Anharmonic Vibrational Wave Functions Research Articles

Tensor Decomposition and Vibrational Coupled Cluster Theory

The use of tensor decomposition in the calculation of anharmonic vibrational wave functions is discussed. The correlation amplitudes of vibrational coupled cluster (VCC) and vibrational configuration interaction (VCI) theories are considered as tensors and decomposed. A pilot code is implemented allowing a numerical study of the performance of the canonical decomposition/parallel factors (CP) for three and higher mode couplings in computations on water, formaldehyde, and 1,2,5-thiadiazole. The results show that there is a significant perspective in applying tensor decomposition in the context of anharmonic vibrational wave functions, with the CP tensor decomposition providing compression of data and a computational convenient representation. The calculations also illustrate how the multiplicative separability of the VCC ansatz with respect to noninteracting degrees of freedom goes well together with a tensor decomposition approach. Tensor decomposition opens for adjusting the computational effort spent on a particular mode-coupling according to the significance of that particular coupling, which is guaranteed to decrease to zero in the case of VCC in the limit of noninteracting subsystems.

A band Lanczos approach for calculation of vibrational coupled cluster response functions: simultaneous calculation of IR and Raman anharmonic spectra for the complex of pyridine and a silver cation

We describe new methods for the calculation of IR and Raman spectra using vibrational response theory. Using damped linear response functions that incorporate a Lorentzian line-shape function from the outset, it is shown how the calculation of Raman spectra can be carried out through the calculation of a set of vibrational response functions in the same manner as described previously for IR spectra. The necessary set of response functions can be calculated for both vibrational coupled cluster (VCC) and vibrational configuration interaction (VCI) anharmonic vibrational wave-functions. For the efficient and simultaneous calculation of the full set of necessary response functions, a non-hermitian band Lanczos algorithm is implemented for VCC, and a hermitian band Lanczos algorithm is implemented for VCI. It is shown that the simultaneous calculation of several response functions is often advantageous. Sample calculations are presented for pyridine and the complex between pyridine and the silver cation.

Franck-Condon simulation, including anharmonicity, of the photodetachment spectrum of P2H−: Restricted-spin coupled-cluster single-double plus perturbative triple and unrestricted-spin coupled-cluster single-double plus perturbative triple -F12x potential energy functions of P2H and P2H−

Geometry optimization and harmonic vibrational frequency calculations have been carried out on the X̃(2)A(') state of P(2)H and the X̃(1)A(') state of P(2)H(-) using the restricted-spin coupled-cluster single-double plus perturbative triple excitation [RCCSD(T)] and explicitly correlated unrestricted-spin coupled-cluster single-double plus perturbative triple excitation [UCCSD(T)-F12x] methods. For RCCSD(T) calculations, basis sets of up to the augmented correlation-consistent polarized valence quintuple-zeta (aug-cc-pV5Z) quality were employed, and contributions from extrapolation to the complete basis set limit and from core correlation of the P 2s(2)2p(6) electrons were also included. For UCCSD(T)-F12x calculations, different atomic orbital basis sets of triple-zeta quality with different associated complementary auxiliary basis sets and different geminal Slater exponents were used. When the P 2s(2)2p(6) core electrons were correlated in these F12x calculations, appropriate core-valence basis sets were employed. In addition, potential energy functions (PEFs) of the X̃(2)A(') state of P(2)H and the X̃(1)A(') state of P(2)H(-) were computed at different RCCSD(T) and UCCSD(T)-F12x levels, and were used in variational calculations of anharmonic vibrational wavefunctions, which were then utilized to calculate Franck-Condon factors (FCFs) between these two states, employing a method which includes allowance for anharmonicity and Duschinsky rotation. The photodetachment spectrum of P(2)H(-) was then simulated using the computed FCFs. Simulated spectra obtained using the RCCSD(T)/aug-cc-pV5Z and UCCSD(T)-F12x(x = a or b)/aug-cc-pCVTZ PEFs are compared and found to be essentially identical. Based on the computed FCFs, a more detailed assignment of the observed vibrational structure than previously reported, which includes "hot bands," has been proposed. Comparison between simulated and available experimental spectra has been made, and the currently most reliable sets of equilibrium geometrical parameters for P(2)H and its anion have been derived. The photodetachment spectrum of P(2)D, yet to be recorded, has also been simulated.

