第四章分子模擬

Chapter4FrequencyCalculations

頻率分析預(yù)測(cè)分子的紅外和拉曼光譜(頻率和強(qiáng)度)幾何構(gòu)型優(yōu)化時(shí)計(jì)算力常數(shù)矩陣確定勢(shì)能面上駐點(diǎn)性質(zhì)計(jì)算零點(diǎn)能和熱力學(xué)數(shù)據(jù)，如系統(tǒng)的熵和焓頻率分析可以用于多種目的:MolecularVibrations4.2分子的振動(dòng)光譜

1.雙原子分子的諧振動(dòng)模型當(dāng)AB間距離RAB偏離Req時(shí)A和B都要受到一個(gè)力（分子的內(nèi)力）的作用（1）在只有分子內(nèi)的作用下，雙原子分子的振動(dòng)運(yùn)動(dòng)可用一個(gè)質(zhì)量為的假想質(zhì)點(diǎn)在平衡距離Req附近的振動(dòng)運(yùn)動(dòng)（2）當(dāng)

RAB

與Req

相差不大時(shí)，可近似地認(rèn)為即一個(gè)特解為：其中，（振動(dòng)頻率或特征頻率）鍵的力常數(shù)求解諧振子的Schr?dinger方程可得其能量的量子化表達(dá)式

E振=（ν+1/2）hν特征，振動(dòng)量子數(shù)ν=0，1，2，···零點(diǎn)振動(dòng)能

E0=1/2hν特征正則振動(dòng)模式ThethreenormalmodesofH2O.Themodev2ispredominantlybending,andoccursatlowerwave-numberthantheothertwo.4.1InputforFrequencyJobs

頻率分析輸入文件關(guān)鍵詞：freq#RHF/6-31G(d)FreqTest注意:頻率分析計(jì)算時(shí)所采用的理論方法和基組必須與幾何構(gòu)型優(yōu)化采用的方法和基組完全相同。4.2OutputofFrequencyJobs

頻率分析輸出文件信息●PredictingtheIRandRamanSpectra●

NormalModes●

Thermochemistry●

CharacterizingStationaryPointsFrequenciesandIntensities頻率和強(qiáng)度

1234B1B2A1A1Frequencies---1336.00411383.64491679.58432028.0971Red.masses---1.36891.34421.10397.2497...---IRIntensities---0.369423.15898.6240150.1861RamanActivities---0.76574.517012.85948.11244.2.1PredictingtheIRandRamanSpectra

預(yù)測(cè)紅外和拉曼光譜4.2.2ScalingFrequenciesandZero-PointEnergies頻率和零點(diǎn)能校正因子方法頻率矯正因子零點(diǎn)能矯正因子HF/3-21G0.90850.9409HF/6-31G(d)0.89290.9135MP2(Full)/6-31G(d)0.94270.9646MP2(FC)/6-31G(d)0.94340.9676SVWN/6-31G(d)0.98331.0079BLYP/6-31G(d)0.99401.0119B3LYP/6-31G(d)0.96130.98044.2.3NormalModes簡(jiǎn)正模式以水分子的計(jì)算結(jié)果為例:Standardorientation:-------------------------------------------------------------Center

AtomicCoordinates(Angstroms)NumberNumberXYZ--------------------------------------------------------------------------60.0000000.000000-0.54250080.0000000.0000000.67750010.0000000.940000-1.08250010.000000-0.940000-1.082500---------------------------------------------------------------------------第一個(gè)振動(dòng)模式是AtomANXYZ160.170.000.0028-0.040.000.0031-0.700.000.0041-0.700.000.004.2.4Thermochemistry

熱化學(xué)Thermochemistry--------------------------Tempeature298.15Kelvin.Pressure1.00000Atm.Atom1hasatomicnumber6andmass12.000???Molecularmass30.01056amu.Gaussian提供在指定溫度和壓力下的熱力學(xué)數(shù)值計(jì)算：

E（Thermal)CVSkcal/molcal/mol-kelvin

cal/mol-kelvinTotal20.1146.25552.101Electronic0.0000.0000.000Translational0.8892.98136.130Rotational0.8892.98115.921Vibrational18.3370.2940.0494.2.5Zero-PointandThermalEnergy零點(diǎn)能和熱能Temperature298.15Kelvinpressure1.0000Atm.Zero-pointcorrection=0.029201ThermalcorrectiontoEnergy=0.032054ThermalcorrectiontoEnthalpy=0.032999ThermalcorrectiontoGibbsFreeEnergy=0.008244Sumofelectronicandzero-pointEnergies=-113.837130SumofelectronicandthermalEnergies=-113.834277SumofelectronicandthermalEnthalpies=-113.833333SumofelectronicandthermalFreeEnergies=-113.858087后面四行的四個(gè)能量分別為E0，E，H，G。計(jì)算關(guān)系為E0=E(elec)+ZPEE=E0+E(vib)+E(rot)+E(trans)H=E+RTG=H-TS4.2.6PolarizabilityandHyperpolarizability

極化率和超極化率極化率的輸出Exactpolarizability:6.4780.00012.9790.0000.00017.641Approxpolarizability:6.2570.00010.1360.0000.00016.1884.3CharacterizingStationaryPoints

表征駐點(diǎn)的性質(zhì)駐點(diǎn):勢(shì)能面上梯度為零的點(diǎn),它既可能是極小值,也可能是鞍點(diǎn)。極小值:在勢(shì)能面的各個(gè)方向都是極小的.鞍點(diǎn):是在某些方向上是極小的,但在某一個(gè)方向上是極大的,因?yàn)榘包c(diǎn)是連接兩個(gè)極小值的點(diǎn)。

描述駐點(diǎn)時(shí)需要考慮的問題目的頻率分析性質(zhì)考慮的問題尋找極小值0個(gè)虛頻是極小值比較其它異構(gòu)體，得到最小值尋找極小值1個(gè)虛頻不是極小值繼續(xù)尋找，嘗試改變對(duì)稱性，或按虛頻的振動(dòng)模式修正分子結(jié)構(gòu)尋找過渡態(tài)0個(gè)虛頻是極小值嘗試Opt=QST或QST3尋找過渡態(tài)尋找過渡態(tài)1個(gè)虛頻是過渡態(tài)判斷其是否與反應(yīng)物，產(chǎn)物相關(guān)尋找過渡態(tài)多個(gè)虛頻是高階鞍點(diǎn)嘗試QST2，或者檢查虛頻對(duì)應(yīng)的振動(dòng)模式，不是連接兩其中之一可能是指向反應(yīng)物和產(chǎn)物，在該點(diǎn)的過渡態(tài)方向下修正分子