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

Friese, Daniel H.; Ringholm, Magnus; Gao, Bin; Ruud, Kenneth

doi:10.1021/acs.jctc.5b00646

Cited by 6 publications

(8 citation statements)

References 67 publications

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“…Recently, Ringholm et al presented an approach involving recursion for the open‐ended calculation of response properties based on the density matrix‐based quasi‐energy formulation of the Kohn‐Sham density functional response theory using perturbation‐ and time‐dependent basis sets of Thorvaldsen et al This approach was extended by Friese et al to enable the calculation of single residues of response functions . Very recently, this approach has furthermore been extended to include molecular environment effects by the polarizable embedding model …”

Section: Introductionmentioning

confidence: 99%

Accelerating Kohn‐Sham response theory using density fitting and the auxiliary‐density‐matrix method

Kumar

Fliegl

Jensen

et al. 2018

Int J of Quantum Chemistry

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An extension of the formulation of the atomic-orbital-based response theory of Larsen et al., JCP 113, 8909 (2000) is presented. This new framework has been implemented in LSDalton and allows for the use of Kohn-Sham density-functional theory with approximate treatment of the Coulomb and Exchange contributions to the response equations via the popular resolution-of-the-identity approximation as well as the auxiliary-density matrix method (ADMM). We present benchmark calculations of ground-state energies as well as the linear and quadratic response properties: vertical excitation energies, polarizabilities, and hyperpolarizabilities. The quality of these approximations in a range of basis sets is assessed against reference calculations in a large aug-pcseg-4 basis. Our results confirm that density fitting of the Coulomb contribution can be used without hesitation for all the studied properties. The ADMM treatment of exchange is shown to yield high accuracy for ground-state and excitation energies, whereas for polarizabilities and hyperpolarizabilities the performance gain comes at a cost of accuracy. Excitation energies of a tetrameric model consisting of units of the P700 special pigment of photosystem I have been studied to demonstrate the applicability of the code for a large system. K E Y W O R D S ADMM, density fitting, Kohn-Sham DFT response theory, RI | I N TR ODU C TI ONIn molecular electronic-structure theory, an essential step is the evaluation of two-electron integrals over one-electron basis functions. The explicit evaluation of these integrals comes at a high computational cost, and from the dawn of quantum chemistry, approximations have been introduced both to speed up molecular calculations and to reduce memory requirements. [1] Such approximate methods have been widely developed for the calculation of energies and gradients, but less attention has been given to developing these methods for the calculation of molecular properties.The most widely used approach to approximate the Coulomb and exchange integrals is density fitting, also known as the resolution-of-theidentity (RI) approximation. In this approximation products of two one-electron basis functions are expanded in one-center auxiliary functions, and thus, the evaluation of four-center two-electron integrals is replaced by the evaluation of two-and three-center two-electron integrals and the solution of a set of linear equations. RI significantly improves performance with a limited impact on the accuracy and has therefore been applied to Hartree-Fock (HF)/Kohn-Sham (KS) theory, as well as correlated methods. [22][23][24][25][26][27] An important alternative approach is the Cholesky-decomposition (CD) technique [28][29][30][31][32] which to a large extent can be thought of as a special kind of density fitting where the auxiliary basis functions are obtained from the set of products between two one-electron basis functions through Cholesky-decomposition.Combined with J-engine techniques [33][34][35] RI gives tremendous speed-ups [8,9] for C...

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Section: Introductionmentioning

confidence: 99%

Accelerating Kohn‐Sham response theory using density fitting and the auxiliary‐density‐matrix method

Kumar

Fliegl

Jensen

et al. 2018

Int J of Quantum Chemistry

View full text Add to dashboard Cite

show abstract

“…[52][53][54][55] We recently extended our open-ended recursive response theory code for transition moments to the inclusion of London orbitals also for higher-order transition moments. 56 With this technique, calculations in the length gauge become origin independent also in case of an incomplete basis set. A reformulation of the 3PCD rotatory strength to a length-gauge formulation can be performed by formulating so-called equivalent expressions for the dipole moment operator following Olsen and Jørgensen.…”

Section: Length-gauge Based Approaches To 3pcdmentioning

confidence: 99%

“…57 Calculations using London orbitals have been carried out using a recently developed recursive open-ended response theory code. 28,56,58 All computational capabilities have already been available and the codes were just modified slightly for the ease of input and evaluation. Calculations have been carried out using the Hartree-Fock method as well as the B3LYP 59 and CAM-B3LYP 60 density functionals.…”

Section: Calculationsmentioning

confidence: 99%

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

Friese

Ruud

2016

Phys. Chem. Chem. Phys.

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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.

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“…25 Very recently, a GIAO-based treatment of TPCD for SCF-based theory has also been realized by one of us. 40 In the following we will adapt the velocity-gauge based approach to the requirements of coupled cluster theory.…”

Section: Introductionmentioning

confidence: 99%

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

Friese

Hättig

Rizzo

2016

Phys. Chem. Chem. Phys.

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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.

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

Cited by 6 publications

References 67 publications

Accelerating Kohn‐Sham response theory using density fitting and the auxiliary‐density‐matrix method

Accelerating Kohn‐Sham response theory using density fitting and the auxiliary‐density‐matrix method

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

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

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