Ab initio calculations on the X̃ B21 and à A21 states of AsH2, and Franck–Condon simulation, including anharmonicity, of the Ã(,,)-X̃ single vibronic level emission spectrum of AsH2

Restricted-spin coupled-cluster single-double plus perturbative triple excitation {RCCSD(T)} calculations were carried out on the X (2)B(1) and A (2)A(1) states of AsH(2) employing the fully relativistic small-core effective core potential (ECP10MDF) for As and basis sets of up to the augmented correlation-consistent polarized valence quintuple-zeta (aug-cc-pV5Z) quality. Minimum-energy geometrical parameters and relative electronic energies were evaluated, including contributions from extrapolation to the complete basis set limit and from outer core correlation of the As 3d(10) electrons employing additional tight 4d3f2g2h functions designed for As. In addition, simplified, explicitly correlated CCSD(T)-F12 calculations were also performed employing different atomic orbital basis sets of up to aug-cc-pVQZ quality, and associated complementary auxiliary and density-fitting basis sets. The best theoretical estimate of the relative electronic energy of the A (2)A(1) state of AsH(2) relative to the X (2)B(1) state including zero-point energy correction (T(0)) is 19,954(32) cm(-1), which agrees very well with available experimental T(0) values of 19,909.4531(18) and 19,909.4910(17) cm(-1) obtained from recent laser induced fluorescence and cavity ringdown absorption spectroscopic studies. In addition, potential energy functions (PEFs) of the X (2)B(1) and A (2)A(1) states of AsH(2) were computed at different RCCSD(T) and CCSD(T)-F12 levels. These PEFs were used in variational calculations of anharmonic vibrational wave functions, which were then utilized to calculate Franck-Condon factors (FCFs) between these two states, using a method which includes allowance for anharmonicity and Duschinsky rotation. The A(0,0,0)-X single vibronic level (SVL) emission spectrum of AsH(2) was simulated using these computed FCFs. Comparison between simulated and available experimental vibrationally resolved spectra of the A(0,0,0)-X SVL emission of AsH(2), which consist essentially of the bending (2(n)) series, suggests that there is a significant loss in intensity in the low emission energy region of the experimental spectrum.

Franck–Condon profiles in photodetachment-photoelectron spectra of and based on vibrational configuration interaction wavefunctions

Explicitly electron correlating coupled cluster calculations, CCSD(T)-F12a, were performed to determine three-dimensional potential energy hypersurfaces of disulphanide and disulphanyl in an automated approach. Surfaces for different electronic states were used in a Watson rovibrational Hamiltonian ansatz to obtain the correlated anharmonic vibrational wavefunctions. Subsequently the anharmonic Franck–Condon overlap integrals were evaluated. The computed Franck–Condon profiles were compared to experimental photodetachment-photoelectron spectra and confirm essentially the assignments made previously. The profiles indicate, however, additional weaker, and as of yet unresolved, additional features.

Franck–Condon simulation of the photoelectron spectrum of AsF2 and the photodetachment spectrum of AsF2− using ab initio calculations: Ionization energy and electron affinity of AsF2

