CASSCF与CAS+1+2理论及其应用
有机-过渡金属配合物的三重态发光问题
有机-过渡金属配合物的三重态发光问题吴世康;汪鹏飞【摘要】近年来,随着OLED器件的发展,有关有机-过渡金属配合物的三重态发光问题受到人们广泛的关注.这不仅是与电致发光器件效率的提高相关联,同时也是一个在光物理研究中值得深入研究的课题,文章对有机-金属化合物激发态的能级分裂,以及发光三重态亚态的零场-分裂(ZFS)等进行了讨论,对具不同电子构型中心金属离子,例如八面体结构与平面四方形构型结构等与它们光物理行为间的关系进行了讨论.特别对这类体系的发光三重态在自旋轨道偶合作用(SOC)和构型相互作用(CI)的影响下,导致单重态与三重态的混合和促进从最低三重态到基态的发光跃迁进行了讨论.%In recent years, the emission of triplet state of organic-transition metal complex at tracted extensive attentions with the development of OLED devices. It not only concerns with the increase the device efficiency, but also with some problems deeply in the field of photo physics. In this article, the energy level splitting of organic-metallic compounds, and the zero field splitting (ZFS) of emissive triplet state are discussed briefly. Simultaneously, the rela tionship of electronic configuration of centered metallic ions, such as the octahedral and square planar coordination and their photo-physical behaviors are also discussed. Especially, the emis sion state of these compounds, under the influence of spin-orbitalcoupling(SOC) and configu ration interaction (CI) which can induce the admixture of singlet and triplet state, then to im prove the emissive transition from the lowest triplet state to ground state, has also been dis cussed.【期刊名称】《影像科学与光化学》【年(卷),期】2011(029)002【总页数】18页(P81-98)【关键词】有机-过度金属配合物;零场-分裂(ZFS);自旋-轨道偶合;光物理行为;三重态的发光【作者】吴世康;汪鹏飞【作者单位】中国科学院,理化技术研究所,北京,100190;中国科学院,理化技术研究所,北京,100190【正文语种】中文【中图分类】O64自上世纪后期有机-电子学,特别是有机发光二极管(OL ED)得到迅速的发展以来,为提高器件的电-光转换效率和寻找新型三重态发光材料,人们对有机-过渡金属配合物,特别是它们的光物理性能进行了大量研究[1,2].众所周知,化合物的光致发光性质决定于分子轨道(MO)中那些被称为“前线轨道”的性质,分子最低激发态与基态间的跃迁对应其发光.同样,在电致发光过程中,器件的发光也同样取决于其分子轨道的性质,当然,二者激发态形成与“布居”过程有所不同.有机分子在受光激发下,其HOMO轨道上的电子跃迁到LUMO轨道形成激发态,导致其基态与激发态的电子构型不同.基态S0具有π2构型,而激发态π1π＊1的构型则可有单重态(S1)和三重态(T1)之分,而其中的T1态又可分裂为3个亚态(substate).从上述两种构型的电子-电子相互作用考虑列出其能级图,通常可以看到存在两种分裂,一种是单重态-三重态间的能级分裂ΔE(S1-T1),另一种是T1态的分裂,亦即所谓的零场-分裂(ZFS).如下图所示[3].从上图左侧简单的HOMO-LUMO图中可以看到,所有来自π1π＊1的4个态,具有相同的能量,它们是简并的(degenerate).然而从光谱研究知道,化合物分子被激发后,其激发单重态与三重态间的分裂甚大,例如,这里要讨论的配体化合物分子,其分裂能约为104cm-1(～1.24 eV).因此,在考虑与HOMO-LUMO激发相关联的电子-电子相互作用时,就可出现如上图右侧所示的能态图,可看到上述的两种分裂.