Electron Momentum Spectroscopy for Saturated Alkanes CnH2n+2(n=4-6)

YANG Ze-Jin GUO Yun-Dong ZHU Zheng-He YANG Xiang-Dong

(1School of Physics and Electronic Information Engineering,Neijiang Normal University,Neijiang 641112,Sichuan Province,P.R.China; 2Institute of Atomic and Molecular Physics,Sichuan University,Chengdu 610065,P.R.China)

Electron Momentum Spectroscopy for Saturated Alkanes CnH2n+2(n=4-6)

YANG Ze-Jin2GUO Yun-Dong1,*ZHU Zheng-He2YANG Xiang-Dong2

(1School of Physics and Electronic Information Engineering,Neijiang Normal University,Neijiang 641112,Sichuan Province,P.R.China;2Institute of Atomic and Molecular Physics,Sichuan University,Chengdu 610065,P.R.China)

Orbital electron momentum spectroscopies for saturated alkanes CnH2n+2(n=4-6)were systematically studiedusing the B3LYP/TZVP//B3LYP/aug-cc-pVTZ model.The effect of saturated alkanes CnH2n+2(n=4-6)isomers on orbital momentum distributions was analyzed.Electronic density distributions of coordinate space were systematically investigated by dual space analysis.The results indicate that the innermost valence orbitals are s-dominated whereas the next innermost valence orbitals exhibit p-dominant orbital profiles.The other valence orbitals are sp-mixed because of strong chemical bonding.The relative intensity of innermost valence orbitals is far larger than that of other orbitals.Furthermore,the relative intensity of n-alkane is larger than that of iso-alkane,which indicates that there is an obvious correlationbetweentherelativeintensityandthenumberofmigratedmethyls.

Electron momentum spectroscopy;Dual space analysis; Saturated alkane

The advantage of electron momentum spectroscopy(EMS)is that it can measure the orbital binding energy and momentum distributions for electrons located on individual orbitals of the molecule target,which provides more comprehensive information on electronic structures of molecules than conventional position space information only.With the development of experimental technique,valence orbitals rather than frontier orbitals for sizable molecules can be resolved[1].As a result,the great potential of EMS for exploring the electron structures of atoms and molecules can be extended[2].

Small saturated hydrocarbon molecules using EMS can be used as prototypes to study larger alkanes and provide necessary information as a probe for the growth of the linear chain structures or turning into branched species.According to the author′s knowledge,only some small saturated hydrocarbons CnH2n+2(n=1-5)have been investigated extensively both theoretically andexperimentally by EMS[3-22],whereas there is very little research on systematical studies to reveal valence orbital responses to the chain growth.For exemple,addition of a methyl shift is still rare.In the present study,individual orbital responses to the isomerization of the saturated alkanes are carried out.It focuses on orbital responses to energy shift caused by the addition of methyl functional group in the molecule using dual space analysis(DSA)[20].

1 Computational methods and details

The B3LYP/TZVP method[20,23-24]has been used to calculate wave functions in coordinate space based on the stable geometry structures for the alkanes obtained using the B3LYP/aug-ccpVTZ model.The Gaussian 03 computational chemistry package is employed for related quantum mechanical calculations[25]. The orbitals obtained in position space are then Fourier transformed into momentum space using the HEMS code[26],under a number of approximations,such as Born-Oppenheimer approximation,independent particle approximation,and the plane wave impulse approximation(PWIA)[26].The overlap between the targetion is the one electron Dyson orbital[27],

σ∝∫dΩ｜φj(p)｜2(1) where Ω is solid angle and p is the momentum of the target electron at the instant of ionization.The Dyson orbital φj(p)in momentum space is approximated by the Kohn-Sham(KS)orbitals in ground electronic states[28].

2 Results and discussion

According to the responses of the valence orbital to the methyl moiety,one could sort out the molecular orbitals as:(a) methyl affected orbitals,which engage with significant changes in intensity and shape,and(b)methyl disturbed orbitals,which experience minor changes in the orbitals.From a comprehensive analysis of the valence orbitals one could know that methyl site changes only cause the changes in certain valence orbitals not all the valence orbitals,indicating a molecular structural dependence.As a result,the nearly unchanged orbitals can be viewed as signature orbitals.The detailed highest occupied molecular orbitals(HOMOs)and total collision reaction cross section of the CnH2n+2(n=4-6)were published elsewhere[23],this article reveals the re sponses of the inner valence molecular orbitals to the branched carbon chains.

