phymath999: HARTREE–FOCK (HF) Computing thermodynamical quantities such as ΔrHΘ, ΔrGΘ, and ΔrSΘ is one of the first steps a theoretical , Binding Energy of

Friday, May 15, 2015

HARTREE–FOCK (HF) Computing thermodynamical quantities such as ΔrHΘ, ΔrGΘ, and ΔrSΘ is one of the first steps a theoretical , Binding Energy of

[PDF]HARTREE–FOCK (HF) METHOD AND DENSITY ...

ajse.kfupm.edu.sa/articles/292A_05P.pdf

Table 1. Binding Energies of Methanol At Different Basis Sets
No. Basis Set Binding Energy of Methanol (kJ/mol)
1 6-31g –114.0
2 6-31g(d) –115.0
3 d95(d,p) –115.1
4 6-311g(d,p). –115.1
One can see (Table 1) that, as the size of the basis set increases, the binding energy of methanol also increases. But
in general the value does not change dramatically. So, we can take any basis set without compromising quality.
After that, the following thermodynamic quantities were calculated: ΔrHΘ (kJ/mol) ΔrGΘ (kJ/mol) and
ΔrSΘ(J/mol/K). The calculations were performed at the following levels of theory. RHF/3-21g, RHF/6-31g and
DFT/B3LYP/d95**. To calculate these quantities, the thermodynamical quantity of the reactant (methanol) is subtracted
from that of the product (dimethylether) (reaction 1). The experimental value is calculated in the same way, but using
heat of formation

Calculations at restricted Hartree–Fock levels (RHF/3-21g and RHF/6-31g) were performed since they are not as
expensive as other levels (DFT/B3LYP/d95**). In the case of the HF method, working with larger basis set (6-31g) has
improved the values slightly, which is as expected. It is noticed that performing calculations at higher levels
(DFT/B3LYP/d95**) than Hartree–Fock does not dramatically improve the situation, which is contrary to what is
normally expected. For many cases, RHF is a reasonable approximation for single gas phase molecule calculations.
From this, one may safely suggest that finding theoretical thermodynamical quantities does not require expensive
methods such as DFT. Hartree–Fock at relatively small basis sets is adequate. Definitely, DFT is dominating the field
of molecular computational studies for well known reasons. It is only in limited cases like this one that DFT shows no
appreciable advantage. The most obvious explanation for our results has to do with the small size of the studied
molecules.
Again, we thought that the geometry would suffer at RHF/3-21g and RHF/6-31g. However, we observed that this is
not the case (Table 3). For instance in the case of methanol, the O–H and CH3–O bond distances are very close to the
experimental values [13]. However, one can see a slight improvement upon going from RHF/3-21g to RHF/6-31g, a
natural outcome of the increase of the basis set.

3.2 Vibrational Infrared Spectra
Obtaining the experimental IR and Raman spectra for DME is not very convenient since it requires a special gas
cell. Thus, we wanted to see what kind of spectra can be obtained using theoretical techniques. In the literature, one can
find some ab initio studies on DME, but such works [14,15] were limited to only certain portions of the spectra or did not
employ the DFT method, but rather the Hartree–Fock method. The vibrational data were calculated at DFT-B3LYP/6-
311+G** level.
The results are summarized in Tables 4–7. The percent error between the experimental frequencies and theoretical
ones is indeed small, except for the CH3 stretching where it is a little higher. This is always the case with such type of
modes. One can also see that indeed there is excellent correlation (especially in the case of methanol) between the
experimental descriptions of the bands in terms of their strength with the calculated ones. With Raman studies, things
become more complicated. Many experimental Raman frequencies are missing due to a combination

CONCLUSION
Computer simulation studies find their applications in many fields including finding thermodynamical quantities
and spectroscopic parameters. In this paper, we calculated thermodynamical parameters (ΔrHΘ, ΔrGΘ, ΔrSΘ) of the MTG
reaction using different theoretical methods at different computational levels. We have also calculated the vibrational
spectra of methanol and dimethylether. We have noticed that performing calculations at higher levels
(DFT/B3LYP/d95**) than Hartree–Fock method does not dramatically improve the situation. Indeed, RHF is a
reasonable approximation for many single gas phase molecule calculations. HF calculations using relatively small basis

by ZS Seddigi - ‎2004 - ‎Cited by 1 - ‎Related articles

HF calculations at relatively small basis sets are adequate. The theoretical ... experimental results. Keywords: MTG; Hartree–Fock; DFT, vibrational spectra.

"1. INTRODUCTION
The methanol-to-gasoline (MTG) process was discovered by accident by researchers at the Mobil Company. This
process provides an alternative to crude oil as a source for gasoline. The process employs a highly selective zeolite
(ZSM-5) catalyst and leads to the synthesis of high-octane gasoline without the need for costly after-production
processing. The process leads to the production of dimethylether, which under the right reaction conditions produces
olefins and eventually paraffins and aromatics. We know that the mixture of these last two is called gasoline.
The MTG [1] process in medium pore-sized aluminosilicate zeolites has been the subject of great theoretical [2–5]
and experimental [1, 6, 7] interest due to its potential industrial importance. Despite this importance, this reaction is not
well understood. The first step in this reaction is believed to be the reaction of two methanol molecules over a suitable
acidic zeolite to give dimethylether and one water molecule:
2CH3OH CH3OCH3 + H2O. (1)
Computing thermodynamical quantities such as ΔrHΘ, ΔrGΘ, and ΔrSΘ is one of the first steps a theoretical or
computational chemist is interested in, since that will help in selecting the appropriate level of theory. Indeed, referencequality
data for thermophysical parameters are a very topical subject. Many studies have been performed to determine
thermodynamical quantities using theoretical methods [8,9]. Both experimental contributions and contributions
describing correlations and modeling are desired.
Hartree–Fock is the most basic ab initio molecular orbital approach. Density functional theory (DFT) is an
approach to the electronic structure of atoms and molecules and states that all the ground-state properties of a system are
function of the charge density. So, DFT calculations cannot be considered a pure ab initio method. In DFT, the electron
density is the basic variable, instead of the wave function. This reduces the computational burden of treating electron–
electron interaction terms, which are treated explicitly as a functional of the density. The DFT approach combines the
capacity to incorporate exchange-correlation effects of electrons with reasonable computational costs and high accuracy.
The past few years has seen a rapid increase in the use of DFT methods"

