稠環(huán)類1,2,4,5-四嗪衍生物結構和性能的理論研究

張 馳, 陳 沫, 陳 湘, 張 聰, 宋紀蓉,2, 馬海霞

(1. 西北大學化工學院, 陜西 西安 710069; 2. 北京故宮博物院文保科技部, 北京 100080)

1 引 言

高氮含能化合物是近年來發(fā)展起來的并具有良好應用前景的高能量密度材料(HEDM),它具有很高的正生成焓,感度較低,熱穩(wěn)定性好,閃點溫度高,且分子結構中的高氮低碳氫含量使其具有較高的密度,也更容易達到氧平衡[1-2]。四嗪類高氮化合物分子結構中含有較多的N—N和C—N鍵,四嗪環(huán)的含氮量高達68.3%,具有能量高、熱穩(wěn)定性好、特征信號低、燃燒無殘渣及無污染等優(yōu)點,廣泛應用于推進劑、新型高能鈍感炸藥和煙火劑等含能材料領域[3-4]。而稠環(huán)含能化合物一般都具有較高的密度和能量,是目前高能量密度材料重要研究方向之一[5-6]。3-肼基-6-(3,5-二甲基吡唑)-s-四嗪可以發(fā)生成環(huán)反應形成稠環(huán)類四嗪含能化合物[7],如s-四嗪并三唑的衍生物1,2,4-三唑[4,3-b]并s-四嗪(TTZ)、6-氨基-1,2,4-三唑[4,3-b]并s-四嗪(ATZ)和3,6-二氨基-1,2,4-三唑[4,3-b]并s-四嗪(AATZ)。其后,研究者合成了許多稠環(huán)類四嗪衍生物[8-14],但有關該類化合物的研究大多集中在該類物質的制備及機理方面的研究,而有關性能研究相對較少。

基于此,本研究選取了一系列五元氮雜環(huán)與母體1,2,4,5-四嗪連接組成稠環(huán)化合物,設計了14種1,2,4,5-四嗪衍生物,在wB97/6-31+G**水平下獲得此類化合物的穩(wěn)定構型,在此基礎上計算了其生成焓及爆轟性能,從理論上研究五元氮雜環(huán)作為取代基構成的稠環(huán)化合物對1,2,4,5-四嗪的影響,考察性能與結構之間的對應關系。

2 計算方法

運用DFT方法,在B3LYP/(6-31G*,6-311G*,6-31+G*,6-31G**,6-311G**,6-31+G**,6-311++G**,cc-pVDZ,cc-pVTZ)水平下計算分析1,2,4,5-四嗪、3,6-二氨基-1,2,4,5-四嗪(DAT)、3,6-二肼基-1,2,4,5-四嗪(DHT)和3,6-二疊氮基-1,2,4,5-四嗪(DIAT)4種化合物的生成焓,通過與實驗值[15]進行對比擬合,在B3LYP/6-31+G**水平下計算的結果與實驗值線性相關性最好,達到0.9863,因此選擇基組6-31+G**和不同方法(B3PW91,M05,M05-2X,M06,M06-2X,wB97)組合計算上述4種化合物生成焓,通過與實驗值進行對比擬合,在wB97/6-31+G**水平下計算的結果與實驗值線性相關性最好,達到0.9896,因此在wB97/6-31+G**水平下對所設計的14種1,2,4,5-四嗪衍生物的幾何結構進行全優(yōu)化,經振動頻率分析表明優(yōu)化構型為勢能面上極小點(無虛頻),得到的熱力學數據采用原子化方案(atomization scheme)[16-20]預測目標化合物的標準生成焓。具體方法是將分子分解為原子:

CaHbOcNd(g)→aC(g)+bH(g)+cO(g)+dN(g)

(1)

則該反應在298K時的標準反應焓ΔH298由下式計算:

ΔH298=ΣΔHf,P-ΣΔHf,R

=aΔHf,C+bΔHf,H+cΔHf,O+dΔHf,N-ΔHf,CaHbOcNd

(2)

式中,ΔHf,R和ΔHf,p分別表示反應物和生成物在298 K的標準生成焓,kJ·mol-1; ΔHf,C、ΔHf,H、ΔHf,O和ΔHf,N分別為原子C、H、O和N在298 K的標準生成焓,可從手冊[21]中查得; ΔHf,CaHbOcNd為分子CaHbOcNd在298 K的標準生成焓,為待求項。同時存在下列關系式:

ΔH298=ΔE298+Δ(pV)

=ΔE0+ΔEZPE+ΔET+ΔnRT

=E0,C+E0,H+E0,O+E0,N-E0,CaHbOcNd-

EZPE,CaHbOcNd-ΔET,CaHbOcNd+ΔnRT

(3)