对目前广泛应用于OL ED的三重态发光有机-过渡金属配合物,例如Ir(ppy)3和Pt(thpy)2等,考察它们的各种分子轨道,以及不同分子轨道间的跃迁,在配合物分子中可以有:以配体-中心(LC)的π-π＊跃迁为特征的激发;以金属-中心(MC)的d-d＊跃迁为特征的激发;金属-配体的电荷转移(MLCT)过程d-π＊为特征的激发……图2列出的是有关金属配合物的HOMO-LUMO能级图,以及它们可能存在的能态模式.图2(a)中列出的为分子单个π、d和π＊的轨道,以及其间可能存在的相应跃迁,如配体分子LC的π-π＊跃迁,金属与配体间的电荷转移(MLCT)跃迁等,这里假设d＊-轨道处于较高的能位,因此在一般情况下不存在d-d＊的特征激发.右图(b)中列出的是与跃迁相关的能态,它包括由MLCT跃迁(1,3d-π＊)形成的单重态与三重态能态,以及由LC(1ππ＊)跃迁形成的单重态与三重态能态.由于三重态存在着3个亚态,因此总共可以得到8个能态,即单重态的1LC和1MLCT两个能态,以及3个3LC和3个3MLCT的亚态.值得注意的是,这些态都受构型的相互作用(CI),以及自旋-轨道偶合(SOC)的作用,即发生了实质上的量子力学混合,其中SOC的作用还引起了三重态的零场-分裂.因此,经过这种混合,列出的这些1,3LC以及1,3MLCT等能态不能再以一种“纯”的三重能态或单重能态来理解.上述的这种因激发态布居而引起的电子-电子相互作用(或在电激励的情况下,电子与空穴的逐步接近,电子与空穴波函数重叠所引起的相互作用)可导致单重态与三重态间的分裂ΔE(S-T)(～104cm-1),这是一种量子力学交换相互作用的结果(其值约为交换积分的2倍).交换积分有如下的表达形式[4]:式中的π和π＊为HOMO与LUMO的波函数,r1与r2代表电子坐标,而r12则为两个电子间的距离.交换相互作用是一种量子力学效应,它与电子波函数的重叠大小相关,因此要考虑其中的自旋相关性.这意味着具有相反自旋取向的两个电子(单重态)有着比具有相同自旋取向的两个电子(三重态)有更多相互接近的机会,而三重态的两个电子则有相互避开的趋势,使三重态的能量较低.通过上面的讨论,可以定性地得到有关交换相互作用和波函数重叠的一些重要结论: 1.随着π和π＊轨道共扼长度的增加,电子在(离域)分子内分布的区域变大,体系的交换积分K值变小.例如,对于有机分子从“苯”到“萘”、再到“蒽”,它们单重态-三重态间的分裂能ΔE(1π π＊-3π π＊)不断降低——从苯[5]的～18000 cm-1(约2.2 eV)降低到萘[6]的～12300 cm-1(～1.5 eV),再降到蒽[6]的10500 cm-1(～1.3eV).2.当分子轨道处于分子内不同空间区域时,分子轨道间的重叠变得很小,其交换积分也相应变小.例如:带有杂原子氧的有机分子——二苯酮的n-π＊跃迁,是从二苯酮中氧原子上的n-电子向π＊-LUMO轨道的跃迁,由于两者处于分子内的不同空间,其单重态与三重态间的分裂能ΔE(1nπ＊-3nπ＊)仅为1750 cm-1(0.22 eV)[7],如图3所示.类似于稠环芳香化合物ΔE值随共轭程度增大而不断减小的现象,也可以在具有不同共轭程度的高分子体系中观察到.如图4所示,随着齐聚物共轭程度的变大,ΔE(S1-T1)值逐步减小,说明其间的波函数重叠的程度也在不断减小.上述现象在有机-过渡金属配合物分子中也可作相应考虑.即:如有小量金属d-轨道或MLCT特征混入到配体中心(LC)态时,会因增大波函数的空间范围而使其交换积分减小,同时,也会引起被扰动的1LC(1π π＊)和3LC(3π π＊)间的单重态与三重态的分裂减小.例如:对于自由配体化合物2-噻吩吡啶(2-H(2-thpy))[9],其分裂能约在104cm-1(1.24 eV)左右,而其金属配合物二(2-噻吩吡啶)钯(Pd(2-thpy)2)[10]的ΔE(1LC-3LC)减小至5418 cm-1.在对有机-过渡金属配合物进行讨论之前,需要简单地对两种最常见的金属离子配位场作一介绍[11].下图左侧(A)为具有Oh对称的八面体配位场d-轨道的分裂,它使中心金属离子从原有能量简并的5个d轨道分为两组,即能量较高的eg和能量较低的t2g.右图(B)则为平面四方形配位,它可看作为八面体结构的上下伸长发生畸变的结果.图6中列出的是八面体与平面四方形两种构型简化了的能态模型,可以看出两者间存在着巨大的差异.在八面体的配位中,包括有配体的3π π＊能级,以及在t2g中d1、d2轨道电子与π＊间跃迁得到的能级1d2π＊和3d1π＊;平面四方形的配位中则包括处于高能位占有轨道与π＊间的电子跃迁,得到单重态与三重态1π＊和3π＊能态,以及低能位占有轨道与π＊间跃迁得到的1,3(dxzdyz)π＊等.需要特别指出的是,不同轨道间的跃迁存在不同的自旋-轨道偶合(SOC)效应,以及不同的零场分裂(ZFS).