宋彩彩，林 進(jìn)，曲占慶，呂仁慶

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4,5-二溴-1-丙基-3-甲基咪唑和1-丙基-3-甲基咪唑基離子液體的密度泛函研究

宋彩彩1，林 進(jìn)1，曲占慶2，*呂仁慶3

（1.中國(guó)石油大學(xué)（華東）化學(xué)工程學(xué)院，山東，青島 266555；2. 中國(guó)石油大學(xué)（華東）石油工程學(xué)院，山東，青島 266555；3. 中國(guó)石油大學(xué)（華東）理學(xué)院，山東，青島 266555）

采用密度泛函理論和DNP基組，對(duì)比研究了4,5-二溴-1-丙基-3-甲基咪唑和1-丙基-3-甲基咪唑與[PF6]-的相互作用。計(jì)算結(jié)果表明，H2原子和丙基支鏈氫原子與[PF6]-的氟原子相互作用形成氫鍵。[PMIM]+[PF6]-的最低未占軌道（LUMO）是分布在咪唑環(huán)上的p*軌道，而[PMIM-Br]+[PF6]-的LUMO為環(huán)原子和Br原子構(gòu)成的s*軌道。

密度泛函理論；基于鹵代咪唑的離子液體；氫鍵

離子液體是指全部由離子組成的液體，由于其獨(dú)特的物理和化學(xué)性質(zhì)，被廣泛的應(yīng)用到有機(jī)/無(wú)機(jī)合成、催化、分離、電化學(xué)和光化學(xué)領(lǐng)域中[1]。在離子液體中，陽(yáng)離子往往是體積較大的有機(jī)陽(yáng)離子，如咪唑、吡啶、吡咯、季銨鹽等物種，和不同的陰離子結(jié)合形成多種離子液體。其中基于二烷基咪唑陽(yáng)離子的離子液體研究最為廣泛。常見(jiàn)的陰離子有[PF6]-、[BF4]-、NO3-、CH3COO-、CF3COO-、CF3SO3-、CF3SO2NSO2CF3-等。由于離子液體的多樣性，可以根據(jù)不同的需要來(lái)調(diào)配離子液體的物理化學(xué)性質(zhì)?？梢圆捎糜?jì)算機(jī)模擬的方法在分子水平上研究離子液體的相互作用，如密度泛函理論[2-26]、Hartree-Fock方法[2,22,25]，半經(jīng)驗(yàn)分子軌道法[9,27]，分子動(dòng)力學(xué)法[3,28-31]，Monte Carlo法[32]等。密度泛函理論法被廣泛用于研究烷基咪唑基離子液體，最近有兩篇文獻(xiàn)綜述了模擬離子液體的不同方法[33-34]。

Mukai和Nishikawa[35-37]合成了一系列鹵代咪唑基離子液體。據(jù)我們所知，目前還沒(méi)有關(guān)于鹵代咪唑基和咪唑基離子液體相互作用的理論研究比較。本研究主要比較了兩種咪唑基離子液體的相互作用，考察了陰陽(yáng)離子相互作用的電子性質(zhì)和拓?fù)湫再|(zhì)。

1 初始結(jié)構(gòu)的設(shè)計(jì)

4,5-二溴-1-丙基-3-甲基咪唑陽(yáng)離子([PMIM-Br]+)、1-丙基-3-甲基咪唑基陽(yáng)離子([PMIM]+)和[PF6]-陰離子的結(jié)構(gòu)如圖1所示。設(shè)計(jì)不同的[PMIM-Br]+和[PMIM]+與[PF6]-相互作用初始模型。

圖1 初始結(jié)構(gòu) (a) [PMIM-Br]+, (b) [PMIM]+, (c) PF6-

2 計(jì)算方法

所有計(jì)算采用DMol3方法。采用GGA/PW91/DNP方法對(duì)初始結(jié)構(gòu)進(jìn)行了未加限制的全優(yōu)化，并進(jìn)行了頻率分析。將所得的優(yōu)化結(jié)構(gòu)進(jìn)行了NBO電子性質(zhì)分析和AIM拓?fù)湫再|(zhì)分析。

3 結(jié)果與討論

3.1 結(jié)構(gòu)和電子性質(zhì)

