Electric properties of the water molecule in 1A1, 1B1, and 3B1 electronic states: Refined CASSCF and CASPT2 calculations

Summary The dipole moments and dipole polarizabilities of the ¹A₁, ¹B₁, and ³B₁ electronic states of the water molecule have been calculated by using the CASSCF approach followed by the evaluation of the dynamic electron correlation contribution by the second-order perturbation scheme CASPT2. All calculations have been carried out in a specifically extended ANO basis set which accounts for the Rydberg character of the two excited states. In order to estimate the correctness and accuracy of the present data a scan over a variety of different active spaces for the CASSCF wave function has been made. The present results are superior to earlier CASSCF calculations, although their qualitative features remain essentially the same. The dipole moments in ¹B₁ and ³B₁ states are predicted to be about 0.49 a.u. and 0.33 a.u., respectively, and have the opposite orientation with respect to the ground state dipole moment. The dipole polarizability tensors of the excited states are characterized by high anisotropy and are dominated by the in-plane component perpendicular to the symmetry axis. All their components are found to be about an order of magnitude larger than those of the ground state polarizability tensor. The excitation energy dependence on the choice of the active orbital space in the CASSCF reference function is also considered and the analysis of the present data concludes in the concept of what is called the mutually compatible active spaces for the two states involved in excitation. All CASPT2 results are in good agreement with the results of recent calculations carried out in the framework of the open-shell coupled cluster formalism. This agreement confirms the high efficiency of the CASSCF/CASPT2 approach to the treatment of the electron correlation effects.     

Theoretical rotational-vibrational spectra of theX 3 B 1,a 1 A 1 andb 1 B 1 states of NH 2 +

Summary The three-dimensional potential energy functions have been calculated from highly correlated multireference configuration interaction electronic wavefunctions for theX ³ B ₁,a ¹ A ₁, andb ¹ B ₁ states of the NH ₂ ⁺ ion. For the quasi-linear electronic ground state this information and the electric dipole moment functions have been used to calculate spectroscopic constants, line intensities and rotationally resolved absorption spectra. For thea ¹ A ₁-b ¹ B ₁ bent/quasi-linear Renner-Teller system ro-vibronic energy levels have been obtained from a variational approach accounting for anharmonicity, rotation-vibration and electronic angular momenta coupling effects. The vibronic levels are given for energies up to 13 500 cm^–1 for the bending levels and up to 8000 cm^–1 for the stretching and combination levels.Dedicated in the honor of Prof. Werner Kutzelnigg     

The valence and Rydberg excited states of CH2: A theoretical exploration

Using the completed active space second‐order perturbation (CASPT2) method, valence and Rydberg excited states of CH₂ molecule are probed with the large atomic natural orbital (ANO‐L) basis set. Five states are optimized and the geometric parameters are in good agreement with the available data in literatures, furthermore, the state of 2¹B₁ is obtained for the first time. Valence and Rydberg excited states of CH₂ are also calculated for the vertical transitions with the ANO‐L+ basis set that is constructed by adding a set of 1s1p1d Rydberg orbitals into the ANO‐L basis set. Two Rydberg states of the p?³A₂ and r?³B₁ at 9.88 and 10.50 eV are obtained for the first time, and the 3a₁ → 3d_yz nature of the state p?³A₂ and the 3a₁ → d_x2?y2 nature of the state r?³B₁ are confirmed. © 2012 Wiley Periodicals, Inc.     

An investigation of the1 B 1 excited states of water

The first seven¹ B ₁ excited states of water are investigated within the framework of the single centre method. Energies, wave-functions and electronic densities are found using one basis set of 25 Slater type orbitals and one of 40 orbitals (both with non-integer principal quantum numbers). All singly excited configurations of¹ B ₁ symmetry are taken into account. For each state the orbital parameters (n's and's) are carefully optimized. The energy differences between neighboring excited states are, when the comparison can be made, in good agreement with experiment as is also the major contributing configuration of each state. Particular emphasis is placed on the electronic rearrangement that occurs during excitation and this is explicitly brought out by the contour maps of the electronic density. These maps show satellite-clouds in the excited states.