式中,E0,C、E0,H、E0,O、E0,N和E0,CaHbOcNd分別為wB97/6-31+G**水平下計算得到的原子C、H、O、N和分子CaHbOcNd在0 K的總能量,a.u.;EZPE,CaHbOcNd和ΔET,CaHbOcNd分別為分子CaHbOcNd的零點能和熱校正值,a.u.,可從振動分析獲得的熱力學數據得到,對原子而言,EZPE和ΔET項均為0; Δn表示氣體產物和反應物的物質的量之差,mol;R是氣體常數,8.314 J·mol-1·K-1;T表示絕對溫度,K。綜合上式,化合物CaHbOcNd在298 K的標準生成焓ΔHf,CaHbOcNd即可求得。

運用半經驗K-J方程[22-25]估算其爆速(D)、爆壓(p)值:

D=Φ0.5(1.011+1.312ρ)

(4)

p=1.558Φρ2

(5)

(6)

研究中所有化合物密度均采用摩爾體積法(ρ=M/Vm)計算得到,其中M為化合物的摩爾質量,Vm為化合物的摩爾體積,是在穩(wěn)定構型下,基于0.001 e·bohr-3等電子密度面所包圍的體積空間,用Monte-Carlo方法對每一個優(yōu)化的穩(wěn)定構型進行了100次單點計算取其平均值求得。所有計算使用Gaussian09[26]量子化學軟件包在wB97/6-31+G**水平下完成。

parameterscomponentsofCaHbOcNdc≥2a+b22a+b2>c≥b2b2>cNb+2c+2d4Mb+2c+2d4Mb+d2MM—4Mb+2c+2d56d+88c-8bb+2c+2d2b+28d+32cb+dQ28.9b+47.04a+0.239ΔHfM28.9b+94.05c2-b4()+0.239ΔHfM57.8c+0.239ΔHfM

Note:Mis the molar mass of a compound, ΔHfis the calculated heat of formation.

3 結果與討論

3.1 幾何結構

在wB97/6-31+G**水平下對1,2,4,5-四嗪衍生物進行幾何結構全優(yōu)化,圖1列出了其優(yōu)化結構圖,標注了部分優(yōu)化幾何參數(鍵長、鍵角)。計算結果表明,與1,2,4,5-四嗪相比四嗪環(huán)上N(1)—N(2)鍵長均縮短,除了T2靠近五元環(huán)一側的N(4)—N(5)鍵長,其余化合物的鍵長均增加,雙環(huán)取代更明顯; 單環(huán)取代四嗪衍生物C(3)—N(4)鍵長均縮短,其他C—N鍵長均增加,雙環(huán)取代四嗪衍生物C—N鍵長均增加,且大部分五元環(huán)的C—N鍵長小于未成五元環(huán)的; 同分異構體化合物中,五元環(huán)上N原子位置不同,使四嗪環(huán)的上的鍵長和鍵角不同,但數值非常接近,因此N原子位置對四嗪環(huán)的鍵長和鍵角影響較小; 除了衍生物T1和T12,其余化合物均不共面,說明隨著N原子數量的增加,稠環(huán)類四嗪衍生物的共面性反而降低。

圖11,2,4,5-四嗪衍生物的分子優(yōu)化結構圖及部分鍵長(nm)和鍵角(°)

Fig.1Optimized molecular structures for the 1,2,4,5-tetrazine derivatives along with their selected bond lengths(nm) and bond angles(°)

3.2 生成焓

在wB97/6-31+G**水平下采用原子化方案估算稠環(huán)四嗪衍生物及傳統(tǒng)含能材料RDX和HMX的生成焓,表2列出了目標化合物的總能量(E0)、零點能(EZPE)、N原子數、溫度校正值(HT)及生成焓(ΔHf)。

計算結果表明,所有1,2,4,5-四嗪衍生物生成焓均大于傳統(tǒng)含能材料RDX和HMX,具有高正生成焓,其中最高的生成焓值為1122.53 kJ·mol-1。所有化合物的生成焓均比未取代的1,2,4,5-四嗪生成焓高,雙環(huán)取代四嗪衍生物生成焓普遍大于相應單環(huán)取代的,幅度為140～280 kJ·mol-1。單環(huán)取代中,化合物T2和T3,T4、T5和T6分別互為同分異構體,T2的生成焓高于T3,T4的生成焓高于T5和T6,是因為T2中的N—N鍵數量多于T3,T4中的N—N鍵數量多于T5和T6,雙環(huán)取代(T22、T42)和單環(huán)取代一致,結果表明,N—N鍵有助于增加1,2,4,5-四嗪衍生物的生成焓。