采用GGA/PW91/DNP方法優(yōu)化了[PMIM-Br]+、[PMIM]+、[PF6]-、[PMIM-Br]+[PF6]-和 [PMIM]+[PF6]-的結(jié)構(gòu)，所得結(jié)構(gòu)如圖2所示。[PMIM-Br]+[PF6]-和[PMIM]+[PF6]-中陽(yáng)離子的結(jié)構(gòu)參數(shù)和單獨(dú)的[PMIM-Br]+和[PMIM]+陽(yáng)離子結(jié)構(gòu)參數(shù)相近，都保留了咪唑環(huán)的平面結(jié)構(gòu)。[PMIM-Br]+[PF6]-中的C2–H2的鍵長(zhǎng)為1.088 ?，而[PMIM-Br]+中的C2–H2的鍵長(zhǎng)為1.081 ?；[PMIM]+[PF6]-中的C2–H2的鍵長(zhǎng)為1.091 ?，而[PMIM]+中的C2–H2的鍵長(zhǎng)為1.082 ?，這是由于[PF6]-中的F2與咪唑環(huán)上H2原子相互作用造成的。單獨(dú)的[PF6]-陰離子中P-F鍵長(zhǎng)1.650 ?相比，[PMIM-Br]+[PF6]-中的P-F1、P-F2和P-F3鍵長(zhǎng)分別增長(zhǎng)了0.027 ?、0.044 ?、0.018 ?，而[PMIM]+[PF6]-中的P-F1、P-F2和P-F3鍵長(zhǎng)分別增長(zhǎng)了0.020 ?、0.040 ?、0.023 ?。與此相對(duì)應(yīng)，P-F4、P-F5和P-F6鍵長(zhǎng)發(fā)生了收縮，這符合鍵級(jí)守恒原則[38]。離子液體陰陽(yáng)離子對(duì)是通過(guò)H原子和F原子相互作用的氫鍵聯(lián)系在一起。

圖2 優(yōu)化結(jié)構(gòu)和部分相互作用距離(a) [PMIM-Br]+ (b) [PMIM]+ (c) [PMIM-Br]+[PF6]- (d) [PMIM]+[PF6]- (?)

表1 (a) [PMIM-Br]+和(b) [PMIM]+陽(yáng)離子咪唑環(huán)的s, p布居數(shù)和自然原子軌道線性組合

表2 (c) [PMIM-Br]+[PF6]-和(d) [PMIM]+[PF6]-陽(yáng)離子咪唑環(huán)的s, p布居數(shù)和自然原子軌道線性組合

[PMIM-Br]+、[PMIM]+、[PMIM-Br]+[PF6]-和[PMIM]+[PF6]-陽(yáng)離子咪唑環(huán)的s、p布居數(shù)和自然原子軌道線性組合能給出陽(yáng)離子環(huán)的軌道信息。表1和表2顯示，咪唑環(huán)上的原子采用sp2雜化，形成五個(gè)s成鍵軌道，其余的垂直于環(huán)的p軌道肩并肩重疊形成大p鍵。咪唑環(huán)上五個(gè)s軌道的電子布居數(shù)為1.977-1.983e。[PMIM-Br]+和[PMIM-Br]+[PF6]-中s(C4-Br1) 和s(C5-Br2)軌道是由環(huán)上碳原子的sp2雜化軌道和Br上的半滿p軌道相互作用形成的。有意思的是，[PMIM-Br]+和[PF6]-相互作用p鍵分布在C5-C4和N3-C2上，[PMIM-Br]+陽(yáng)離子上的p鍵分布在C5-C4和N1-C2上。孤對(duì)電子向反鍵軌道離域可用二級(jí)微擾穩(wěn)定化能來(lái)估算。表3所示為[PMIM-Br]+和[PMIM-Br]+[PF6]-中Br1和Br2涉及孤對(duì)電子的受-授NBO相互作用及其二級(jí)微擾穩(wěn)定化能（(2)）。Br1和Br2孤對(duì)電子和p*(C4-C5)的強(qiáng)烈相互作用表示為L(zhǎng)P(Br1)?p*(C4-C5)和LP(Br2)?p*(C4-C5)。在[PMIM-Br]+中為15.59 kcal/mol和15.60 kcal/mol，在[PMIM-Br]+[PF6]-中為14.25 kcal/mol和14.02 kcal/mol，二級(jí)微擾穩(wěn)定化能很大，這表明LP(Br1)和LP(Br2)向p*(C4-C5)有很大程度的電子離域。表3所示，LP(Br1) 和LP(Br2)向環(huán)上s*反鍵軌道有一定程度的遷移。在[PMIM-Br]+中，二級(jí)微擾穩(wěn)定化能LP(Br1)?s*(C4-C5)、 LP(Br1)?s*(C4-N3)、LP(Br2)?s*(C4-C5)和LP(Br2)?s*(C5-N1)分別為 5.44 kcal/mol、 8.95 kcal/mol,、5.43 kcal/mol和8.99 kcal/mol，而在[PMIM-Br]+[PF6]-中，二級(jí)微擾穩(wěn)定化能LP(Br1)?s*(C4-C5)、LP(Br1)?s*(C4-N3)、LP(Br2)?s*(C4-C5)和LP(Br2)?s*(C5-N1)分別為5.33 kcal/mol、8.35 kcal/mol、5.18 kcal/mol和8.47 kcal/mol。盡管Br的Pauling電負(fù)性(2.96)比C的電負(fù)性(2.55)大，由于Br原子上孤對(duì)電子向環(huán)上的離域，導(dǎo)致Br的正電性，在[PMIM-Br]+中分別為Br1 (+0.23342)和Br2 (+0.23252)，在[PMIM-Br]+[PF6]-中分別為Br1 (+0.18699)和Br2 (+0.18456)。