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Zusammenfasung Die ersten sieben¹B₁-Zustände von Wasser werden mittels der Einzentrenmethode untersucht. Energien, Wellenfunktionen und Elektronendichten werden auf Grund je eines Basissatzes von 25 bzw. 40 Slater-Funktionen mit nicht-ganzzahligen Exponenten bestimmt. Dabei werden alle einfach angeregten¹ B ₁-Konfigurationen mit einbezogen and für jeden Zustand die Orbitalparameter sorgfältig optimalisiert. Die Energiedifferenzen zwischen benachbarten Zuständen sind in den Fällen, in denen der Vergleich mit dem Experiment möglich ist, richtig. Besondere Bedeutung wird den Elektronenumlagerungen beigemessen, die während der Anregung auftreten; sie werden in den Konturen-Bildern, die die Satellitenwolken in den angeregten Zuständen zeigen, wiedergegeben.

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Resumé Les sept premiers états excités¹ B ₁ de l'eau sont étudiés dans le cadre de la méthode à un seul centre. Les énergies, les fonctions d'onde et les densités électroniques sont trouvés successivement dans des bases de 25 et de 40 orbitales de type Slater (dans les deux cas avec des nombres quantiques prin cipaux non entiers). Toutes les configurations monoexcitées de symétrie¹ B ₁ sont prises en compte. Les paramètres orbitaux (n et sont soigneusement optimisés pour chaque état. Lorsque la comparaison avec l'expérience peut être faite on trouve des différences correctes entre les énergies d'état excités voisins, ainsi qu'une bonne identification des configurations essentielles correspondantes. On insiste particulièrement sur le réarrangement électronique qui se produit au cours de l'excitation et qui est explicitement révélé par les cartes d'isodensité. Ces cartes présentent des nuages satellites dans les états excités.

     

Theoretical study of the excited singlet and triplet states of alloxan

The possibility of excited‐state protomeric shifts in the biologically important molecule, alloxan, is investigated. We have focused on the S₁ and T₁ excited states of alloxan and its hydroxy tautomers. Modifications brought in by excitation on the relative stabilities, activation barriers, and optimized geometries, computed at the MNDO, AM1, and PM3 levels of approximation, have been discussed for both excited electronic states. The absorption and fluorescence spectra for the three tautomers are also discussed. Results show significant changes in the geometries on excitation, although the changes are similar for the singlet and triplet excited states. Though the relative stability orders do not change, the 2‐hydroxy tautomer is stabilized, while the 4‐hydroxy tautomer gets destabilized on excitation. The excited states are (n,π*) states, involving the promotion of a nonbonding oxygen lone pair from the CO? CO? CO moiety, which explains why the oxygens of this group become less basic and the 4‐hydroxy tautomer gets destabilized on excitation. However, the activation barriers do not reduce significantly on excitation, and this precludes the possibility of ground‐ or excited‐state proton transfer in the gas phase. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Theoretical study of the π→π* excited states of linear polyenes: The energy gap between 11Bu+ and 21Ag− states and their character

Multireference perturbation theory with complete active space self-consistent field (CASSCF) reference functions is applied to the study of the valence π→π* excited states of 1,3-butadiene, 1,3,5-hexatriene, 1,3,5,7-octatetraene, and 1,3,5,7,9-decapentaene. Our focus was put on determining the nature of the two lowest-lying singlet excited states, 1¹B_u⁺ and 2¹A_g⁻, and their ordering. The 1¹B_u⁺ state is a singly excited state with an ionic nature originating from the HOMO→LUMO one-electron transition while the covalent 2¹A_g⁻ state is the doubly excited state which comes mainly from the (HOMO)²→(LUMO)² transition. The active-space and basis-set effects are taken into account to estimate the excitation energies of larger polyenes. For butadiene, the 1¹B_u⁺ state is calculated to be slightly lower by 0.1 eV than the doubly excited 2¹A_g⁻ state at the ground-state equilibrium geometry. For hexatriene, our calculations predict the two states to be virtually degenerate. Octatetraene is the first polyene for which we predict that the 2¹A_g⁻ state is the lowest excited singlet state at the ground-state geometry. The present theory also indicates that the 2¹A_g⁻ state lies clearly below the 1¹B_u⁺ state in decapentaene with the energy gap of 0.4 eV. The 0–0 transition and the emission energies are also calculated using the planar C_2h relaxed excited-state geometries. The covalent 2¹A_g⁻ state is much more sensitive to the geometry variation than is the ionic 1¹B_u⁺ state, which places the 2¹A_g⁻ state significantly below the 1¹B_u⁺ state at the relaxed geometry. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 157–175, 1998     