2.1 Isomer independence of the relative intensity of the inner most valence orbitals

Fig.1(a,b)reports the simulated inner most valence molecular orbitals(MOs)of the alkanes in momentum and coordinate spaces.Strong s-dominated orbital profiles in momentum space are also seen in the orbital electron density distributions in coordinate space.The very similar s-electron dominant shape of the orbital momentum profile suggests that the momentum space information is not sensitive to reflect small orbital electron density changes in the alkanes.The normal linear alkanes exhibit slightly stronger intensities than their isomers but in the order of n-bu-tane＞iso-butane,n-pentane＞iso-pentane＞neo-pentane,hexane＞iso-hexane＞3-methylhexane≈2,3-dimethylbutane＞2,2-dimethylbutane.

Fig.1 Electron momentum spectroscopies(EMS)and electron density distributions(EDD)of the innermost molecular orbitals of butane,pentane(a),and hexane(b)

Compared to n-alkanes,the iso-alkanes have smaller intensities and the neo-alkanes have the smallest intensities,suggesting that linear species corresponds to the more intensive electron distributions in momentum space.Therefore,the general variation tendencies of the relative intensity in the innermost valence orbitals are correlated with the carbons saturated by the number of the other carbon atoms.Moreover,the relative intensity of the innermost valence orbital quickly reaches zero at about 1 a.u., which is slightly smaller than the other valence orbitals,indicating that the electrons in the innermost valence orbitals spread over the molecular backbone into long range.From analyses of the orbital electron density distributions in coordinate space,it is clearly seen that all of the electrons contribute to this orbital.

2.2 Isomer dependence of the relative intensity of other valence orbitals

Other valence orbitals,such as the second innermost valence orbitals,however,reveal bell-shaped orbital profiles.The orbital cross sections exhibit a bell-shaped distributions,as shown in Fig.2(a,b).The similarities in the shape of the orbital momentum distributions indicate that the related orbitals contain a nodal plane in the orbitals,that is,the orbital electron density distributions contain positive and negative contributions,separated by a zero charge plane.

The second innermost valence orbital of pentane exhibits a similar trend that has been seen in the innermost s-dominated profiles.That is the maximum momentum intensity order of n-pentane＞iso-pentane＞neo-pentane with values of 0.50,0.40, and 0.30,respectively,is observed.Similarly,this order of relative intensity variation for hexane is clearly observed.For example,n-hexane has the largest intensity with a value of 0.60,the relative intensity reduces to about 0.50 for iso-hexane and 3-methylpentane,whereas the maximum relative intensity decreases to about 0.40 for 2,2-dimethylbutane and 2,3-dimethylbutane.

Comparison of the three n-alkanes,it is found that the intensity increases with the increase of the number of the carbons,and the order of the maximum peak value of butane,pentane,and hexane is given by n-butane＜n-pentane＜n-hexane as more electrons are bound with hexane.The fact that the bell-shaped orbital momentum profiles of these second innermost valence orbitals of the alkanes distribute into larger momentum region of up to 1.5 a.u.,whereas the innermost valence orbitals spread to smaller momentum region of＜1.0 a.u.,indicated the latter(innermost valence orbitals)spread into larger space in position space. The nodal plane in the former(the second innermost valence orbitals)contributes to the shrinkage of the electron density in this orbital.

2.3 Isomer dependence of the relative intensity of valence orbitals of alkane

Fig.2 EMS and EDD of the next innermost valence orbitals of butane,pentane(a)and hexane(b)