表2均四嗪衍生物及HMX和RDX的總能量、零點能、溫度校正值和生成焓

Table2CalculatedE0,EZPE,HTand ΔHfof s-tetrazine derivatives together with HMX and RDX

compd.formulaE0/a.u.EZPE/a.u.HT/a.u.numberofNΔHf/kJ·mol-1TC2H2N4-296.28570.05270.00514527.49T1C5H4N4-411.80010.09480.00674606.69T2C4H5N5-428.98800.10610.00725744.06T3C4H5N5-429.01810.10590.00735664.85T4C3H4N6-445.01060.09390.00706825.63T5C3H4N6-445.04780.09440.00706729.00T6C3H4N6-445.03610.09420.00706759.44T7C2H3N7-461.05650.08190.00697846.05T12C8H6N4-527.29020.13590.00894749.08T22C6H8N6-561.69950.16010.00916937.70T32C6H8N6-561.75080.15970.00956802.88T42C4H6N8-593.74020.13580.008981112.41T52C4H6N8-593.80790.13580.00948936.04T62C4H6N8-593.80230.13720.00878952.80T72C2H4N10-625.84420.11190.0087101122.53RDXC3H6N6O6-897.35320.14700.01346244.21HMXC4H8N8O8-1196.47500.19720.01788317.19

Note:E0is total energy ,EZPEis zero point energy,HTis correction of temperature.

選取相同N原子數中生成焓最大的化合物,對其總能量(E0)和生成焓(ΔHf)與N原子數的關系作線性擬合,由圖2和圖3可知,不論是單環(huán)取代還是雙環(huán)取代,隨著N原子數的增加,分子總能量逐漸降低,且具有很好的線性關系,生成焓則逐漸增大,表明N原子數的增加有助于提升1,2,4,5-四嗪衍生物的生成焓。綜上所述,N—N鍵及N原子數的增加在提升1,2,4,5-四嗪衍生物的生成焓方面起了重要的作用。

圖2總能量(E0)與N原子數的關系

Fig.2The relationship ofE0and N atom numbers

圖3生成焓(ΔHf)與N原子數的關系

Fig.3The relationship of ΔHfand N atom numbers

3.3 前線軌道能量

分子軌道理論表明,化合物的穩(wěn)定性與其分子軌道能量有關,最高占據軌道能量(EHOMO)越低,最低空軌道能量(ELUMO)越高,則其分子軌道能級差(ΔELUMO-HOMO=ELUMO-EHOMO)越大,化合物就越穩(wěn)定。運用量子化學的方法計算了1,2,4,5-四嗪衍生物的EHOMO及ELUMO,進一步分析得到ΔELUMO-HOMO,列于表3。計算結果表明,單環(huán)取代衍生物的分子軌道能級差與T比較均減小,雙環(huán)取代衍生物除了T12和T32,其它分子軌道能級差與T比較均增大,T62的分子軌道能級差在所有體系中較高,使電子躍遷幾率降低,預示其反應活性最低,最穩(wěn)定。

表3目標化合物的前線軌道能量

Table3CalculatedEHOMO,ELUMO和ΔELUMO-HOMOof the title compounds

a.u.

3.4 爆轟性能

爆速和爆壓是研究爆轟性能的兩個較為重要的參數,本文在wB97/6-31+G**水平下預測了1,2,4,5-四嗪衍生物及HMX和RDX的爆速(D)和爆壓(p),如表4所示。無論是單環(huán)取代還是雙環(huán)取代的衍生物,D和p都是隨著體系中N原子數的增加而增加; 除了單環(huán)取代的T1、T2、T3及雙環(huán)取代的T12、T22、T32,其他衍生物的密度、爆速和爆壓均高于未取代的T; 帶有同一種環(huán)單取代和雙取代,對D和p的影響較小,且有些單環(huán)取代衍生物的D和p略偏高,如單環(huán)取代化合物T1、T2和T3比相應雙環(huán)取代的T12、T22、T32高,說明稠環(huán)四嗪衍生物D和p與所含N原子數關系較大,與環(huán)的個數關系較小?；衔颰7和T72的D接近于傳統(tǒng)含能材料RDX,p略低于RDX,ρ則遠遠小于RDX,從能量角度來看,提高四嗪衍生物的密度,其爆轟性能也將提高,所以T7和T72可以作為潛在的含能材料。