Doubly excited3Se,3De and3Ge states of two-electron atomic systems

Summary Time-dependent perturbation theory has been applied to calculate the doubly excited triplet statesNsns:³S^e,Npnp:³D^e andNdnd:³G^e (N=2, 3, 4,n=N+1, ... ,5) for He, Li⁺, Be²⁺ and B³⁺. A time-dependent harmonic perturbation causes simulataneous excitation of both the electrons with a change of spin state. The doubly excited energy levels have been identified as the poles of an appropriately constructed linearized variational functional with respect to the driving frequency. In addition to the transition energies, effective quantum numbers of these doubly excited states have been calculated and analytic representations of their wave functions are obtained. These are utilized to estimate the Coulomb repulsion term for these states which checks the consistency of the wave functions. These wave functions may also be used for calculating other physical properties of the systems.     

Effect of solvent polarizability on dual fluorescence of EE-1-phenyl,4-(1′-pyrenyl)-1,3-butadiene

The properties of the lowest excited states of EE-1-phenyl,4-(1′-pyrenyl)-1,3-butadiene were studied by absorption and emission spectrometry in solvents of different polarity and polarizability. The effect of the latter on the energy and relative position of the two lowest excited singlet states (of B_u and A_g parentage) was investigated. Dual fluorescence was observed in low polarizability solvents at room temperature. The emission from a thermally populated upper state disappears at low temperature and in higher polarizability solvents, such as CS₂, where the lowest excited state acquires an allowed character. The excited molecule relaxes mainly by the radiative pathway. Internal conversion also plays an important role while the triplet population is scarce and photoisomerization is practically negligible. The behaviour is compared with those of related compounds.     

Theoretical study with rovibrational and dipole moment calculation of sextet states of the CrCl molecule

The potential energy curves have been investigated for the 13 lowest sextet electronic states in the representation below 53,000 cm^?1 of the molecule CrCl via CASSCF and MRCI (single and double excitation with Davidson correction) calculations. The harmonic frequency ω_e, the internuclear distance r_e, the rotational constant B_e, the electronic energy with respect to the ground state T_e, and the permanent dipole moment μ have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v, and the abscissas of the turning points r_min and r_max have been calculated for the considered electronic states up to the vibrational level v = 16. Nine electronic states have been studied theoretically here for the first time. The comparison of these values with the theoretical and experimental results available in the literature shows a good agreement. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Low‐lying singlet excited states of isocyanogen

Recent photofragment fluorescence excitation (PHOFEX) spectroscopy experiments have observed the ùA″ singlet excited state of isocyanogen (CNCN) for the first time. The observed spectrum is not completely assigned and significant questions remain about the excited states of this system. To provide insight into the energetically accessible excited states of CNCN, optimized geometries, harmonic vibrational frequencies, and excitation energies for the first three singlet excited states are determined using equation‐of‐motion coupled‐cluster theory with singles and doubles (EOM‐CCSD) and correlation‐consistent basis sets. Additionally, excited state coupled‐cluster methods which approximate the contributions from triples (CC3) are utilized to estimate the effect of higher‐order correlation on the energy of each excited state. For the ùA″ state, our best estimate for T₀ is about 42,200 cm^?1, in agreement with the experimentally estimated upper limit for the zero‐point level of 42,523 cm^?1. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