RCCSD(T) and/or CASSCF/MRCI calculations were carried out on the X(2)B(1) state of AsF(2), the X(1)A(1), ã(3)B(1) and A(1)B(1) states of AsF(2)(+), and the X(1)A(1) state of AsF(2)(-) employing the fully-relativistic small-core effective core potential (ECP10MDF) for As and basis sets of up to augmented correlation-consistent polarized valence quintuple-zeta (aug-cc-pV5Z) quality. Minimum-energy geometrical parameters and relative electronic energies were evaluated, including contributions from extrapolation to the complete basis set limit and from outer core correlation of the As 3d(10) electrons. In addition, simplified, explicitly correlated RHF/UCCSD(T)-F12x calculations were also performed employing different atomic orbital basis sets, and associated complementary auxiliary and density-fitting basis sets. The best theoretical estimates of the adiabatic ionization energies (AIE(0)) of AsF(2)(X(2)B(1)) to the X(1)A(1) and ã(3)B(1) states of AsF(2)(+), including corrections for zero-point vibrational energy (DeltaZPE), are 9.099(8) and 13.290(22) eV respectively. The best estimated electron affinity (EA(0)) of AsF(2) is 1.182(16) eV, also including Delta(ZPE). These are currently the most reliable AIE(0) and EA(0) values for AsF(2). Potential energy functions (PEFs) of the X(2)B(1) state of AsF(2), the X(1)A(1) and ã(3)B(1) states of AsF(2)(+) and X(1)A(1) state of AsF(2)(-) were computed at RCCSD(T)/aug-cc-pV5Z, RCCSD(T)/aug-cc-pCV5Z and RHF/UCCSD(T)-F12a/aug-cc-pCVTZ levels. These PEFs were employed in variational calculations of anharmonic vibrational wavefunctions, which were then utilised to calculate Franck-Condon factors (FCFs), using a method which includes allowance for anharmonicity and Duschinsky rotation. The computed FCFs were used to simulate the first two bands in the photoelectron spectrum of AsF(2) and the first band in the photodetachment spectrum of AsF(2)(-), both yet to be recorded. The simulated spectra obtained using different sets of PEFs were found to be almost identical, suggesting that the simplified explicitly correlated UCCSD(T)-F12x method with a relatively small basis set can be a reliable alternative to the conventional RCCSD(T) correlation methods with a relatively large basis set, but at a significantly lower cost.

Few-cycle laser pulses to obtain spatial separation of OHF− dissociation products

In a two-part theoretical study, field-free orientation of OHF(-) is achieved by means of moderately intense half-cycle, infrared laser pulses. In the first step, a short linearly polarized pulse excites a superposition of rigid rotor rotational eigenstates via interaction with the permanent dipole moment of OHF(-). After the field has been switched off, pronounced molecular orientation is observed for several picoseconds. In the second step, femtosecond few-cycle laser pulses are applied to the oriented system to steer vibrational dynamics, modeled by anharmonic vibrational wave functions calculated on a potential energy surface obtained with unrestricted fourth order Moller-Plesset ab initio calculations. The result is selective bond breaking of OHF, followed by the spatial separation of dissociation products in the space-fixed frame. Due to revivals in the rotational wavepacket, product yields can be enhanced over long times.

A combined ab initio and Franck–Condon simulation study of the photodetachment spectrum of [formula omitted

RCCSD(T) potential energy functions (PEFs) of the X∼1A1 state of ZrO2 and the X∼2A1 state of ZrO2- have been computed employing the fully relativistic ECP28MDF ECP and associated aug-cc-pwCVQZ basis set for Zr (aug-cc-pVQZ for O). These PEFs were used in variational calculations of anharmonic vibrational wavefunctions of the ground electronic states of ZrO2 and ZrO2-. Franck–Condon factors which include allowance of Duschinsky rotation between these two electronic states were then computed and used to simulate the photodetactment spectrum of ZrO2-. Excellent agreement between the simulated and observed spectra is obtained, confirming the reliability of the PEFs used.

Ab initio calculations on the X̃A′1 and ÃA″1 states of HPO and Franck-Condon simulation of the single vibronic level emission spectra of HPO and DPO

