Hartree–Fock energy derivatives with respect to basis set exponents. Integral derivatives using Rys polynomials

1987 ◽  
Vol 87 (1) ◽  
pp. 514-519 ◽  
Author(s):  
Glauco Tonachini ◽  
H. Bernhard Schlegel
Keyword(s):  
Basis Set ◽  
Energy Derivatives ◽  
Hartree Fock

Analytic derivative theory based on the Hellmann–Feynman theorem

1992 ◽  
Vol 70 (2) ◽  
pp. 434-442 ◽  
Author(s):  
K. Hirao
Keyword(s):  
Present Theory ◽  
Basis Functions ◽  
Force Constants ◽  
Basis Set ◽  
Energy Derivatives ◽  
First Order ◽  
Hartree Fock ◽  
Derivative Method ◽  
Derivatives Of ◽  
Feynman Theorem

General formulae for the second, third, and fourth derivatives of the energy with respect to the nuclear coordinates of a molecule are derived from the Hellmann–Feynman theorem. Hurley's condition is used to obtain approximations to the first-order wavefunction, from which the second, third, and fourth energies can be obtained, leading to quadratic, cubic, and quartic force constants. The procedure is equivalent to minimizing the derivative energy by perturbed variation techniques. The expressions for these higher energy derivatives are much simpler than those of the direct analytic derivative method. The electrostatic calculation involves only one-electron integrals. The coupled Hartree–Fock equations to obtain the wavefunction derivatives become much simpler. The present theory provides a great conceptual simplification. However, the theory is correct only if the basis set is complete or basis functions are independent of the perturbation. Keywords: analytic derivative theory, Hellmann–Feynman theorem, force constants, the curvature theorem.

Ab initio predictions of the zero field splittings and the singlet–triplet transition strengths for the n → π* transition of selenoformaldehyde

1993 ◽  
Vol 71 (10) ◽  
pp. 1706-1712 ◽  
Author(s):  
D.C. Moule ◽  
L. Chantranupong ◽  
R.H. Judge ◽  
D.J. Clouthier
Keyword(s):  
Energy Levels ◽  
Random Phase ◽  
Open Shell ◽  
Oscillator Strengths ◽  
Basis Set ◽  
Zero Field ◽  
Zero Field Splitting ◽  
Hartree Fock ◽  
Lower Valence ◽  
Polarization Functions

The energy levels of the lower valence and Rydberg states of selenoformaldehyde, CH2Se, have been calculated by the SCF/CI method. Wavefunctions for the ROHF (restricted open shell Hartree–Fock) states were obtained with the Binnings–Curtis double-ζ basis set, augmented with Rydberg and polarization functions. Configuration interaction was applied to the parent configurations, PCMO (parent configuration molecular orbital). Oscillator strengths were evaluated for the allowed electric dipole transitions by the RPA (random phase approximation), and SOPPA (second-order polarization propagator approximation) methods. The spin-orbit contribution to the zero field splitting of the first triplet state, 3A2(n,π*) as well as the oscillator strengths to the three spin components were calculated by perturbation theory. These calculations predict that the Sx, Sy, and Sz components are shifted by −96.091,−96.707, and + 29.167 cm−1, respectively, from their unperturbed position. The oscillator strengths for the three components fx, fy, and fz of the 3A2(n,π*) ← 1A1(g.s.) transition were calculated to be 3.45 × 10−7, 1.15 × 10−7, and 173.0 × 10−7.

scholarly journals Optical Properties of Silver-Mediated DNA from Molecular Dynamics and Time Dependent Density Functional Theory

2018 ◽  
Vol 19 (8) ◽  
pp. 2346 ◽  
Author(s):  
Esko Makkonen ◽  
Patrick Rinke ◽  
Olga Lopez-Acevedo ◽  
Xi Chen
Keyword(s):  
Molecular Dynamics ◽  
Density Functional ◽  
Time Dependent ◽  
Basis Set ◽  
Dna Nanostructures ◽  
Exchange Correlation ◽  
Hartree Fock ◽  
Spurious Peak ◽  
20 Nm ◽  
Dependent Density

We report a combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics and time-dependent density functional (TDDFT) study of metal-mediated deoxyribonucleic acid (M-DNA) nanostructures. For the Ag + -mediated guanine tetramer, we found the maug-cc-pvdz basis set to be sufficient for calculating electronic circular dichroism (ECD) spectra. Our calculations further show that the B3LYP, CAM-B3LYP, B3LYP*, and PBE exchange-correlation functionals are all able to predict negative peaks in the measured ECD spectra within a 20 nm range. However, a spurious positive peak is present in the CAM-B3LYP ECD spectra. We trace the origins of this spurious peak and find that is likely due to the sensitivity of silver atoms to the amount of Hartree–Fock exchange in the exchange-correlation functional. Our presented approach provides guidance for future computational investigations of other Ag + -mediated DNA species.