The Role of the nπ* 1Au State in the Photoabsorption and Relaxation of Pyrazine

The geometric, energetic, and spectroscopic properties of the ground state and the lowest four singlet excited states of pyrazine have been studied by using DFT/TD‐DFT, CASSCF, CASPT2, and related quantum chemical calculations. The second singlet nπ* state, ¹A_u, which is conventionally regarded dark due to the dipole‐forbidden ¹A_u←¹A_g transition, has been investigated in detail. Our new simulation has shown that the state could be visible in the absorption spectrum by intensity borrowing from neighboring nπ* ¹B_3u and ππ* ¹B_2u states through vibronic coupling. The scans on potential‐energy surfaces further indicated that the ¹A_u state intersects with the ¹B_2u states near the equilibrium of the latter, thus implying its participation in the ultrafast relaxation process.     

Ground and Electronically Excited Singlet‐State Structures of 5‐Fluoroindole Deduced from Rotationally Resolved Electronic Spectroscopy and ab Initio Theory

The structure and electronic properties of the electronic ground state and the lowest excited singlet state (S₁) of 5‐fluoroindole (5FI) were determined by using rotationally resolved spectroscopy of the vibration‐less electronic origin of 5FI. From the parameters of the axis reorientation Hamiltonian, the absolute orientation of the transition dipole moment in the molecular frame was determined and the character of the excited state was identified as L_b.     

An SCF-MS-Xα study of the bonding and nuclear quadrupole coupling in diatomic halogens and interhalogens in the ground X Σ and B Π 0 excited states

SCF-MS-Xα calculations of the electronic structure of diatomic halogens and interhalogens XY (X = I, Br, Cl; Y = I, Br, Cl, F) have been used to investigate the bonding and nuclear quadrupole coupling in these molecules. Calculations have been carried out for the ground X ¹ Σ electronic state, and for the excited B ³ Π₀ state in the case of I₂, Br₂, ICl and IBr. Good agreement (to within 10% in most cases) is obtained between the calculated and observed nuclear quadrupole coupling constants for the molecules in the ground state. For the excited state the agreement is not as good, but the calculation does reproduce the observed decrease in the coupling constants to less than one quarter of their ground state values, and analysis of the contributions to the field gradients clearly shows the reasons for this. The electric dipole moments and electric quadrupole moments of the molecules have also been calculated. However, these prove to be much more strongly dependent on the variables used in the calculation (atomic sphere radii, inclusion of d orbitals). The results of the calculations have also been used to test some of the assumptions made in the Townes and Dailey method of analysis of nuclear quadrupole coupling data.     

Geometrical relaxation in the excited singlet states of propylene

The consequences of the twist around the double bond in propylene for the properties of its low lying excited singlet states have been investigated by the ab initio large-scale multireference configuration interaction method (MRD-CI). A substantial increase in the dipole moments of the S₁ and S₂ excited states was found for a large interval of the twist angel θ = 50–130°. The variation of the VB covalent VB ionic contributions to the correlated wavefunctions of these two states a function of twisting has been analyzed. The connection with the occurence of an avoided crossing of the two excited singlets near the twist angel θ = 75°, which results in no change in dipole moment directions, is pointed out. The existence of destructive or constructive interference between acceptor and donor substitution has been investigated on the example of the pyramidalization at one of the vinylic C atoms. A competition of opposing effects matrix can invert the dipole moment direction in the excited states. Preliminary investigation of the nonadiabatic coupling elements indicates that the “sudden polarization” effect willnot disappear through vibronic coupling, and that the return of excited molecules to the ground electronic state will not be immediate.     

Full configuration interaction calculation of singlet excited states of Be3

The full configuration interaction (FCI) study of the singlets vertical spectrum of the neutral beryllium trimer has been performed using atomic natural orbitals [3s2p1d] basis set. The FCI triangular equilibrium structure of the ground state has been used to calculate the FCI vertical excitation energies up to 4.8 eV. The FCI vertical ionization potential for the same geometry and basis set amounts to 7.6292 eV. The FCI dipole and quadrupole transition moments from the ground state are reported as well. The FCI electric quadrupole moment of the X (3)A(1) (') ground state has been also calculated with the same basis set (Theta(zz)=-2.6461 a.u., Theta(xx)=Theta(yy)=-1/2Theta(zz)). Twelve of the 19 calculated excited singlets are doubly excited states. Most of the states have large multiconfigurational character. These results provide benchmark values for electronic correlation multireference methods. (4ex6MO)CAS-SDCI values for the same energies and properties are also reported.     