Minimum-energy geometries and relative electronic energies of the X (1)A(') and A (1)A(") states of HPO have been computed employing the coupled-cluster single-double plus perturbative triple excitations {RCCSD(T)} and/or complete-active-space self-consistent-field (CASSCF) multireference internally contracted configuration interaction (MRCI) methods with basis sets of up to the augmented correlation-consistent polarized-valence quintuple-zeta (aug-cc-pV5Z) quality. In addition, RCCSD(T)/aug-cc-pVQZ and CASSCF/MRCI/aug-cc-pVQZ potential energy functions, anharmonic vibrational wave functions, and energies involving all three vibrational modes for both electronic states of HPO and DPO, and Franck-Condon factors between the two electronic states, which allow for Duschinsky rotation and anharmonicity, were computed. Computed Franck-Condon factors were then used to simulate single vibronic level (SVL) emission spectra recently reported by Tackett and Clouthier [J. Chem. Phys. 117, 10604 (2002)]. Excellent agreement between the simulated and observed spectra was obtained for the A (1)A(")(1,0,0)-->X (1)A(') SVL emission of HPO and DPO, when the best estimated ab initio geometries of the two states, which include contributions from core correlation and extrapolation to the complete basis set limit, were used in the simulation, suggesting that the best estimated ab initio geometry of the A (1)A(") state of HPO, particularly the bond angle of 94.5 degrees , is more reliable than the available experimentally derived geometry. A discussion on the geometrical parameters derived from rotational constants obtained from the rotational analysis of a high-resolution spectrum and from Franck-Condon simulation of the vibrational structure of an electronic spectrum is given.

Ab initio calculations on low-lying electronic states of SbO2− and Franck-Condon simulation of its photodetachment spectrum

Geometry optimization and harmonic vibrational frequency calculations have been carried out on the low-lying singlet and triplet electronic states of the antimony dioxide anion (SbO2-) employing a variety of ab initio methods. Both large-core and small-core relativistic effective core potentials were used for Sb in these calculations, together with valence basis sets of up to augmented correlation-consistent polarized-valence quintuple-zeta (aug-cc-pV5Z) quality. The ground electronic state of SbO2- is determined to be the X (1)A1 state, with the a (3)B1 state, calculated to be approximately 48 kcal mole(-1) (2.1 eV) higher in energy. Further calculations were performed on the X (2)A1, A (2)B2, and B (2)A2 states of SbO2 with the aim to simulating the photodetachment spectrum of SbO(2) (-). Potential energy functions (PEFs) of the X (1)A1 state of SbO2- and the X (2)A1, A (2)B2, and B (2)A2 states of SbO2 were computed at the complete-active-space self-consistent-field multireference internally contracted configuration interaction level with basis sets of augmented correlation-consistent polarized valence quadruple-zeta quality. Anharmonic vibrational wave functions obtained from these PEFs were used to compute Franck-Condon factors between the X (1)A1 state of SbO2- and the X (2)A1, A (2)B2, and B (2)A2 states of SbO2, which were then used to simulate the photodetachment spectrum of SbO2-, which is yet to be recorded experimentally.

Ab initio calculations on SnCl2 and Franck-Condon factor simulations of its ã-X̃ and B̃-X̃ absorption and single-vibronic-level emission spectra

Minimum-energy geometries, harmonic vibrational frequencies, and relative electronic energies of some low-lying singlet and triplet electronic states of stannous dichloride, SnCl(2), have been computed employing the complete-active-space self-consistent-field/multireference configuration interaction (CASSCF/MRCI) and/or restricted-spin coupled-cluster single-double plus perturbative triple excitations [RCCSD(T)] methods. The small core relativistic effective core potential, ECP28MDF, was used for Sn in these calculations, together with valence basis sets of up to augmented correlation-consistent polarized-valence quintuple-zeta (aug-cc-pV5Z) quality. Effects of outer core electron correlation on computed geometrical parameters have been investigated, and contributions of off-diagonal spin-orbit interaction to relative electronic energies have been calculated. In addition, RCCSD(T) or CASSCF/MRCI potential energy functions of the X(1)A(1), ã(3)B(1), and B(1)B(1) states of SnCl(2) have been computed and used to calculate anharmonic vibrational wave functions of these three electronic states. Franck-Condon factors between the X (1)A(1) state, and the ã (3)B(1) and B (1)B(1) states of SnCl(2), which include anharmonicity and Duschinsky rotation, were then computed, and used to simulate the ã-X and B-X absorption and corresponding single-vibronic-level emission spectra of SnCl(2) which are yet to be recorded. It is anticipated that these simulated spectra will assist spectroscopic identification of gaseous SnCl(2) in the laboratory and/or will be valuable in in situ monitoring of SnCl(2) in the chemical vapor deposition of SnO(2) thin films in the semiconductor gas sensor industry by laser induced fluorescence and/or ultraviolet absorption spectroscopy, when a chloride-containing tin compound, such as tin dichloride or dimethyldichlorotin, is used as the tin precursor.