表3 [PMIM-Br]+和[PMIM-Br]+[PF6]-中Br1和Br2涉及孤對(duì)電子的受-授NBO相互作用及其二級(jí)微擾穩(wěn)定化能

圖3和圖4所示為[PMIM-Br]+[PF6]-和[PMIM]+[PF6]-的最高已占軌道（HOMO）和最低未占軌道（LUMO）及其能量示意圖。福井謙一的前線軌道理論能反映出陰陽(yáng)離子的相互作用情況。由圖3所示，PMIM-Br]+[PF6]-和[PMIM]+[PF6]-的HOMO主要來(lái)源于咪唑環(huán)的p型軌道， [PMIM-Br]+[PF6]-的HOMO不僅包含環(huán)上的原子還有Br原子，而[PMIM]+[PF6]-的HOMO主要包含環(huán)上的原子。[PMIM-Br]+[PF6]-和[PMIM]+[PF6]-的HOMO有明顯的不同，[PMIM-Br]+[PF6]-的HOMO主要來(lái)源于環(huán)原子和Br原子構(gòu)成的s型軌道，而[PMIM]+[PF6]-的HOMO主要來(lái)源于環(huán)原子所構(gòu)成的p型軌道。[PMIM-Br]+[PF6]-和[PMIM]+[PF6]-的HOMO和LUMO均來(lái)源于陽(yáng)離子，該結(jié)論與[C4MIM]+[PF6]-的HOMO和LUMO均來(lái)源于[C4MIM]+陽(yáng)離子是一致的[39]。[PMIM-Br]+和[PF6]-相互作用能為79.9 kcal/mol，而[PMIM]+和[PF6]-相互作用能為76.6 kcal/mol，由此可見(jiàn)，Br原子取代到咪唑環(huán)的4,5位，對(duì)相互作用能的影響不大。

圖3 HOMO軌道(a) [PMIM-Br]+[PF6]-、(c) [PMIM]+[PF6]-和LUMO軌道(b) [PMIM-Br]+[PF6]-、(d) [PMIM]+[PF6]-

圖4 HOMO和LUMO軌道能量示意圖(a) [PMIM-Br]+[PF6]-和(b) [PMIM]+[PF6]-

Fig. 4 The HOMO and LUMO energy scheme of (a) [PMIM-Br]+[PF6]- and (b) [PMIM]+[PF6]-

3.2 氫鍵

離子液體中陰陽(yáng)離子的主要相互作用之一是氫鍵。NBO分析可用來(lái)評(píng)估電荷的分布和成鍵性質(zhì)。[PMIM-Br]+中H2的NBO電荷為+0.27581，[PMIM]+中H2的NBO電荷為+ 0.27227，由于N1和N2原子的電負(fù)性很大，所以導(dǎo)致H2原子具有最大的正電荷。[PMIM-Br]+[PF6]-和[PMIM]+[PF6]-中[PF6]-的電荷數(shù)分別為-0.95335和-095493，這說(shuō)明負(fù)電荷從[PF6]-向[BMIM-Br]+和[PMIM]+陽(yáng)離子發(fā)生了遷移。[PMIM-Br]+[PF6]-中H2原子的NBO電荷為0.30477，而[PMIM]+[PF6]-中H2原子的NBO電荷為0.30983，F(xiàn)2的負(fù)電荷增大，這是由于氫鍵的形成所致。非鍵范德華相互作用的判定標(biāo)準(zhǔn)之一就是相應(yīng)的原子間距小于兩個(gè)原子的范德華半徑之和。[PMIM-Br]+[PF6]-和[PMIM]+[PF6]-中F2×××H2和F1×××H71的距離分別為1.931 ?、2.318 ?和1.868 ?、2.322 ?，小于Bondi范德華半徑之和(2.67 ?)[40]。

