988 research outputs found
Franck-Condon simulation of the single-vibronic-level emission spectra of HPCI/DPCl and the chemiluminescence spectrum of HPCI, including anharmonicity
No full textRestricted-spin coupled-cluster single-double plus perturbative triple excitation [RCCSD(T)] potential energy functions (PEFs) were calculated for the (X) over tilde (2)A" and (A) over tilde (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) over tilde (2)A'-(X) over tilde (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) over tilde (2)A' state of HPCl of r(e)(PCI)=2.0035 +/- 0.0015 Angstrom, theta(e) = 116.08 +/- 0.60degrees, and r(e)(HP) = 1.4063 +/- 0.0015 Angstrom via the iterative Franck-Condon analysis procedure. Comparison between simulated and observed chemiluminescence spectra confirms that the vibrational population distribution of the (A) over tilde (2)A' state-of HPCl is non-Boltzmann, as proposed by Baraille, et al. [Chem. Phy. 289, 263 (2003)]
An SGBM-XVA demonstrator: a scalable Python tool for pricing XVA
No full textIn this work, we developed a Python demonstrator for pricing total valuation adjustment (XVA) based on the stochastic grid bundling method (SGBM). XVA is an advanced risk management concept which became relevant after the recent financial crisis. This work is a follow-up work on Chau and Oosterlee in (Int J Comput Math 96(11):2272–2301, 2019), in which we extended SGBM to numerically solving backward stochastic differential equations (BSDEs). The motivation for this work is basically two-fold. On the application side, by focusing on a particular financial application of BSDEs, we can show the potential of using SGBM on a real-world risk management problem. On the implementation side, we explore the potential of developing a simple yet highly efficient code with SGBM by incorporating CUDA Python into our program.Numerical Analysi
The singlet-triplet separation in CF2: state-of-the-art ab initio calculations and Franck-Condon simulations including anharmonicity
No full textGeometrical parameters, vibrational frequencies and relative electronic energies of the X(2)B(1) state of CF(2) (-) and the X(1)A(1) and a(3)B(1) states of CF(2) 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 X(2)B(1) state of CF(2) (-) and the X(1)A(1) and a(3)B(1) states of CF(2) 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 a-X emission spectrum of CF(2) determined by S. Koda [Chem. Phys. Lett. 1978, 55, 353] and the 364 nm laser photodetachment spectrum of CF(2) (-) 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 CF(2)(X(1)A(1))+e?CF(2) (-)(X(2)B(1)) and CF(2)(a(3)B(1))+e?CF(2) (-)(X(2)B(1)) bands in the photoelectron spectrum of CF(2) (-) and a reliable singlet-triplet gap for CF(2). It is therefore concluded that the same theoretical approach should give reliable simulated CCl(2)(X(1)A(1))+e?CCl(2) (-)(X(2)B(1)) and CCl(2)(a(3)B(1))+e?CCl(2) (-)(X(2)B(1)) bands in the photodetachment spectrum of CCl(2) (-) and a reliable singlet-triplet gap for CCl(2)
Ab initio calculations on PO2 and anharmonic Franck-Condon simulations of its single-vibrational-level emission spectra
No full textGeometry optimisation and harmonic vibrational frequency calculations were carried out on some low-lying electronic states Of PO2 at the CIS, CASSCF, MP2, and RCCSD(T) levels with various standard basis sets of at least valence triple-zeta quality. Relative electronic energies, including vertical excitation energies from the (X) over tilde (2)A(1) state {with the electronic configuration of... (7a(1))(2)(8a(1))(1)} and T-e values, were computed at the RCCSD(T) and CASSCF/MRCI levels with basis sets of up to aug-cc-pVQZ quality. These computed results, particularly the computed T, values, suggest that the upper electronic state of the laser induced fluorescence (LIF) and single-vibrational-level (SVL) emission spectra Of PO2 reported recently by Lei et al. [J. Phys. Chem. A 2001, 165, 7828] is the 2(2)A(1) state Of PO2 {with the electronic configuration of... (7a(1))(1)(8a(1))(2)}. RCCSD(T)/ aug-cc-pVQZ and CASSCF/MRCI/aug-cc-pVQZ(no g) energy scans were carried out on the (X) over tilde (2)A(1) and 2(2)A(1) states Of PO2, respectively, in the symmetric stretching and bending coordinates. Franck-Condon factors (FCFs) between the two states, which allow for the Duschinsky and anharmonic effects, were calculated employing the potential energy functions obtained from the,ab initio scans. Comparison between the simulated spectra based on the computed FCFs and observed SVL emission spectra led to reassignments of the vibrational designations of the emitting SVLs in the upper state. On the basis of the excellent agreement between the simulated spectra for the revised SVLs and the observed emission spectra, the electronic transition involved in the LIF and SVL emission spectra reported by Lei et al. is confirmed to be 2(2)A(2)-(X) over tildeA(1) of PO2. Following the revised vibrational assignments of the upper electronic state in the SVL emissions, the vibrational assignments of the LIF excitation bands given by Lei et al. are revised and a revised To value of 30660 cm(-1) is estimated for the 2(2)A(1) state of PO2. In addition, employing the iterative Franck-Condon analysis (IFCA) procedure in the simulation of the SVL emission spectra, the equilibrium geometry of the 2(2)A(1) state of PO2 is derived for the first time (r(e) = 1.560 Å; ?(e) = 116.5°)
A combined ab initio and Franck-Condon factor simulation study on the photdetachmnent spectrumn of the HfO2 anion
No full textRestricted-spin coupled-cluster single-double plus perturbative triple excitation {RCCSD(T)} potential energy functions (PEFs) of the X̃ 1A1 state of HfO2 and the X̃ 2A1 state of HfO2 - were computed, employing the quasi-relativistic effective core potential, ECP60MWB, and an associated contracted [13s6p6d4f3g2h] basis set designed for Hf, and the augmented correlation-consistent polarized valence quadruple-zeta (aug-cc-pVQZ) basis set for O. Based on the differences between the computed r0 and re geometrical parameters obtained from the PEF, and available experimentally derived r0 geometrical parameters of the X̃ 1A1 state of HfO2, the experimental r e geometrical parameters of the X̃ 1A1 state of HfO2 were estimated as:-re(HfO) = 1.7751 Å and θe(OHfO) = 107.37°. In addition, Franck-Condon factors for the HfO2 (X̃ 1A1) + e ← HfO 2 - (X̃ 2A1) electron detachment process, which include allowance for Duschinsky rotation and anharmonicity, were calculated using the computed RCCSD(T) PEFs, and were used to simulate the HfO2 (X̃ 1A1) + e← HfO 2 - (X̃ 2A1) photodetachment band of HfO2 -. Employing the estimated experimental r e geometrical parameters of the X̃ 1A1 state of HfO2 obtained in this work, the iterative Franck-Condon analysis (IFCA) procedure was carried out to optimize the geometrical parameters of the X̃ 2A1 state of HfO2 - until the simulated spectrum matched best with the experimental 355 nm photodetachment spectrum of W. Zheng, et. al., J. Phys. Chem. A, 1998, 102, 9129. The equilibrium geometrical parameters of X̃ 2A 1 state of HfO2 - derived via the IFCA procedure are re(HfO) = 1.823 Å and θe(OHfO) = 111.5°. Further calculations on low-lying triplet states of HfO2 gave adiabatic electronic energies (Te's) of, and vertical excitation energies (Tvert's) to, the ã 3B2, b̃ 3B1, c̃ 3A1 and d̃ 3A2 states of HfO2 (from the X̃ 1A1 state of HfO2), as well as electron affinities (EAs) and vertical detachment energies (VDEs) to these neutral states from the X̃ 2A1 state of HfO2 -.Department of Applied Biology and Chemical Technolog
A combined ab initio and Franck-Condon simulation study of the photodetachment spectrum of ZrO2
No full textRCCSD(T) potential energy functions (PEFs) of the state of ZrO2 and the state of 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 . 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 . Excellent agreement between the simulated and observed spectra is obtained, confirming the reliability of the PEFs used
An ab initio study of the low-lying electronic states of YO2 and Franck-Condon simulation of the first photodetachment band of YO2