Ab initio calculations on SF2 and its low-lying cationic states: Anharmonic Franck-Condon simulation of the uv photoelectron spectrum of SF2

Geometry optimization calculations were carried out on the (approximate)X(1)A(1) state of SF2 and the (approximate)X(2)B(1), (approximate)A(2)A(1), (approximate)B(2)B(2), (approximate)C(2)B(2), (approximate)D(2)A(1), and (approximate)E(2)A(2) states of SF2(+) employing the restricted-spin coupled-cluster single-double plus perturbative triple excitation [RCCSD(T)] method and basis sets of up to the augmented correlation-consistent polarized quintuple-zeta [aug-cc-pV(5+d)Z] quality. Effects of core electron (S 2s(2)2p(6) and F 1s(2) electrons) correlation and basis set extension to the complete basis set limit on the computed minimum-energy geometries and relative electronic energies (adiabatic and vertical ionization energies) were investigated. RCCSD(T) potential energy functions (PEFs) were calculated for the (approximate)X(1)A(1) state of SF2 and the low-lying states of SF2(+) listed above employing the aug-cc-pV(5+d)Z and aug-cc-pV5Z basis sets for S and F, respectively. Anharmonic vibrational wave functions of these neutral and cationic states of SF2, and Franck-Condon (FC) factors of the lowest four one-electron allowed neutral photoionizations were computed employing the RCCSD(T) PEFs. Calculated FC factors with allowance for Duschinsky rotation and anharmonicity were used to simulate the first four photoelectron bands of SF2. The agreement between the simulated and observed first bands in the He I photoelectron spectrum reported by de Leeuw et al. [Chem. Phys. 34, 287 (1978)] is excellent. Our calculations largely support assignments made by de Leeuw et al. on the higher ionization energy bands of SF2.

Ab initio calculations on SCl2 and low-lying cationic states of SCl2+: Franck-Condon simulation of the UV photoelectron spectrum of SCl2

Geometry optimization calculations were carried out on the (approximate)X (1)A(1) state of SCl(2) and the (approximate)X(2)B(1), (approximate)A(2)B(2), (approximate)B(2)A(1), (approximate)C(2)A(1), (approximate)D(2)A(2), and (approximate)E (2)B(2) states of SCl(2) (+) at the restricted-spin coupled-cluster single-double plus perturbative triple excitation [RCCSD(T)] level with basis sets of up to the augmented correlation-consistent polarized quintuple-zeta [aug-cc-pV(5+d)Z] quality. Effects of core electron correlation, basis set extension to the complete basis set limit, and relativistic contributions on computed minimum-energy geometrical parameters and/or relative electronic energies were also investigated. RCCSD(T) potential energy functions (PEFs) were calculated for the (approximate)X (1)A(1) state of SCl(2) and the low-lying states of SCl(2)(+) listed above employing the aug-cc-pV(5+d)Z basis set. Anharmonic vibrational wave functions of these neutral and cationic states of SCl(2), and Franck-Condon (FC) factors of the lowest four one-electron allowed neutral photoionizations were computed employing the RCCSD(T)aug-cc-pV(5+d)Z PEFs. Calculated FC factors with allowance for the Duschinsky rotation and anharmonicity were used to simulate the first four photoelectron (PE) bands of SCl(2). The agreement between simulated and observed He I PE spectra reported by Colton et al. [J. Electron Spectrosc. Relat. Phenom. 3, 345 (1974)] and Solouki et al. [Chem. Phys. Lett. 26, 20 (1974)] is excellent. However, our FC spectral simulations indicate that the first observed vibrational component in the first PE band of SCl(2) is a "hot" band arising from the SCl(2)(+)(approximate)X(2)B(1)(0,0,0)<--SCl(2)(approximate)X (1)A(1)(1,0,0) ionization. Consequently, the experimental adiabatic ionization energy of SCl(2) is revised to 9.55+/-0.01 eV, in excellent agreement with results obtained from state-of-the-art ab initio calculations in this work.