研究氫鍵是否存在，它們的拓?fù)湫再|(zhì)也可以作為一種判據(jù)。根據(jù)Bader的AIM拓?fù)淅碚揫41]，化學(xué)鍵可以用電子密度r(r)和其相應(yīng)的Laplacian?2r(r)進(jìn)行描述。鍵關(guān)鍵點(diǎn)(BCP)的r(r)和?2r(r)反映鍵的性質(zhì)。?2r(r) > 0說(shuō)明鍵以離子性為主，?2r(r) < 0表明鍵以共價(jià)鍵為主。[PMIM-Br]+[PF6]-和[PMIM]+[PF6]-中氫鍵的拓?fù)湫再|(zhì)列入表4中。根據(jù)形成氫鍵的拓?fù)湫再|(zhì)標(biāo)準(zhǔn)rBCP= 0.002~0.035 a.u.，?2BCP= 0.024~0.139 a.u.[42]，[PMIM-Br]+[PF6]-和[PMIM]+[PF6]-中各有二個(gè)氫鍵。[PMIM-Br]+[PF6]-和[PMIM]+[PF6]-中F2×××H2的rBCP和?2BCP較大，這和H2的高正電性及短的氫鍵鍵長(zhǎng)是一致的。形成氫鍵的電子受-授相互作用(2)如表5所示。(2)反映出電子授-受軌道相互作用的強(qiáng)度，(2)越大，相互作用程度越大。[PMIM-Br]+[PF6]-和[PMIM]+[PF6]-中LP(F2)?s*(C2-H2)的(2)較大，說(shuō)明H2形成的氫鍵最強(qiáng)。

表4 [PMIM-Br]+[PF6]-和[PMIM]+[PF6]-優(yōu)化結(jié)構(gòu)中陰陽(yáng)離子相互作用的拓?fù)湫再|(zhì)

表5 [PMIM]+[PF6]- and [PMIM-Br]+[PF6]-中氫鍵的授-受相互作用及二級(jí)微擾穩(wěn)定化能E(2) (kcal/mol)

5 結(jié)論

采用密度泛函理論方法考察了4,5-二溴-1-丙基-3-甲基咪唑和1-丙基-3-甲基咪唑與[PF6]-的相互作用。研究結(jié)果表明，陰陽(yáng)離子之間的作用取決于電子效應(yīng)和空間效應(yīng)。NBO和AIM分析表明，兩種離子液體的陰陽(yáng)離子之間相互作用主要是氫鍵作用。但由于Br取代咪唑環(huán)的4,5位，導(dǎo)致兩種離子液體的前線軌道組成發(fā)生了變化。陰陽(yáng)離子之間的相互作用能基本相同。

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DENSITY FUNCTIONAL study on 4,5-dibromo-1-propyl-3-methylimidazolYL and 1-propyl-3-methylimidazolYL hexafluorophosphate LIQUID

SONG Cai-cai1，LIN Jin1，QU Zhan-qing2，*LV Ren-qing3

(1. College of Chemical Engineering, China University of Petroleum (East China), Qingdao, Shandong 266555, China;2 .College of Petroleum Engineering, China University of Petroleum (East China), Qingdao, Shandong 266555, China;3. College of Science, China University of Petroleum (East China), Qingdao, Shandong 266555, China)

The interaction of 4,5-dibromo-1-propyl-3-methylimidazole and 1-propyl-3-methylimidazole with [PF6]-was comparatively studied. The calculated results suggested that H2 and the propyl side-chain hydrogen atoms interact with fluorine atoms of [PF6]-to form hydrogen bondings. The lowest unoccupied molecular orbital (LUMO) of [PMIM]+[PF6]-is theptype orbital distributed on the imidazole ring, but that of [PMIM-Br]+[PF6]-is thestype orbital composed of ring and bromine atoms.

density functional theory; halogen substituted imidazole ring-based ionic liquid; hydrogen bonding

1674-8085(2012)03-0040-09

O641

A

10.3969/j.issn.1674-8085.2012.03.009

2012-01-24；

2012-03-12

國(guó)家重大專項(xiàng)大型油氣田及煤層氣開(kāi)發(fā)項(xiàng)目(2011ZX05051)

宋彩彩(1989-)，女，山東萊陽(yáng)人，中國(guó)石油大學(xué)(華東)化學(xué)工程學(xué)院本科生(E-mail:393691299@qq.com);

林 進(jìn)(1990-)，男，江西井岡山人，中國(guó)石油大學(xué)(華東)化學(xué)工程學(xué)院本科生(E-mail:1311870044@qq.com)’

曲占慶(1963-)，男，山東萊州人，教授，博士生導(dǎo)師，主要從事能源開(kāi)發(fā)與應(yīng)用研究(E-mail:quzhq@upc.edu.cn);

*呂仁慶(1969-)，男，山東萊陽(yáng)人，副教授，博士，主要從事離子液體及脫硫脫氮的理論研究(E-mail:lvrenqing@upc.edu.cn).