valence-Rydberg Mixing Research Articles

UV excitations of halons.

In the present study, we examined the UV excitations of a newly introduced molecular set, Halons-9, composed of nine gaseous halon molecules. The performance of the density functional-based multi-reference configuration interaction method (DFT/MRCI) and time-dependent density functional theory with CAM-B3LYP functional (TD-CAM-B3LYP) in the computation of singlet and triplet excited states of this set was evaluated against coupled-cluster with singles and doubles (CCSD). Excited states up to the corresponding ionization limits, including both localized and delocalized excitations, have been benchmarked. TD-CAM-B3LYP significantly underestimates excitation energies of the higher mixed valence-Rydberg and Rydberg states, with computed mean absolute deviations from the equation of motion (EOM)-CCSD results 1.06 and 0.76 eV, respectively. DFT/MRCI gives a significantly better description of higher excited states, albeit still poor, compared to the TD-CAM-B3LYP. The mean absolute deviations of mixed valence-Rydberg and Rydberg states from the reference EOM-CCSD values are 0.66 and 0.47 eV, respectively. The performance of DFT/MRCI for description of strongly correlated states with valence-Rydberg mixing is still not satisfactory enough. On the other hand, oscillator strengths of most of singlet states obtained with both methods are close to the EOM-CCSD values. The largest deviations, occurring in the case of several high-lying multiconfigurational states, are of an order of magnitude.

Quasi-degenerate perturbation theory using matrix product states.

In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner's 2n + 1 rule. Further, our formulation satisfies Granovsky's requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost.

Two-Photon Excited State Dynamics of Dark Valence, Rydberg, and Superexcited States in 1,3-Butadiene.

Two-photon absorption in systems with parity permits access to states that cannot be prepared by one-photon absorption. Here we present the first time-resolved photoelectron spectroscopy study using this technique, applied to 1,3-butadiene, in which we investigated the dynamics of its dark valence, Rydberg, and superexcited states. The dark valence state dynamics are accessed via the Rydberg manifold, excited by two photons of 400 nm. We find that the 'dark' 2(1)Ag state populated in this manner has a much longer lifetime than when accesses via the 1(1)Bu 'bright' valence state when populated by one photon of 200 nm. In addition, we compared the dynamics of the 3sπ- and 3dπ-Rydberg states. These Rydberg states relax to the valence manifold on a subpicosecond time scale, with the 3sπ-Rydberg state decay rate being larger due to a stronger valence-Rydberg mixing. Finally, we investigated superexcited valence states that fragment or autoionize within 200 fs, likely without involving Rydberg states.

Excited states of PbF: A four-component relativistic study

The electronic states of lead monofluoride (PbF) are studied from the (Pb 6s)(2) (F 2p-pi)(4) (F 2p-sigma)(2) (Pb 6p-pi)(1) X(1) ground state up to the F state, using the four-component relativistic configuration interaction and Fock-space coupled-cluster singles and doubles methods. Difficulties arising from the valence-Rydberg mixing are overcome by using a flexible basis set including Rydberg-type diffuse functions and by large-scale correlation calculations. The excited states are successfully characterized with the help of computed transition dipole moments. The three lowest-lying states (X(1), X(2), and A) are confirmed to be valence states arising from the (Pb 6p) spinors. The B state is assigned to the lowest Rydberg state (Omega=1/2), represented by a single excitation from the (Pb 6p-pi) spinor to the (F 3s) Rydberg spinor. Its calculated excitation energy (4.30 eV) is comparable to the observed one (4.42 eV). The C state is a multiconfigurational valence state whose dominant configuration is represented by (Pb 6s)(2) (F 2p-pi)(4) (F 2p-sigma)(1) (Pb 6p-pi)(2). Its calculated excitation energy (4.71 eV) is in good agreement with experiment (4.72 eV). The remaining D, E, and F states are assigned as Rydberg states. The calculated ionization potential (7.44 eV) is also close to the value (7.55 eV) determined recently by multiphoton ionization experiments.

Theoretical investigation of the electronic spectrum of pyrazine

The description of Rydberg states by the complete active space self-consistent field (CASSCF) electronic structure method is known to be a difficult topic. In particular, two problems are frequently encountered: (a) the simultaneous presence of valence and Rydberg excited states in the same energy region can potentially lead to artificial valence–Rydberg mixing in the electronic wave functions. (b) Rydberg states have a tendency to be difficult to converge. We have implemented an approach for the consistent description of both valence and Rydberg excited states within the CASSCF electronic structure model. By employing the multiconfigurational second- and third-order perturbation theory (CASPT2/3) methods based on CASSCF reference wave functions, the procedure is verified by comparison with spectroscopic results for the example molecule pyrazine. Vertical excitation energies and other properties have been calculated for various electronic states. Basis sets and active spaces were selected to provide accurate results. Two combinations of aug-cc-pVTZ level basis sets complemented by Rydberg functions have been employed to calculate estimates for the properties of 19 singlet excited states of pyrazine. While many of the assignments made in previous studies could be confirmed, there are also several new aspects emerging from the present investigation.