1,2,4,5-四嗪衍生物的D和p與N原子數的線性擬合關系如圖4所示,圖4a與圖4c為單環(huán)取代四嗪衍生物的D和p與N原子數的線性關系,圖4b與圖4d為雙環(huán)取代四嗪衍生物的D和p與N原子數的線性關系。從圖4可以看出,無論是單環(huán)取代還是雙環(huán)取代,1,2,4,5-四嗪衍生物的D和p與N原子數均有很好的線性關系,相關系數r分別為0.987、0.998(單取代D、p)和0.988、0.996(雙取代D、p)。

a. D, one ring substituted

b. D, double rings substituted

c. p, one ring substituted

d. p, double rings substituted

圖4爆速(D)及爆壓(p)與氮原子數目的關系

Fig.4The relationship ofDandpwith N atom numbers

表4目標化合物及RDX和HMX的摩爾質量、平均摩爾體積、理論密度、爆熱、爆速和爆壓

Table4PredictedM,V,ρ,Q,Dandpof the title molecules together with RDX and HMX

compd.V/cm3·mol-1M/g·mol-1ρ/g·cm-3Q/J·g-1D/km·s-1p/GPaT55.99182.0281.471536.9177.3621.08T183.833120.0441.431207.8856.1114.29T285.218123.0551.441445.1357.0919.33T385.345123.0551.441291.2916.9018.27T482.443124.0501.501590.6977.7423.64T584.790124.0501.461404.5257.3721.05T683.456124.0501.491463.1727.5422.37T780.086125.0451.561617.0668.2227.40T12110.857158.0591.431132.6775.5911.94T22115.064164.0811.431365.8516.9018.21T32115.618164.0811.421169.4736.6116.62T42106.731166.0721.561600.9128.0526.25T52106.707166.0721.561347.0927.7124.08T62106.296166.0721.561371.2117.7424.30T72103.365168.0621.631596.3438.6531.24RDX129.53222.041.71(1.82[27])1679.208.76(8.75[27])33.05(34.00[27])HMX162.87296.051.82(1.91[27])1672.409.11(9.10[27])37.08(39.00[27])

Note:Mis molar mass,Vis average molar volume,ρis theoretical density,Qis explosion heat,Dis detonation velocity andpis detonation pressure.

3.5 熱力學性質

運用量子化學計算的方法,以分子統(tǒng)計熱力學為基礎,計算了稠環(huán)類1,2,4,5-四嗪衍生物在200～800K的熱力學性質,即標準摩爾熱容(Cp,m)、標準摩爾熵(Sm)和標準摩爾焓(Hm),列于表5。由表5可以看出,Cp,m、Sm及Hm均隨T的升高而增加,其中Cp,m和Sm增大的比例均隨著T的升高而逐步減小,而Hm增大的比例則隨著T的升高而逐步增大。在T較低時,分子的轉動及平動對Cp,m、Sm和Hm貢獻相對較大; 但是隨著溫度升高到一定程度后,分子的振動增強,對Cp,m、Sm和Hm貢獻大,而導致Cp,m、Sm和Hm值增加。在同一T下,隨著N原子數的增加,Cp,m、Sm及Hm與溫度之間沒有線性的變化; 同時,雙取代環(huán)的Cp,m、Sm和Hm明顯大于相應的單取代環(huán)的,說明取代環(huán)的增加有利于這些熱力學函數值的增加。

表5目標化合物200～800 K時的Cp,m、Sm和Hm

Table5CalculatedCp,m,SmandHmat 200～800 K for the title molecules

T1T12TCp,m/J·mol-1·K-1Sm/J·mol-1·K-1Hm/kJ·mol-1TCp,m/J·mol-1·K-1Sm/J·mol-1·K-1Hm/kJ·mol-1200 69.10289.168.83200 94.96321.5011.16273.15 94.54314.3914.80273.15 131.59356.4519.43298.15103.48323.0617.28298.15144.24368.5322.88400137.82358.3829.61400192.36417.8040.08500165.98392.2744.85500231.58465.1061.35600188.37424.5962.61600262.74510.1986.13700206.04455.0082.36700287.40552.61113.68800220.14483.47103.70800307.16592.32143.44T2T22TCp,m/J·mol-1·K-1Sm/J·mol-1·K-1Hm/kJ·mol-1TCp,m/J·mol-1·K-1Sm/J·mol-1·K-1Hm/kJ·mol-1200 74.68296.559.53200 97.98324.1611.38273.15100.80323.6215.94273.15136.76360.3219.94298.15110.06332.8518.57298.15150.58372.8923.53400146.04370.3231.65400204.33424.8141.66500175.90406.2347.80500248.61475.3464.38600199.80440.5066.63600283.81523.9091.07700218.79472.7787.60700311.69569.83120.90800234.08503.03110.26800334.13612.96153.23

