Extension of accompanying coordinate expansion and recurrence relation method for general-contraction basis sets

2014 ◽  
Vol 35 (20) ◽  
pp. 1517-1527 ◽  
Author(s):  
Masao Hayami ◽  
Junji Seino ◽  
Hiromi Nakai
Keyword(s):  
Recurrence Relation ◽  
Basis Sets ◽  
General Contraction

PRACTICAL PERFORMANCE ASSESSMENT OF ACCOMPANYING COORDINATE EXPANSION RECURRENCE RELATION ALGORITHM FOR COMPUTATION OF ELECTRON REPULSION INTEGRALS

2005 ◽  
Vol 04 (01) ◽  
pp. 139-149 ◽  
Author(s):  
MICHIO KATOUDA ◽  
MASATO KOBAYASHI ◽  
HIROMI NAKAI ◽  
SHIGERU NAGASE
Keyword(s):  
Computer Program ◽  
Recurrence Relation ◽  
Basis Set ◽  
Basis Sets ◽  
Processing Unit ◽  
Central Processing ◽  
Cpu Time ◽  
Electron Repulsion ◽  
Electron Repulsion Integrals ◽  
Practical Performance

We have developed a computer program for evaluation of electron repulsion integrals (ERIs) based on the accompanying coordinate expansion recurrence relation (ACE-RR) algorithm, which has been recently developed as an efficient algorithm for computation of ERIs using Pople-type basis sets (STO-3G and 6-31G, for example) and derivatives of ERIs [Kobayashi and Nakai, J Chem Phys121:4050 2004]. The computer program can be linked to GAMESS ab initio quantum chemistry program. The practical performance of the ACE-RR method is assessed by means of the central processing unit (CPU) time for the first direct self-consistent field cycle on a model system (4 × 4 × 4 cubic hydrogen lattice), taxol ( C 47 H 51 NO 14), and valinomycin ( C 54 H 90 N 6 O 18) using Pople-type basis sets. The considerable efficiency of the present ACE-RR method is demonstrated by measuring the CPU time. The present ACE-RR method is comparable to or at most 30% faster than the Pople–Hehre method which is also designed for efficient computation of ERIs using Pople-type basis sets. Furthermore, the ACE-RR method is drastically faster than the Dupuis–Rys–King method in the case where the degree of contraction of Pople-type basis sets is high: 7.5 times faster in the case of valinomycin using STO-6G basis set, for example.

General contraction of Gaussian basis sets. I. Atomic natural orbitals for first‐ and second‐row atoms

1987 ◽  
Vol 86 (7) ◽  
pp. 4070-4077 ◽  
Author(s):  
Jan Almlöf ◽  
Peter R. Taylor
Keyword(s):  
Basis Sets ◽  
Gaussian Basis Sets ◽  
Natural Orbitals ◽  
General Contraction ◽  
Atomic Natural Orbitals

Sebuah Generalisasi Baru Barisan Fibonacci-Lucas

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Musraini M Musraini M ◽  
Rustam Efendi ◽  
Rolan Pane ◽  
Endang Lily
Keyword(s):  
Recurrence Relation ◽  
Initial Conditions ◽  
Lucas Sequence ◽  
Binet’S Formula

Barisan Fibonacci dan Lucas telah digeneralisasi dalam banyak cara, beberapa dengan mempertahankan kondisi awal, dan lainnya dengan mempertahankan relasi rekurensi. Makalah ini menyajikan sebuah generalisasi baru barisan Fibonacci-Lucas yang didefinisikan oleh relasi rekurensi B_n=B_(n-1)+B_(n-2),n≥2 , B_0=2b,B_1=s dengan b dan s bilangan bulat  tak negatif. Selanjutnya, beberapa identitas dihasilkan dan diturunkan menggunakan formula Binet dan metode sederhana lainnya. Juga dibahas beberapa identitas dalam bentuk determinan.   The Fibonacci and Lucas sequence has been generalized in many ways, some by preserving the initial conditions, and others by preserving the recurrence relation. In this paper, a new generalization of Fibonacci-Lucas sequence is introduced and defined by the recurrence relation B_n=B_(n-1)+B_(n-2),n≥2, with ,  B_0=2b,B_1=s                          where b and s are non negative integers. Further, some identities are generated and derived by Binet’s formula and other simple methods. Also some determinant identities are discussed.

Experimental and Theoretical (ab initio and DFT) Analysis of UV-Vis Spectra, Thermodynamic Functions and Non-linear Optical Properties of 2-Chloro-3,4-Dimethoxybenzaldehyde

2015 ◽  
Vol 8 (2) ◽  
pp. 2122-2134
Author(s):  
Sarvendra Kumar ◽  
Rajesh Kumar ◽  
Jayant Teotia ◽  
M. K. Yadav
Keyword(s):  
Thermodynamic Functions ◽  
Title Compound ◽  
Density Functional ◽  
Structural Characteristics ◽  
Basis Sets ◽  
Ultraviolet Absorption Spectrum ◽  
Non Linear ◽  
Different Temperatures ◽  
Linear Optical Properties ◽  
Linear Optical