Excited states of the water molecule: Analysis of the valence and Rydberg character

The excited states of the water molecule have been analyzed by using the extended quantum-chemical multistate CASPT2 method, namely, MS-CASPT2, in conjunction with large one-electron basis sets of atomic natural orbital type. The study includes 13 singlet and triplet excited states, both valence and 3s-, 3p-, and 3d-members of the Rydberg series converging to the lowest ionization potential and the 3s- and 3p-Rydberg members converging to the second low-lying state of the cation, 1 (2)A(1). The research has been focused on the analysis of the valence or Rydberg character of the low-lying states. The computation of the 1 (1)B(1) state of water at different geometries indicates that it has a predominant 3s-Rydberg character at the equilibrium geometry of the molecule but it becomes progressively a valence state described mainly by the one-electron 1b(1)-->4a(1) promotion, as expected from a textbook of general chemistry, upon elongation of the O-H bonds. The described valence-Rydberg mixing is established to be originated by a molecular orbital (MO) Rydbergization process, as suggested earlier by R. S. Mulliken [Acc. Chem. Res. 9, 7 (1976)]. The same phenomenon occurs also for the 1 (1)A(2) state whereas a more complex behavior has been determined for the 2 (1)A(1) state, where both MO Rydbergization and configurational mixing take place. Similar conclusions have been obtained for the triplet states of the molecule.

An application of second and third-order n-electron valence state perturbation theory to the calculation of the vertical electronic spectrum of furan

The vertical electronic spectrum of furan is investigated by second and third-order multireference perturbation theory (NEVPT). The excitation energies of the three lowest-energy valence states, as well as the 3 l Rydberg states are reported. The effects of the size of the active space and the valence–Rydberg mixing are discussed. The application of the quasi-degenerate NEVPT approach has proved to be necessary in order to handle the consistent valence–Rydberg interactions occurring for the two 1 A 1 + and 1 B 2 + valence states. For the three valence states and the low-lying Rydberg states, the computed excitation energies agree with those computed in the more recent high-level theoretical studies.

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.

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.

The multi-state CASPT2 method

An extension of the multiconfigurational second-order perturbation approach CASPT2 is suggested, where several electronic states are coupled at second order via an effective-Hamiltonian approach. The method has been implemented into the MOLCAS-4 program system, where it will replace the single-state CASPT2 program. The accuracy of the method is illustrated through calculations of the ionic-neutral avoided crossing in the potential curves for LiF and of the valence-Rydberg mixing in the V-state of the ethylene molecule.

On the interpretation of the NEXAFS spectrum of molecular oxygen

Calculations with extended basis sets and full intrachannel coupling of discrete and continuum states suggest an alternative interpretation of the NEXAFS spectrum of molecular oxygen. In this interpretation the roles of valence-Rydberg mixing and intrachannel discrete-continuum interaction are stressed at the expense of the exchange splitting mechanism. Calculations indicate that only the doublet-parent channel holds discrete strong transitions with σ ∗ character, while the quarter-parent channel contains preferentially Rydberg-like transitions.

Autoionization of NO in an excited valence state affected by perturbations from valence-Rydberg mixing

A two-dimensional photoelectron spectrum of NO has been measured in the photon energy range of 10.7–13.4eV. The spectrum exhibits many salient features due to autoionization. The vibrational distribution for NO + ( X 1∑ +) is simulated by means of Franck-Condon analysis, using a harmonic or anharmonic potential energy curve for the autoionizing state. The vibrational levels of this state are substantially perturbed by the Rydberg states converging to NO + ( X 1∑ +).

Inner-shell electron excitation in the methylmethoxysilanes

The effect of electron-donating substituents on the low-lying unoccupied valence orbitals in the series of silanes Si(CH 3) x (OCH 3) 4− x is investigated in an examination of electron-impact energy-loss spectra near the Si 2p ionization edge, and by means of ab initio calculations of the core-hole states populated by the inner-shell excitation. The substituent effect on the LUMO energies, as well as upon the 29Si NMR shieldings, is considered along with the consequences of valence—Rydberg mixing.

Valence—Rydberg mixing in the excited doublet states of HCO: potential surfaces for HCO separation

Valence—Rydberg mixing of the doublet electronic states of HCO along the HCO dissociation path is investigated by means of ab initio configuration interaction calculations. The character of the species in question and the form of the corresponding potential surfaces are discussed in terms of composition and energy changes of the molecular orbitals, generated in SCF computations, with geometry variation.