Performance of small basis set Hartree–Fock methods for modeling non-covalent interactions

2021 ◽  
Vol 3 (3) ◽  
pp. 034007
Author(s):  
Viki Kumar Prasad ◽  
Alberto Otero-de-la-Roza ◽  
Gino A DiLabio
Keyword(s):  
Basis Set ◽  
Hartree Fock ◽  
Non Covalent Interactions ◽  
Covalent Interactions

ΚΒΑΝΤΟΜΗΧΑΝΙΚΟΙ ΥΠΟΛΟΓΙΣΜΟΙ ΤΩΝ ΗΛΕΚΤΡΙΚΩΝ ΠΟΛΩΣΙΜΟΤΗΤΩΝ ΚΑΙ ΥΠΕΡΠΟΛΩΣΙΜΟΤΗΤΩΝ ΜΕΡΙΚΩΝ ΟΡΓΑΝΙΚΩΝ ΜΟΡΙΩΝ ΚΑΙ ΑΝΙΟΝΤΩΝ

1984 ◽  
Author(s):  
John Waite
Keyword(s):  
Basis Set ◽  
Hartree Fock

ΠΑΡΟΥΣΙΑΖΕΤΑΙ ΜΙΑ ΜΕΘΟΔΟΣ ΓΙΑ ΤΟΝ ΥΠΟΛΟΓΙΣΜΟ ΤΗΣ ΜΕΣΗΣ ΗΛΕΚΤΡΙΚΗΣ ΠΟΛΩΣΙΜΟΤΗΤΑΣΑ, ΚΑΙ ΤΩΝ ΥΠΕΡΠΟΛΩΣΙΜΟΤΗΤΩΝ Β ΚΑΙ Γ ΟΡΓΑΝΙΚΩΝ ΜΟΡΙΩΝ. Η ΜΕΘΟΔΟΣ ΑΥΤΗ ΣΤΗΡΙΖΕΤΑΙ ΣΕ ΜΙΑ ΗΜΙΕΜΠΕΙΡΙΚΗ ΚΥΜΑΤΟΣΥΝΑΡΤΗΣΗ (CNDO), Η ΟΠΟΙΑ ΠΡΟΣΔΙΟΡΙΖΕΤΑΙ ΜΕ ΤΗΝ ΒΟΗΘΕΙΑ ΜΙΑΣ ΜΙΚΡΗΣ ΒΑΣΗΣ (BASIS SET) ΠΡΟΣΕΚΤΙΚΑ ΕΠΙΛΕΓΜΕΝΗΣ. Η ΚΥΜΑΤΟΣΥΝΑΡΤΗΣΗ ΔΙΑΤΑΡΑΣΣΕΤΑΙ ΚΑΤΑ ΤΟΝ ΤΡΟΠΟ ΠΟΥ ΟΡΙΖΕΙ Η ΘΕΩΡΙΑ COUPLED HARTREE- FOCK. Η ΘΕΩΡΙΑ ΧΡΗΣΙΜΟΠΟΙΗΘΗΚΕ ΚΑΤΑ ΤΗΝ ΜΟΡΦΗ ΠΟΥ ΠΡΟΤΑΘΗΚΕ ΑΠΟ ΤΟΝ MCWEENY ΚΑΙ ΤΟΥΣ ΣΥΝΕΡΓΑΤΕΣ ΤΟΥ. Η ΣΥΓΚΕΚΡΙΜΕΝΗ ΤΕΧΝΙΚΗ ΥΠΟΛΟΓΙΣΜΟΥ ΤΩΝ Α,Β ΚΑΙ Γ ΔΙΑΜΟΡΦΩΘΗΚΕ ΥΣΤΕΡΑ ΑΠΟ ΜΕΛΕΤΗ ΠΟΛΛΩΝ ΕΝΑΛΛΑΚΤΙΚΩΝ ΛΥΣΕΩΝ. (ΠΕΡΙΚΟΠΗ)

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