Anharmonic vibrational levels of the two cyclic isomers of SiC3

Using coupled-cluster approach full six-dimensional analytic potential energy surfaces for two cyclic SiC(3) isomers [C-C transannular bond (I) and Si-C transannular bond (II)] have been generated and used to calculate anharmonic vibrational wave functions. Several strong low-lying anharmonic resonances have been found. In both isomers already some of the fundamental transitions cannot be described within the harmonic approximation. Adiabatic electron affinities and ionization energies have been calculated as well. The Franck-Condon factors for the photodetachment processes c-SiC(3) (-)(I)-->c-SiC(3)(I) and c-SiC(3) (-)(II)-->c-SiC(3)(II) are reported.

Franck-Condon factors based on anharmonic vibrational wave functions of polyatomic molecules

Franck-Condon (FC) integrals of polyatomic molecules are computed on the basis of vibrational self-consistent-field (VSCF) or configuration-interaction (VCI) calculations capable of including vibrational anharmonicity to any desired extent (within certain molecular size limits). The anharmonic vibrational wave functions of the initial and final states are expanded unambiguously by harmonic oscillator basis functions of normal coordinates of the respective electronic states. The anharmonic FC integrals are then obtained as linear combinations of harmonic counterparts, which can, in turn, be evaluated by established techniques taking account of the Duschinsky rotations, geometry displacements, and frequency changes. Alternatively, anharmonic wave functions of both states are expanded by basis functions of just one electronic state, permitting the FC integral to be evaluated directly by the Gauss-Hermite quadrature used in the VSCF and VCI steps [Bowman et al., Mol. Phys. 104, 33 (2006)]. These methods in conjunction with the VCI and coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] method have predicted the peak positions and intensities of the vibrational manifold in the X 2B1 photoelectron band of H2O with quantitative accuracy. It has revealed that two weakly visible peaks are the result of intensity borrowing from nearby states through anharmonic couplings, an effect explained qualitatively by VSCF and quantitatively by VCI, but not by the harmonic approximation. The X 2B2 photoelectron band of H2CO is less accurately reproduced by this method, likely because of the inability of CCSD(T)/cc-pVTZ to describe the potential energy surface of open-shell H2CO+ with the same high accuracy as in H2O+.

The Singlet–Triplet Separation in CF2: State‐of‐the‐Art Ab Initio Calculations and Franck–Condon Simulations Including Anharmonicity

Geometrical parameters, vibrational frequencies and relative electronic energies of the X2B1 state of CF2- and the X1A1 and ã3B1 states of CF2 have been calculated. Core-electron effects on the computed minimum-energy geometries and relative electronic energies have been investigated, and relativistic contributions to the computed relative electronic energies calculated. Potential energy functions of the X2B1 state of CF2- and the X1A1 and ã3B1 states of CF2 have been determined, and anharmonic vibrational wavefunctions of these states calculated variationally. Franck-Condon factors including anharmonicity and Duschinsky rotation have been computed and used to simulate the ã-X emission spectrum of CF2 determined by S. Koda [Chem. Phys. Lett. 1978, 55, 353] and the 364 nm laser photodetachment spectrum of CF2- obtained by R. L. Schwartz et al. [J. Phys. Chem. A 1999, 103, 8213]. Comparison between theory and experiment shows that the theoretical approach benchmarked in the present study is able to give highly reliable positions for the CF2(X1A1) + e <-- CF2-(X2B1) and CF2(ã3B1) + e <-- CF2-(X2B1) bands in the photoelectron spectrum of CF2- and a reliable singlet-triplet gap for CF2. It is therefore concluded that the same theoretical approach should give reliable simulated CCl2(X1A1) + e <-- CCl2-(X2B1) and CCl2(ã3B1) + e <-- CCl2-(X2B1) bands in the photodetachment spectrum of CCl2- and a reliable singlet-triplet gap for CCl2.