續(xù)表5

Table5continued

T3T32TCp,m/J·mol-1·K-1Sm/J·mol-1·K-1Hm/kJ·mol-1TCp,m/J·mol-1·K-1Sm/J·mol-1·K-1Hm/kJ·mol-1200 76.23296.609.58200 101.65329.8711.93273.15102.76324.2316.12273.15140.49367.2020.76298.15111.99333.6318.80298.15154.21380.0924.45400147.61371.6232.06400207.22432.9842.91500177.07407.8448.35500250.74484.0765.89600200.67442.2967.28600285.32532.9692.76700219.44474.6888.32700312.74579.08122.71800234.55505.00111.05800334.81622.33155.13T4T42TCp,m/J·mol-1·K-1Sm/J·mol-1·K-1Hm/kJ·mol-1TCp,m/J·mol-1·K-1Sm/J·mol-1·K-1Hm/kJ·mol-1200 72.99296.019.49200 95.30322.4911.29273.1597.41322.3115.70273.15130.60357.3219.53298.15106.05331.2118.2298.15143.09369.3022.95400139.59367.1530.79400191.50418.2540.04500167.33401.3946.18500231.31465.4361.25600189.45433.9364.07600262.88510.5086.03700206.93464.5083.92700287.74552.96113.61800220.89493.08105.34800307.58592.73143.40T5T52TCp,m/J·mol-1·K-1Sm/J·mol-1·K-1Hm/kJ·mol-1TCp,m/J·mol-1·K-1Sm/J·mol-1·K-1Hm/kJ·mol-1200 73.16295.339.44200 100.87334.7012.28273.1597.64321.7015.68273.15135.22371.1520.90298.15106.22330.6218.23298.15147.26383.5124.43400139.46366.5830.77400193.93433.4441.85500167.00400.7646.14500232.54481.0163.24600189.02433.2363.99600263.37526.2588.10700206.47463.7383.79700287.79568.75115.70800220.43492.24105.16800307.36608.50145.49T6T62TCp,m/J·mol-1·K-1Sm/J·mol-1·K-1Hm/kJ·mol-1TCp,m/J·mol-1·K-1Sm/J·mol-1·K-1Hm/kJ·mol-1200 73.00296.149.49200 93.30322.4411.15273.1597.36322.4415.71273.15127.84356.5219.22298.15105.94331.3418.25298.15140.15368.2522.56400139.26367.2230.77400188.30416.2939.34500166.90401.3646.13500228.31462.7660.23600189.00433.8363.97600260.23507.3284.73700206.50464.3383.77700285.46549.41112.06800220.49492.85105.15800305.64588.89141.65T7T72TCp,m/J·mol-1·K-1Sm/J·mol-1·K-1Hm/kJ·mol-1TCp,m/J·mol-1·K-1Sm/J·mol-1·K-1Hm/kJ·mol-1200 72.12294.079.36200 93.42323.3311.37273.1595.15319.9215.47273.15125.33357.1119.35298.15103.12328.5917.95298.15136.45368.5622.62400133.81363.2830.05400179.25414.7838.75500159.11395.9544.74500214.32458.6858.49600179.27426.8261.70600242.03500.3181.37700195.13455.6980.45700263.70539.31106.70800207.71482.60100.62800280.80575.68133.95

Note:Cp,mis standard molar heat capacity,Smis standard molar entropy andHmis standard molar enthalpy.

4 結 論

利用wB97/6-31+G**方法對稠環(huán)類1,2,4,5-四嗪衍生物的幾何結構、前線軌道能量、生成焓、爆轟性能及熱力學性質進行計算研究。

(1) 計算結果表明,雙環(huán)取代四嗪衍生物生成焓普遍大于相應單環(huán)取代的,N—N鍵及N原子數的增加有助于提升1,2,4,5-四嗪衍生物的生成焓。

(2) 爆轟性能結果表明,稠環(huán)四嗪衍生物D和p主要與所含N原子數有關,與環(huán)的個數關系較小,且D和p與N原子數均有良好的一次線性相關關系。

(3) 熱容Cp,m、熵Sm及焓Hm均隨著T的升高而增加,Cp,m和Sm增大的比例均隨著T的升高而逐步減小,而Hm增大的比例則隨著T的升高而逐步增大。

(4) 化合物T7和T72的爆速接近于傳統(tǒng)含能材料RDX,爆壓略低于RDX,可以作為備選的HEDM。

致謝感謝臨沂大學化學化工學院夏其英教授在Gaussian09計算中提供的幫助。

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