low-lying electronic states of tetrathiafulvalene (TTF) and its radical cation (TTF+) have been studied using the multistate extension of a multiconfigurational second-order perturbation method (MS−CASPT2). The minimum-energy equilibrium geometries optimized at the CASSCF level have a boatlike conformation for the neutral molecule, with no significant barrier toward planarity. A more aromatic planar structure is, however, found for the ionic system. For TTF, the calculations of the vertical excitation energies comprise valence singlet and triplet states as well as the lowest members of the Rydberg series converging to the first ionization limit. Valence doublet states have been considered for TTF+. The results obtained lead to elucidate controversial assignments, yielding a full interpretation of the available experimental absorption spectra. In addition, vertical ionization energies of TTF have been computed, and the lowest-energy peaks of the gas-phase photoelectron spectra have been interpreted in the light of the present findings.

A MS-CASPT2 study of the low-lying electronic excited states of CH 2BrCl

The low-lying singlet excited states of CH 2BrCl have been calculated using multiconfigurational CASSCF, second-order perturbation theory CASPT2 and its multistate extension MS-CASPT2. The CASSCF method shows spurious valence–Rydberg mixing and a wrong order of states. Inclusion of dynamical correlation by single root CASPT2 lowers dramatically the energy of the valences states but does not lead to a complete separation between valence and Rydberg states. This situation is improved by the MS-CASPT2 calculations, which gives two valence states for both A ′ and A″ symmetries below the lowest Rydberg state, corresponding to n(Br)→σ *(C–Br) and n(Cl)→σ *(C–Cl) transitions at 6.1 eV (203 nm) and 7.2 eV (173 nm), and being repulsive along C–Br and C–Cl coordinates.

A Theoretical Insight into the Photophysics of Acridine

The electronic absorption and emission spectra of acridine have been studied by means of a multiconfigurational second-order perturbation method (CASSCF/CASPT2) and its multistate extension (MS-CASPT2). The low-lying valence singlet and triplet π → π* and n → π* excited states have been computed. The location of the lowest Rydberg state (3s) has been also estimated. By optimization of the geometries of the ground and low-lying excited states and the calculation of transition energies and properties, the obtained results lead to a complete analysis and assignment of the available experimental singlet−singlet and triplet−triplet absorption spectra and to the description of the basic features of the fluorescence and phosphorescence processes of acridine. The photophysics of acridine and its protonated form are analyzed and the effects of solvation are discussed. The present findings support the model of a state reversal on the lowest singlet excited state upon increasing the solvent polarity.

Theoretical Analysis of the Electronic Spectra of Benzaldehyde

The electronic spectrum of benzaldehyde has been studied by using multiconfigurational second-order perturbation theory through the multistate extension (MS-CASPT2). The nπ* 11A‘ ‘ state, placed vertically at 3.71 eV, is assigned to the lowest band. The 11A‘ → 21A‘ and 11A‘ → 31A‘ transitions, of ππ* nature, located at 4.33 and 4.89 eV, are responsible for the second- and third-energy bands, respectively. The most intense feature involves the 41A‘ and 51A‘ ππ* excited states, calculated to be 5.98 and 6.23 eV above the ground state. In addition, excited states corresponding to the low-lying Rydberg series are related to the available experimental data. Geometry optimizations for the ground state and low-lying excited states of both nπ* and ππ* characters have been carried out at the CASSCF level. The relative ordering of the lowest nπ* and ππ* triplet states varies depending on the geometry employed. Furthermore, the S1(nπ*) and T2(ππ*) potential hypersurfaces are found to intersect upon relaxation in S1, providing a possible explanation for the efficient singlet−triplet intersystem crossing occurring in benzaldehyde.

Electronic Excitation in a Saturated Chain: An MS-CASPT2 Treatment of the Anti Conformer of n-Tetrasilane

The singlet−singlet electronic spectrum of the anti conformer of n-tetrasilane has been studied using multiconfigurational wave functions (CASSCF), second-order perturbation theory (CASPT2), and its multi-state extension (MS-CASPT2), in conjunction with large ANO-type basis sets including Rydberg functions. The calculations include the 4s, 4p, and 3d members of the Rydberg series converging on the first ionization. Mixing of valence and Rydberg states observed in the CASSCF wave functions is not fully rectified by single-reference CASPT2 theory, whereas the MS-CASPT2 method separates the valence and Rydberg states effectively. At the MS-CASPT2 level, six valence excited states have been found below the lowest Rydberg transition, predicted at 7.40 eV. In terms of natural orbitals, they correspond to single electron promotions from the σ-symmetry HOMO to four σ* and two π* valence orbitals. Vertical dipole-allowed valence transition energies (oscillator strengths) are computed at 6.33 eV (1.12), 6.68 eV (0.01), and 6.96 eV (0.15), for excitation to 11Bu, 11Au, and 21Bu states, respectively. Three vertical dipole-forbidden valence transitions are predicted to be interleaved among them at 6.55 eV (21Ag), 6.87 eV (31Ag), and 7.10 eV (11Bg). The results are consistent with the available experimental data and are easily rationalized in terms of a simple Hückel model of σ delocalization.