Ab Initio Calculations and Franck–Condon Simulation of the Absorption Spectra of GeCl2 Including Anharmonicity

Geometrical parameters, vibrational frequencies and relative electronic energies of the X1A1, ã3B1 and A1B1 states of GeCl2 have been calculated at the CCSD(T) and/or CASSCF/MRCI level with basis sets of up to aug-cc-pV5Z quality. Core electron correlation and relativistic contributions were also investigated. RCCSD(T)/ aug-cc-pVQZ potential energy functions (PEFs) of the X1A1 and ã3B, states, and a CASSCF/MRCl/aug-cc-pVQZ PEF of the A1B1 state of GeCl2 are reported. Anharmonic vibrational wavefunctions of these electronic states of GeCl2, obtained variationally using the computed PEFs, are employed to calculate the Franck-Condon factors (FCFs) of the ã-X and A-X transitions of GeCl2. Simulated absorption spectra of these transitions based on the computed FCFs are compared with the corresponding experimental laser-induced fluorescence (LIF) spectra of Karolczak et al. [J. Chem. Phys. 1993, 98, 60-70]. Excellent agreement is obtained between the simulated absorption spectrum and observed LIF spectrum of the ã-X transition of GeCl2, which confirms the molecular carrier, the electronic states involved and the vibrational assignments of the LIF spectrum. However, comparison between the simulated absorption spectrum and experimental LIF spectrum of the A-X transition of GeCl2 leads to a revision of vibrational assignments of the LIF spectrum and suggests that the X1A1 state of GeCl2 was prepared in the experimental work, with a non-Boltzmann vibrational population distribution. The X(0,0,1) level is populated over 4000 times more than expected from a Boltzmann distribution at 60 K, which is appropriate for the relative population of the other low-lying vibrational levels, such as the X(1,0,0) and X(0,1,0) levels.

Franck-Condon simulation of the single-vibronic-level emission spectra of HPCl/DPCl and the chemiluminescence spectrum of HPCl, including anharmonicity.

Restricted-spin coupled-cluster single-double plus perturbative triple excitation [RCCSD(T)] potential energy functions (PEFs) were calculated for the X (2)A" and A (2)A' states of HPCl employing the augmented correlation-consistent polarized-valence-quadruple-zeta (aug-cc-pVQZ) basis set. Further geometry optimization calculations were carried out on both electronic states of HPCl at the RCCSD(T) level with all electron and quasirelativistic effective core potential basis sets of better than the aug-cc-pVQZ quality, and also including some core electrons, in order to obtain more reliable geometrical parameters and relative electronic energy of the two states. Anharmonic vibrational wave functions of the two states of HPCl and DPCl, and Franck-Condon (FC) factors of the A (2)A'-X (2)A" transition were computed employing the RCCSD(T)/aug-cc-pVQZ PEFs. Calculated FC factors with allowance for Duschinsky rotation and anharmonicity were used to simulate the single-vibronic-level (SVL) emission spectra of HPCl and DPCl reported by Brandon et al. [J. Chem. Phys. 119, 2037 (2003)] and the chemiluminescence spectrum reported by Bramwell et al. [Chem. Phys. Lett. 331, 483 (2000)]. Comparison between simulated and observed SVL emission spectra gives the experimentally derived equilibrium geometry of the A (2)A' state of HPCl of r(e)(PCl) = 2.0035 +/- 0.0015 A, theta(e) = 116.08 +/- 0.60 degrees, and r(e)(HP) = 1.4063+/-0.0015 A via the iterative Franck-Condon analysis procedure. Comparison between simulated and observed chemiluminescence spectra confirms that the vibrational population distribution of the A (2)A' state of HPCl is non-Boltzmann, as proposed by Baraille et al. [Chem. Phys. 289, 263 (2003)].

Franck-Condon simulation of the single vibronic level emission spectra of HSiF and DSiF including anharmonicity.