Fig.3 EMS and EDD of the selected valence orbitals of n-buane and iso-butane

Selected electron orbital momentum distributions for n-butane and iso-butane are shown in Fig.3 to understand the carbon chain branching in butane.The selected representative orbitals reveal that the methyl moiety indeed causes significant changes to electron distributions.For example,MO7 of n-butane is formed by mixed sp-electrons,whereas a bell-shaped profile is observed in iso-butane.However,opposite contributions are found in orbital MO9.The orbital profiles vary from a half bell shaped orbital profiles in iso-butane to a bell shaped orbital profiles in butane.Moreover,in orbital MO15,the half bell-shaped orbital profiles in n-butane are distorted to reflect the methyl addition,as given in Fig.3.This figure indicates strong distortion of the orbital momentum distributions as the addition of the methyl moiety,depending on the number of electron density nodal planes and the degree of the electron density overlap.Fig. 4 and Fig.5 present orbital distributions of pentane and hexane, respectively.In Fig.4,momentum distributions of MO10 of pentane gradually vary from bell-shaped to half bell shaped orbital distributions,which are the opposite trend found in Fig.4 for MO14 and MO19,respectively.In Fig.5,it is found that the more complicated momentum distributions among five hexane isomers have been occurred.The orbital momentum distributions show three clusters of orbital profile behaviors,consisting of bell-shaped,half bell-shaped,and sp-hybridized shaped orbitals.Further analysis finds that certain pzelectrons have contributed to the distributions of MO15 in 3-methylpentane and 2,3-dimethylbutane,together with MO24 in n-hexane.The sphybrided two peaks in MO15 of n-hexane and in MO24 of 2,2-dimethylbutane revealed the strong interactions between different electrons.

Fig.4 EMS and EDD of the selected valence orbitals of n-pentane and iso-pentane presented

Fig.5 EMS and EDD of the selected valence orbitals of n-hexane,iso-hexane

3 Conclusions

Valence orbitals for three saturated alkanes(butane,pentane, and hexane)and their isomers have been studied on their valence orbitals using dual space analysis.The innermost valence orbitals of the alkanes show certain similarities,differing only in their relative intensities.The second innermost valence orbitals of the alkanes reveal bell shaped orbital distributions,indicating the existence of a nodal plane in their orbital electron density distrubitions.The selected valence orbitals further reveal the structural dependence of the orbitals.The n-alkanes show stronger intensities than their isomers and the intensities increase with the number of the carbon atoms.

Acknowledgments： One of the authors,YANG Ze-Jin(ZY),thanks Swinburne University of Technology (SUT,Australia)for hospitality. ZY completed doctoral thesis research at SUT supervised by Professor WANG Feng.

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飽和烷烴分子CnH2n+2(n=4-6)的電子動(dòng)量光譜

楊則金2郭云東1,*朱正和2楊向東2

(1內(nèi)江師范學(xué)院物理與電子信息工程學(xué)院,四川內(nèi)江 641112;2四川大學(xué)原子與分子物理研究所,成都 610065)

使用B3LYP/TZVP//B3LYP/aug-cc-pVTZ方法系統(tǒng)研究了飽和烷烴分子CnH2n+2(n=4-6)的軌道電子動(dòng)量光譜,比較了同分異構(gòu)體CnH2n+2(n=4-6)對(duì)軌道動(dòng)量分布的影響.結(jié)合二維空間分析方法對(duì)電子在坐標(biāo)空間中的密度分布進(jìn)行了系統(tǒng)的研究.計(jì)算結(jié)果表明,最內(nèi)價(jià)殼層電荷分布主要由s電子貢獻(xiàn),第二近鄰芯價(jià)殼層則主要由p電子貢獻(xiàn),而其余的價(jià)殼層則為sp雜化.最內(nèi)價(jià)軌道表現(xiàn)出最大的譜線強(qiáng)度并且遠(yuǎn)大于其它軌道的譜線強(qiáng)度,而且正烷烴的譜線強(qiáng)度要大于異烷烴等同分異構(gòu)體的譜線強(qiáng)度,表現(xiàn)出了明顯的與甲基移動(dòng)的個(gè)數(shù)有關(guān)的性質(zhì).

電子動(dòng)量光譜; 二維空間分析; 飽和烷烴

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Received:April 10,2010;Revised:July 16,2010;Published on Web:July 19,2010.

*Corresponding author.Email:g308yd@126.com;Tel:+86-832-2341982;Fax:+86-832-2341679.

The project was supported by the National Natural Science Foundation of China(10676025,10574096),China Scholarship Council(CSC),and Science-Technology Foundation for Young Scientist of Sichuan Province,China(09ZQ026-049).

國(guó)家自然科學(xué)基金(10676025,10574096),國(guó)家留學(xué)基金委員會(huì)(CSC)和四川省青年科技基金(09ZQ026-049)資助項(xiàng)目

?Editorial office of Acta Physico-Chimica Sinica