[PPT]内层电子的结合能增加

202.38.64.11/~mams/escalab/ES-3.pps 轉為繁體網頁

电子的结合能(EB)代表了原子中电子(n,l,s)与核电荷(Z)之间的相互作用强度，可用XPS直接实验 ... 它可用非相对论的Hartree-Fock自洽场(HF-SCF)方法计算出来。

[PDF]萘分子最高占据轨道和次最高占据轨道的电子动量 ... - 中国科学

phys.scichina.com:8083/sciG/.../downloadArticleFile.do?... 轉為繁體網頁

1500 eV 加结合能. 通过Hartree-Fock 和密度泛函方法计算得到了萘分子1au 和2b3u 轨道的动量谱, 理论与实 ... 和成熟手段, 它不仅能获取原子和分子轨道结合能,.

hartree-fock 的翻译结果--cnki翻译助手

dict.cnki.net/h_50756847000.html 轉為繁體網頁

hartree-fock 的翻译结果：hartree-fock理论;hartreefock方法;hartree-fock方法||双语例句| ... 本文用Hartree-Fock方法计算了Λ超核_Λ~5He与_Λ~9Be的Λ的结合能及粲Λ(Λ_c) ... with Hartree-Fock (HF) and density functional theory (DFT) calculations.

哈特里－福克方程- 維基百科，自由的百科全書 - Wikipedia

zh.wikipedia.org/zh-hk/哈特里－福克方程

哈特里—福克方程式，又稱為HF方程，是一個應用變分法計算多電子系統波函數的方程式， .... 這個方程形式上具有一般本徵方程的形式，可以近似求解，是Hartree-Fock自洽場方法、 ... 矩陣後，將這些係數與基函數結合代入 \psi_a=\sum_i c_{ia}\phi_i ...

Hartree-Fock,Hartree-Fock,在线英语词典,英文翻译,专业英语

www.dictall.com/indu/005/004515264FF.htm 轉為繁體網頁

利用高斯98中的Hartree-Fock(HF)方法研究了OH-与Si(100)面的吸附和脱附作用 ... 然后用DFTPBE方法,选取6-311++G(3d,3p)基组对复合物的结合能进行计算,结果 ...

[PDF]物理化学学报 - Acta Phys Chim Sin 2015, Vol.31 No.4

www.whxb.pku.edu.cn/EN/.../downloadArticleFile.do?... 轉為繁體網頁

到目前为止, 运用光电子谱学方法)已对饱和烷烃的价壳层结合能谱进行了广泛的研究[3],. 但是用e, 2e ... 能谱数-, 以及.用/0性Hartree-Fock HF( )方法和密度泛函.

环己烯分子2b和3a轨道的电子动量谱学研究 - 中国科学技术大学

cjcp.ustc.edu.cn/hxwlxb_cn/ch/.../view_abstract.aspx?file... 轉為繁體網頁

由任雪光著作 - ‎相關文章

通过Hartree-Fock和密度泛函方法计算得到了C6H10分子2b和3a轨道的动量谱，在动量 ... orbitals was compared with Hartree Fock (HF) and density functional theory ... 下的能量多道型电子动量谱仪下完成，入射电子的能量为1200 eV加结合能．

[PDF]传统氢键(X—H…Y)还是X—H…π 相互作用？ - 上海有机化学 ...

sioc-journal.cn/Jwk_hxxb/.../downloadArticleFile.do?... 轉為繁體網頁

由梁雪著作 - ‎2008 - ‎被引用 3 次 - ‎相關文章

C6H6 弱(结合能数值相差4 kJ/mol 左右). 对称匹配微扰 .... 其中HF int. E 表示超分子的Hartree-Fock 水平相互作用能,. 表示为: HF. (10). (10). (20). (20). HF int.

[PDF]从原子到大分子体系的计算机模拟———计算化学50 年

homepage.hit.edu.cn/.../从原子到大分子体系的计算机模... 轉為繁體網頁

由 E Clementi 著作 - ‎2011 - ‎相關文章

用Hartree-Fock-Heitler-London （ HF-HL）对从双原子分子到小的多原子分子进行计算所得的结果，与用传统 ...... ΨHL 和ΨHF-HL 模型的计算结合能分别是：－ 29.

高能材料分子动力学_百度百科

baike.baidu.com/item/高能材料分子动力学轉為繁體網頁

... 了用子体系与子体系之间的相互作用能（即体系的结合能）表征它们之间的相容性。 ... 解法1.2.5 MD计算流程1.3量子分子动力学1.3.1 Hartree—Fock（HF）方程1.3.2 ...

phymath999