Note: Derivation of two-photon circular dichroism—Addendum to “Two-photon circular dichroism” [J. Chem. Phys. <b>62</b>, 1006 (1975)]

Phys. Chem. Chem. Phys.

Ruud

2016

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We present the theory of three-photon circular dichroism (3PCD), a novel non-linear chiroptical property not yet described in the literature. We derive the observable absorption cross section including the orientational average of the necessary seventh-rank tensors and provide origin-independent expressions for 3PCD using either a velocity-gauge treatment of the electric dipole operator or a length-gauge formulation using London atomic orbitals. We present the first numerical results for hydrogen peroxide, 3-methylcyclopentanone (MCP) and 4-helicene, including also a study of the origin dependence and basis set convergence of 3PCD. We find that for the 3PCD-brightest low-lying Rydberg state of hydrogen peroxide, the dichroism is extremely basis set dependent, with basis set convergence not being reached before a sextuple-zeta basis is used, whereas for the MCP and 4-helicene molecules, the basis set dependence is more moderate and at the triple-zeta level the 3PCD contributions are more or less converged irrespective of whether the considered states are Rydberg states or not. The character of the 3PCD-brightest states in MCP is characterized by a fairly large charge-transfer character from the carbonyl group to the ring system. In general, the quadrupole contributions to 3PCD are found to be very small.

Section: Theory Of 3-photon Circular Dichroismmentioning

confidence: 96%

Three-photon circular dichroism: towards a generalization of chiroptical non-linear light absorption

Phys. Chem. Chem. Phys.

Ruud

2016

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“…25 Just recently the theory by Tinoco has been discussed in more detail by one of us. 42 As all properties that involve the magnetic dipole and electric quadrupole operators TPCD also suffers in the length gauge formulation from the problem of origin dependence which occurs as long as the calculations are not carried out in a complete one-electron basis set. 25 In CC theory also an untruncated cluster operator would be needed.…”

Section: Theorymentioning

confidence: 99%

Origin-independent two-photon circular dichroism calculations in coupled cluster theory

Phys. Chem. Chem. Phys.

Hättig

Rizzo

2016

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We present the first origin-independent approach for the treatment of two-photon circular dichroism (TPCD) using coupled cluster methods. The approach is assessed concerning its behavior on the choice of the basis set and different coupled cluster methods. We also provide a comparison of results from CC2 with those from density functional theory using the CAM-B3LYP functional. Concerning the basis set we note that in most cases an augmented triple zeta basis or a doubly augmented double zeta basis is needed for reasonably converged results. In the comparison of different coupled cluster methods results from CCSD, CC3 and CC2 have been found to be quite similar in most cases, while CCS results differ remarkably from the results at the higher levels. However, this proof-of-principle study also shows that further benchmarking of DFT and CC2 against accurate coupled cluster reference values (e.g. CCSD or CC3) is needed.

“…The rotatory strength is obtained from ,, where b 1 , b 2 , and b 3 are coefficients depending on the propagation direction and polarization of the incident photons. In this study, we investigate TPCD as a difference between the absorption cross-sections for two left and two right circularly polarized photons propagating parallel to each other and orthogonal to the polarization plane, and for this setup, b 1 =6, b 2 =2, and b 3 =−2. , The three transition strength contributions are defined as where M p ,0 q and P 0 q are the electric dipole–magnetic dipole transition moment tensor and the electric dipole–electric dipole transition moment tensor, respectively, with the electric dipole operator expressed in velocity gauge.…”

Section: Computational Detailsmentioning

confidence: 99%

Open-Ended Recursive Calculation of Single Residues of Response Functions for Perturbation-Dependent Basis Sets

J. Chem. Theory Comput.

Ringholm

Gao

et al. 2015

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We present theory, implementation and applications of a recursive scheme for the calculation of single residues of response functions which can treat perturbations that affect the basis set. This scheme enables the calculation of non-linear light absorption properties to arbitrary order for other perturbations than the electric field. We apply this scheme for the first treatment of two-photon circular dichroism (TPCD) using London orbitals at the Hartree-Fock level of theory. In general TPCD calculations suffer from the problem of origin dependence which has so far been solved by using the velocity gauge for the electric dipole operator. This work now enables comparison of results from London orbital and velocity gauge based TPCD calculations. We find that the results from the two approaches both exhibit strong basis set dependence but that they are very similar with respect to their basis set convergence.