Nonadiabatic coupling and diabatic electronic population dynamics on 11A2 and 11B1 states of ozone molecule

In this work, we examine nonadiabatic population dynamics for 1¹B₁ and 1¹A₂ states of ozone molecule (O₃). In O₃, two lowest singlet excited states, ¹A₂ and ¹B₁, can be coupled. Thus, population transfer between them occurs through the seam involving these two states. At any point of the seam (conical intersection), the Born-Oppenheimer approximation breaks down, and it is necessary to investigate nonadiabatic dynamics. We consider a linear vibronic coupling Hamiltonian model and evaluate vibronic coupling constant, diabatic frequencies for three modes of O₃, bilinear and quadratic coupling constants for diabatic potentials, displacements, and Huang-Rhys coupling constants using ab initio calculations. The electronic structure calculations have been performed at the multireference configuration interaction and complete active space with second-order perturbation theory with a full-valence complete active space self-consistent field methods and augmented Dunning's standard correlation-consistent-polarized quadruple zeta basis set to determine ab initio potential energy surfaces for the ground state and first two excited states of O₃, respectively. We have chosen active space comprising 18 electrons distributed over 12 active orbitals. Our calculations predict the linear vibronic coupling constant 0.123 eV. We have obtained the population on the 1¹B₁ and 1¹A₂ excited electronic states for the first 500 fs after photoexcitation.     

Structure of electronically excited complexes in styrene and α-methylstyrene anion polymerizations

The spatial and electronic structure of styrene and α-methylstyrene monomer molecules and their complexes with living polymers in the ground singlet state (S ₀) and excited singlet (S ₁) and triplet (T ₁) states has been studied by RHF, ROHF/6-31G*, and DH quantum-chemical methods. The mechanism of anionic polymerization is considered in the context of the concept of electronic excitation in an elementary process. The excited states of (S·T)₁ biradical type are characterized by low energies (6–15 kcal/mole), which have the sense of activation energies E _a of chain propagation. Calculation gave higher values of E _a for free C^? anions compared to those for C^?M⁺ ion pairs, which indicates that anions show lower chemical activity in the general polymerization process.     

Dynamic dipole polarizabilities of the ground and excited states of confined hydrogen atom computed by means of a mapped Fourier grid method

Accurate theoretical estimates of static and dynamic dipole polarizabilities are reported for the ground and excited states of hydrogen atom confined at the center of a spherical “box” with impenetrable walls using a novel theoretical algorithm that combines the variational–perturbation approach with an appropriately adapted mapped Fourier grid method and uniformly maintains the numerical accuracy. A variation of computed polarizabilities is observed as a function of the number of grid points. However, rapid convergence to their correct values, even far into the anomalous dispersion region, is achieved by an extrapolation procedure to the limit of an infinitely large number of grid points using a small number of the lowest‐order Padé approximants. It is shown that dipole polarizabilities strongly depend upon the electronic state and the radius of confinement. In particular, the static polarizability of 2s state changes sign under strong confinement. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Theoretical study with vibration–rotation and dipole moment calculations of quartet states of the CrCl molecule

The potential energy curves have been investigated for the 10 lowest quartet electronic states in the ^2s+1Λ^± representation below 30,000 cm^?1 of the molecule CrCl via CASSCF and MRCI (singly and doubly excitation with Davidson correction) calculations. The harmonic frequency ω_e, the internuclear distance r_e, the rotational constant B_e, the electronic energy with respect to the ground state T_e, and the permanent dipole moment μ have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v, and the abscissas of the turning points r_min and r_max have been calculated for the considered electronic states up to the vibrational level v = 19. Seven electronic states have been studied here theoretically for the first time. The comparison of these values to the theoretical results available in the literature shows a good agreement. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011