No full textA variety of density functional theory and ab initio methods, including B3LYP, B98, BP86, CASSCF, CASSCF/RS2, CASSCF/MRCI, BD, BD(T), and CCSD(T), with ECP basis sets of up to the quintuple-zeta quality for Y, have been employed to study the X?2B2 state of YO2 and the X?1A1 state of YO2?. Providing that the Y 4s24p6 outer-core electrons are included in the correlation treatment, the RCCSD(T) method gives the most consistent results and is concluded to be the most reliable and practical computational method for YO2 and YO2?. In addition, RCCSD(T) potential energy functions (PEFs) of the X?2B2 state of YO2 and the X?1A1 state of YO2? were computed, employing the ECP28MDF_aug-cc-pwCVTZ and aug-cc-pVTZ basis sets for Y and O, respectively. Franck?Condon factors, which include allowance for Duschinsky rotation and anharmonicity, were calculated using the computed RCCSD(T) PEFs and were used to simulate the first photodetachment band of YO2?. The simulated spectrum matches very well with the corresponding experimental 355 nm photodetachment spectrum of Wu, H.; Wang, L.-S. J. Phys. Chem. A 1998, 102, 9129, confirming the reliability of the RCCSD(T) PEFs used. Further calculations on low-lying electronic states of YO2 gave Te's and Tvert's of the A?2A1, B?2B1, and C?2A2 states of YO2, as well as EAs and VDEs to these states from the X?1A1 state of YO2?. On the basis of the ab initio VDEs obtained in the present study, previous assignments of the second and third photodetachment bands of YO2? have been revised
A combined ab initio/Franck-Condon study of the Ã-X single-vibronic-level emission spectrum of CCl<sub>2</sub> and the photodetachment spectrum of CCl
No full textState-of-the-art ab initio calculations have been carried out on the X1A1, a3B1 and A1B1 states of CCl2 and the (XB1)-B-2 state of CCl2-. Franck-Condon factors including anharmonicity have been calculated, between the CCl2 states, and between the CCl2- X2B1 state and the CCl2 states. They are used to simulate the A-X single-vibronic-level (SVL) emission spectra of CCl2 determined by MA. Lui et a]. [PCCP 2003, 5, 352] and the 364 nm laser photo detachment spectrum of CCl2- obtained by R. L. Schwartz et al. [J. Phys. Chem. A 7999, 103, 8213]. Comparison between simulated and observed spectra confirms the vibrational assignments of the X2B1 SVL emission spectra and the T0 position of the A(1)B1 state of CCl2. For the photodetachment spectrum of CCl2-, spectral simulation shows that the higher binding energy 6 3 B, (CCl2) CCl2-X2B1 detachment process. Further ab initio calculations carried out in the present investigation support the suggestion that the second band in the 364 nm photodetachment spectrum of CCl2- is due to detachment from an excited state of CCl2-, a linear quartet state, to a triplet state of CC12. These calculations identify the anionic state to be the lowest (4)Sigma(g)(-) ((4)Sigma(-)) state, which photodetaches vertically to the (3)Sigma(g)(-) ((3)Sigma(-); adiabatically a3B1 and/or (3)Pi(u) ((3)Pi) states of CCl2 to give the second band observed in the 364 nm photodetachment spectrum of CCl2-
Ab initio calculations on the (A)over-tilde(1)Pi and (X)over-tilde(1)Sigma(+) states of AlNC and simulation of the AlNC (A)over-tilde (1)Pi-(X)over-tilde(1)Sigma(+) emission spectra
No full textGeometry optimization and harmonic vibrational frequencies calculations were carried out on the (A) over tilde (1)Pi and (X) over tilde states of AlNC, employing a variety of ab initio molecular orbital methods, including the SERHF, CIS, MP2, and QCISD methods, with basis sets up to the size of the cc-pVQZ basis set. In addition, single-point energy calculations at the CCSD(T) and CASSCF/MRCI levels were performed to determine the transition energy (T,) between the two electronic states. Franck-Condon calculations were carried out for the (A) over tilde (1)Pi- (X) over tilde (1)Sigma +SVL emission, with the geometry of the ground state being fixed to the available experimental geometry. The best match between the simulated and observed spectra gave the first experimentally derived geometry of the (A) over tilde (1)Pi state (Al-N = 1.785 +/- 0.005 Angstrom and N-C = 1.150 +/- 0.008 Angstrom)
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