Potential energy functions (PEFs) of the X (1)A(') and A (1)A(") states of HSiF have been computed using the coupled-cluster single-double plus perturbative triple excitations and complete-active-space self-consistent-field multireference internally contracted configuration interaction methods, respectively, employing augmented correlation-consistent polarized-valence quadruple-zeta basis sets. For both electronic states of HSiF and DSiF, anharmonic vibrational wavefunctions and energies of all three modes have been calculated variationally with the ab initio PEFs and using Watson's Hamiltonian for nonlinear molecules. Franck-Condon factors between the two electronic states, allowing for Duschinsky rotation, were computed using the calculated anharmonic vibrational wavefunctions. These Franck-Condon factors were used to simulate the single vibronic level (SVL) emission spectra recently reported by Hostutler et al. in J. Chem. Phys. 114, 10728 (2001). Excellent agreement between the simulated and observed spectra was obtained for the A (1)A(")(1,0,0)-->X (1)A(') SVL emission of HSiF. Discrepancies between the simulated and observed spectra of the A (1)A(")(0,1,0) and (1,1,0) SVL emissions of HSiF have been found. These are most likely, partly due to experimental deficiencies and, partly to inadequacies in the ab initio levels of theory employed in the calculation of the PEFs. Based on the computed Franck-Condon factors, minor revisions of previous vibrational assignments are suggested. The calculated anharmonic wave functions of higher vibrational levels of the X (1)A(') state show strong mixings between the three vibrational modes of HSi stretching, bending, and SiF stretching.

Potential energy functions of the X̃ 2B1, Ã 2B2, B̃ 2A1, and C̃ 2A2 states of Cl2O+ and the X̃ 1A1 state of Cl2O: Franck–Condon simulations of photoelectron bands of Cl2O which include anharmonicity

Restricted-spin coupled-cluster single and double plus perturbative triple excitations [RCCSD (T)] and/or complete-active-space self-consistent-field multireference internally-contracted configuration interaction (CASSCF/MRCI) potential energy functions of the X̃ 2B1, à 2B2, B̃ 2A1, and C̃ 2A2 states of Cl2O+ and the X̃ 1A1 state of Cl2O, with basis sets of up to the augmented-correlation-consistent-polarized-valence-quadruple-zeta quality, have been reported. For each of these states, vibrational wave functions of the symmetric stretching and bending modes have been computed, employing the potential energy function obtained at the highest level of calculation, with Watson’s Hamiltonian and anharmonic vibrational wave functions expressed as linear combinations of harmonic basis functions. The helium I photoelectron spectrum of Cl2O has been simulated with Franck–Condon factors calculated using computed anharmonic vibrational wave functions and allowing for Duschinsky rotation. The adiabatic ionization energies (AIEs) to the four lowest cationic states of Cl2O+ have been evaluated at the RCCSD(T) level with basis sets of up to polarized-valence-quintuple-zeta quality and by various extrapolation techniques to the basis set limit. Revised equilibrium geometrical parameters of the X̃ 2B1 and C̃ 2A2 states of Cl2O+ were obtained from the iterative Franck–Condon analysis procedure, and revised AIEs for the à 2B2 and B̃ 2A1 states of Cl2O+ were estimated based on comparison between the simulated and observed photoelectron spectra. It was found that inclusion of anharmonicity in the Franck–Condon factor calculations for each electronic state improves the quality of the simulated spectrum. The computed T1 diagnostics from the RCCSD calculations suggest that the B̃ 2A1 state of Cl2O+, with the ⋯(9a1)1(3b2)2(10a1)0 electronic configuration, possesses multiconfigurational character in the region of r(ClO)=1.87 Å and θ(ClOCl)=125°. CASSCF/MRCI/aug-cc-pVQZ(no g) calculations show an avoided crossing between the B̃ 2A1 state and (2)2A1 state [with the ⋯(9a1)2(3b1)0(10a1)1 electronic configuration], in the region of 1.96&amp;gt;r&amp;gt;1.80 Å and 137.0&amp;gt;θ&amp;gt;132.0°.