Size-inconsistency effects in molecular properties for states with valence-Rydberg mixing: The low-lying π→π* states of ethylene and butadiene

A b initio results for the low-lying 1B1u states of ethylene are used to discuss size-inconsistency effects on calculated molecular properties for states where valence-Rydberg mixing is important. Results for the expectation value of x2, x being the coordinate perpendicular to the plane of the molecule, are presented from quasidegenerate variational perturbation theory and multireference configuration-interaction calculations. These results are compared with values from previous studies. It is argued that size inconsistency in configuration-interaction studies can have a significant effect on estimated molecular properties. Calculations on several low-lying states of butadiene are also reported where similar size-inconsistency effects are found.

Full configuration-interaction benchmark calculations for AlH

The X 1Σ+, A 1Π, and C 1Σ+ states of AlH are studied using a [7s 5p 2d/4s 3p] basis set and incorporating valence correlation using the complete active space self-consistent-field (CASSCF)/second-order configuration-interaction (SOCI) and full configuration-interaction (FCI) methods. A principal focus of this work is to provide FCI calibration calculations for approximate methods of describing the energies, dipole moments, and transition moments when there is a variable degree of valence–Rydberg mixing. The state-averaged CASSCF/SOCI method is found to be capable of providing an accurate description of these states when the CASSCF active space is sufficiently flexible to describe both the important correlation effects and the Rydberg character. Having found a CASSCF/SOCI procedure that nearly reproduces the FCI results in a [7s 5p 2d/4s 3p] basis set, we take this procedure to near the basis set limit. The calculated dissociation energies (De in eV with experimental values in parentheses) are 3.16 (3.16) for the X 1Σ+ state, 0.24 (0.24) for the A 1Π state, and 0.80 (0.76) for the inner minimum of the C 1Σ+ state. Our calculated radiative lifetimes for the v=0, N=5 and v=1, N=7 levels of the A 1Π state are 64.3 and 96.6 ns, in quite good agreement with a previous CASSCF study, and with the experimental values of 66±4 and 83±6 ns. The radiative lifetimes for the v=0, N=0 and v=1, N=0 levels of the inner minimum of the C 1Σ+ state are 5.5 and 4.1 ns, respectively.

Multiconfigurational Hartree–Fock studies of avoided curve crossing using the Newton–Raphson technique

A mode controlling scheme for use in second order Newton–Raphson multiconfigurational Hartree–Fock calculations has been developed and applied on the avoided curve crossing for the lowest three states of 4Π symmetry of BO and on the valence-Rydberg mixing in the lowest two states of 3Σ−u symmetry in O2. Convergence of the multiconfigurational Hartree–Fock calculations was easily obtained in all calculations, even where root-flipping occurred. We further demonstrate how an MCSCF calculation may occasionally be reparametrized, that is, the same MCSCF total energy may be obtained using two different sets of configuration lists. One parameter list may give root-flipping, whereas another parameterization may not. This is exemplified in a calculation on the E 3Σ−u state of O2 at 2.13 a.u..

Excited states of CH+: Potential curves and transition moments

Wave functions and potential curves for the ground X 1Σ+ state and eight excited states of 1Σ+ and 1Π symmetry of CH+ have been obtained using ab initio configuration interaction (CI) methods. In order to take proper account of valence–Rydberg mixing, Rydberg functions were included in the basis set. The orbitals used in the set of reference configurations for the CI wave functions included both valence and Rydberg orbitals, determined from a multiconfiguration self-consistent field and a natural orbital calculation, respectively. Transition moments between the ground electronic state and the 2 1Σ+, 3 1Σ+, A 1Π, and 2 1Π states have been computed, and the importance of these states in photodissociation of CH+ is discussed.

Term-values and valence-rydberg mixing in core-excited states, SiH 4 and PH 3

The controversial interpretation on the XUV spectra of PH 3 and SiH 4 have been examined experimentally and theoretically. An assigned consistent with measured 2p-absroption spectra of gaseous and solid SiH 4 and PH 3, and with CI calculation on core-excited states of SiH 4 is presented. The predictions of the equivalent ionic core virtual orbital model are confirmed. Term-values for core-excited states differ systematically from those for valence-excited states.

Ion-pair states of O2

Valence states of O2 that correlate adiabatically to the ion pair asymptote, O+(4S)+O−(2P), have been calculated using the multiconfiguration description of the electronic structure. The production of the ion pair is attributed to valence–Rydberg mixing that predissociates Rydberg states of the excited O2+ ion such as those leading to the b 4Σ−g state. The electronic states required the calculation of excited states of a given symmetry. This is possible with the BISON-MC codes if the rigorous restriction on orthogonality to the lower states is relaxed. For homonuclear valence states, in particular, this should be a good approximation.