The Agricultural Research, Extension, and Education Reform Act of 1998: Examining Its Key Provisions

The Agricultural Research, Extension, and Education Reform Act of 1998 (AREERA) represents a concerted effort on the part of federal legislative leaders to rethink the manner in which agricultural research and extension programming are undertaken within the land-grant university system of our nation. For the first time ever, land-grant schools are being mandated to increase their energies in support of “multi” activities; namely, multiinstitutional, multidisciplinary, multifunctional, and multistate activities. The intent is to bring about greater efficiencies in carrying out the research and extension missions of our land-grant entities. In this presentation, the key provisions of AREERA are outlined. These elements include: 1) the commitment of 25% of Hatch formula funds in support of multidisciplinary research involving another agricultural experiment station, Agricultural Research Service, or college/university that collectively are seeking to solve problems that concern more than one state; 2) the expenditure of Smith-Lever formula funds for support of multistate extension activities equivalent to 25% of these formula funds, or twice the level of resources devoted to such activities using FY97 funds; and 3) a directing of 25% of Smith-Lever and Hatch funds received by an institution in FY2000 for integrated research and extension activities (or twice the level of effort committed to such efforts in FY97). It is further noted that while 1890 and 1994 institutions are required to engage in multidisciplinary, multistate, and integrated research and extension activities, they are not compelled to meet the 25% goal outlined in the AREERA legislation. Aside from the resources that must be devoted to certain activities within the Agricultural Experiment Station and the Extension Service, AREERA makes quite clear the need to actively engage stakeholders in giving shape to the priority activities of these land-grant entities. Moreover, it notes the importance of documenting the impact of the institution's research and extension investments on the priority concerns of its stakeholders. Among the key questions that will be employed to evaluate the quality of an institution's efforts are the following: Did the program address a critical issue? Did it address the needs of underserved and underrepresented populations in the state(s)? Did the investments result in improved program effectiveness and/or efficiency? Indeed, AREERA changes the landscape for many of the South's land-grant institutions. However, if efforts undertaken to date are any indication, the leadership and faculty of the region's land-grant system will successfully respond to the challenges that AREERA poses for them.

Constitutive activity of glucagon receptor mutants.

Increased constitutive activity has been observed in the PTH receptor in association with naturally occurring mutations of two residues that are conserved between members of the glucagon/vasoactive intestinal peptide/calcitonin 7TM receptor family. Here, the corresponding residues of the glucagon receptor, His178 and Thr352, were probed by mutagenesis. An elevated level of basal cAMP production was observed after the exchange of His178 into Arg, but not for the exchange into Lys, Ala, or Glu. However, for all of these His178 substitutions, an increased binding affinity for glucagon was observed [dissociation constant (Kd) ranging from 1.1-6.4 nM, wild type: Kd = 12.0 nM]. A further increase in cAMP production was observed for the [H178R] construct upon stimulation with glucagon, albeit the EC50 surprisingly was increased approximately 10-fold relative to the wild-type receptor. Substitution of Thr352, located at the intracellular end of transmembrane segment VI, with Ala led to a slightly elevated basal cAMP level, while the introduction of Pro or Ser at this position affected rather the binding affinity of glucagon or the EC50 for stimulation of cAMP production. The large extracellular segment, which is essential for glucagon binding, was not required for constitutive activation of the glucagon receptor as the introduction of the [H178R] mutation into an N-terminally truncated construct exhibited an elevated basal level of cAMP production. The analog des-His1-[Glu9]glucagon amide, which in vivo is a glucagon antagonist, was an agonist on both the wild-type and the [H178R] receptor and did not display any activity as an inverse agonist. It is concluded that the various phenotypes displayed by the constitutively active glucagon receptor mutants reflect the existence of multiple agonist-preferring receptor conformers, which include functionally active as well as inactive states. This view agrees with a recent multi-state extension of the ternary complex model for 7TM receptor activation.

An exactly solvable 4-state IRF model

A new 4-state IRF model is constructed by solving the star-triangle equation. The model is a multi-state extension of Baxter's hard hexagon model and the 3-state model by the authors. This result strongly suggests that there exists a solvable hierarchy which corresponds to Gordon's generalization of the Rogers-Ramanujan identities.