In the present work, UV- Visible spectra of 2-Chloro-3,4-Dimethoxybenzaldehyde (2,3,4-CDMB) compound  have been carried out experimentally and theoretically. The ultraviolet absorption spectrum of title compound in three solvents (Acetone, Diethyl Ether, CCl4) of different polarity were examined in the range of 200–500 nm. The structure of the molecule was optimized and the structural characteristics were determined by HF and DFT (B3LYP) methods with 6-31+G(d,p) and 6-311++G(d,p) as basis sets. The excitation energy, wavelength corresponds to absorption maxima () and oscillator strength (f) are calculated by Time-Dependent Density Functional Theory (TD-DFT) using B3LYP/6-31+G(d,p) and B3LYP/6-311++G(d,p) as basis sets. The electric dipole moment (μ), polarizability (α) and the first hyperpolarizability (β ) have been computed to evaluate the non-linear optical (NLO) response of the investigated compound by HF and DFT (B3LYP) with already mentioned basis sets. Thermodynamic functions of the title compound at different temperatures were also calculated.

Electronic Structure Benchmark Calculations of Inorganic and Biochemical Carboxylation Reactions

2018 ◽  
Author(s):  
Oscar A. Douglas-Gallardo ◽  
David A. Sáez ◽  
Stefan Vogt-Geisse ◽  
Esteban Vöhringer-Martinez
Keyword(s):  
Electronic Structure ◽  
Chemical Reactions ◽  
Density Functional ◽  
Correlation Energy ◽  
Electronic Energy ◽  
Basis Sets ◽  
Electronic Correlation ◽  
Correct Description ◽  
Carbon Dioxide Co2 ◽  
High Level

<div><div><div><p>Carboxylation reactions represent a very special class of chemical reactions that is characterized by the presence of a carbon dioxide (CO2) molecule as reactive species within its global chemical equation. These reactions work as fundamental gear to accomplish the CO2 fixation and thus to build up more complex molecules through different technological and biochemical processes. In this context, a correct description of the CO2 electronic structure turns out to be crucial to study the chemical and electronic properties associated with this kind of reactions. Here, a sys- tematic study of CO2 electronic structure and its contribution to different carboxylation reaction electronic energies has been carried out by means of several high-level ab-initio post-Hartree Fock (post-HF) and Density Functional Theory (DFT) calculations for a set of biochemistry and inorganic systems. We have found that for a correct description of the CO2 electronic correlation energy it is necessary to include post-CCSD(T) contributions (beyond the gold standard). These high-order excitations are required to properly describe the interactions of the four π-electrons as- sociated with the two degenerated π-molecular orbitals of the CO2 molecule. Likewise, our results show that in some reactions it is possible to obtain accurate reaction electronic energy values with computationally less demanding methods when the error in the electronic correlation energy com- pensates between reactants and products. Furthermore, the provided post-HF reference values allowed to validate different DFT exchange-correlation functionals combined with different basis sets for chemical reactions that are relevant in biochemical CO2 fixing enzymes.</p></div></div></div>

A Systematic DFT Study of Two Elementary Steps Involving Hydrogen Peroxide and the Hydroxyl Radical in the Fenton Reaction

2018 ◽  
Author(s):  
Danilo Carmona ◽  
David Contreras ◽  
Oscar A. Douglas-Gallardo ◽  
Stefan Vogt-Geisse ◽  
Pablo Jaque ◽  
...  
Keyword(s):  
Hydrogen Peroxide ◽  
Hydroxyl Radical ◽  
Ab Initio ◽  
Fenton Reaction ◽  
Basis Set ◽  
Basis Sets ◽  
Dft Methods ◽  
Elementary Steps ◽  
Oxygen Oxygen ◽  
Complete Basis Set

The Fenton reaction plays a central role in many chemical and biological processes and has various applications as e.g. water remediation. The reaction consists of the iron-catalyzed homolytic cleavage of the oxygen-oxygen bond in the hydrogen peroxide molecule and the reduction of the hydroxyl radical. Here, we study these two elementary steps with high-level ab-initio calculations at the complete basis set limit and address the performance of different DFT methods following a specific classification based on the Jacob´s ladder in combination with various Pople's basis sets. Ab-initio calculations at the complete basis set limit are in agreement to experimental reference data and identified a significant contribution of the electron correlation energy to the bond dissociation energy (BDE) of the oxygen-oxygen bond in hydrogen peroxide and the electron affinity (EA) of the hydroxyl radical. The studied DFT methods were able to reproduce the ab-initio reference values, although no functional was particularly better for both reactions. The inclusion of HF exchange in the DFT functionals lead in most cases to larger deviations, which might be related to the poor description of the two reactions by the HF method. Considering the computational cost, DFT methods provide better BDE and EA values than HF and post--HF methods with an almost MP2 or CCSD level of accuracy. However, no systematic general prediction of the error based on the employed functional could be established and no systematic improvement with increasing the size in the Pople's basis set was found, although for BDE values certain systematic basis set dependence was observed. Moreover, the quality of the hydrogen peroxide, hydroxyl radical and hydroxyl anion structures obtained from these functionals was compared to experimental reference data. In general, bond lengths were well reproduced and the error in the angles were between one and two degrees with some systematic trend with the basis sets. From our results we conclude that DFT methods present a computationally less expensive alternative to describe the two elementary steps of the Fenton reaction. However, choice of approximated functionals and basis sets must be carefully done and the provided benchmark allows a systematic validation of the electronic structure method to be employed

Sign in / Sign up

Export Citation Format

Share Document