从图6中可以看出,在八面体构型的条件下,无论是SOC或ZFS 都是较大的,而从最低三重态T1到基态S0的衰减时间也比平面四方形的短,充分说明这种具有八面体构型的发光配合物更适合在OL ED中应用.更为详细的情况,将于下文中做进一步说明.在图1和图2中还可看到,其中的三重态可分裂为3个亚态,这对将在OLED应用的有机-过渡金属化合物颇为重要.由于这一分裂系在零-磁场下发生的,因此被称为零场-分裂[12,13](ZFS).有机分子三重激发态3π π＊的零场分裂,主要是经三重态中两个非成对电子的自旋-自旋相互作用而诱导发生的,由这种相互作用诱导而得的ZFS值约在0.1 cm-1(约1.2×10-5eV)的水平.而对有着较大配体中心3LC态的有机-过渡金属配合物,其3LC态的ZFS值也处于相同量级,例如[Rh(bpy)3]3+[14,15]所测得的ZFS值为0.125 cm-1(约1.55×10-5eV),而Pd(qol)2[16]的也约为0.25 cm-1(约3.1×10-5eV).这些有机-过渡金属化合物3LC(3π π＊)态的ZFS值不易受外来微小扰动的影响,与“纯”的有机分子相类似.但要指出的是,由于金属的存在,它们仍可显著地增大其激发态的辐射和/或非辐射衰减的速度,即SOC的作用仍然有效.例如,它可使激发单重态向三重态的布居增大几个数量级,从而使ISC量子产率接近100%.此外,它也使一些以3LC态为发光机制的有机-金属配合物Pd(thpy)2和Pt(qol)2的ISC弛豫寿命分别快达τISC=800 fs[10]和500 fs[17].更为重要的是,它们T1→S0的辐射衰减速度也比“纯”有机分子快几个数量级,这意味着这类化合物的辐射衰减速度可超过非辐射失活过程,导致其高的发光量子效率.有机-过渡金属配合物的MLCT最低激发三重态同样也存在零场-分裂,其ZFS值的大小可作为这类配合物能否用作发光材料的一个重要量度.对于一种适用于OL ED的发光化合物,其ZFS值应处于10 cm-1(1.2×10-3eV)的水平,更大时更好.上文对图2的讨论中已经指出,存在有MLCT跃迁的体系情况比较复杂,体系中3LC、1LC、3MLCT以及1MLCT各态间的量子力学混合及相互影响,决定其最低三重态的性质,以及其在OLED中得到应用的可能.研究表明,一个化合物当它具有“纯”的3LC发光态时,并不适宜作为OL ED的发光物种,而具有3LC/3MLCT混合态的配合物则是一种很好的候选者.例如,一种主要为π-特征而有d-轨道混入的HOMO轨道,即可有πd→π＊跃迁的混合体系出现,可因金属5d-轨道的存在引起自旋-轨道的偶合(SOC)作用.从图2中就可看到,由前线轨道,如HOMO-1、HOMO、LUMO 等所形成的电子(跃迁)态,以及由存在的各种混合和相互作用所引起的这些电子态性质的变化,包括MLCT的特征、SOC的影响、三重态的分裂、以及辐射衰减的速度等.总的说来,图2中列出的3个轨道模型中存在着两种激发,即相应分子轨道间的MLCT跃迁和LC跃迁.而所构成的8个能态都是通过构型相互作用(CI)和自旋轨道偶合作用(SOC)经受了实质上的量子力学混合,因此,它们也就不能再作为各种“纯”的能级分类.应当指出,上面所讨论的是有机-过渡金属配合物的一种简化模型,但它仍有重要的指导意义,并得到了一些一般性结论:1.图2的HOMO/LUMO模型中,并无单重态与三重态之分,所列出的HOMO-1与HOMO的相对位置,也不能直接预示相应能态的能级次序.从HOMO和HOMO-1的次序似可以建议3MLCT为最低能态,但图中示出的3LC却为最低能态,这可能与HOMO与HOMO-1间的能量差比交换积分间的能差要小有关.2.有机-过渡金属配合物简化了的模型中出现的能态数目仍相当多,如图2中所示,该模型就有两个单重态(1LC、1MLCT)和2×3=6个三重态亚态(3LC、3MLCT)共8个能态之多.3.不同电子构型间通过电子-电子相互作用以及SOC的作用,可诱导8个能态间发生量子力学混合,特别是1MLCT与3MLCT间的SOC作用,以及3MLCT与3LC间的构型相互作用(CI),可大大改变最低三重态的性质.处于最低能态的3LC态零场-分裂为亚态,导致这些态与基态间的跃迁变为允许,从而使发光衰减时间减小,光致发光量子产率增大,并导致发生光谱位移等.从上面的讨论可以看出,要定量地描述这类有机-过渡金属配合物的特征,即使采用了比上述简化模型更为复杂、涉及更多能态的模型体系,也不能认为就完全可行.然而,上述方法仍不失为一种有效的手段,对这类化合物的特征做出某种判断,同时对涉及不同分子轨道的空间分布、最终能态的状况等提供有益的信息,并对它们所具有的某些趋势性变化提供可参考的内容,以此来预测化学结构的变化、电子给体与受体取代基团的引入、共扼长度的变化、配位场强度及氧化还原电位的变动等对其光物理性质的影响.有关这类体系光物理行为定量化的工作主要基于从头算起的方法,如用时间依赖的密度泛函数理论[19.20](TDDFT)或CASSCF/CASPT2程序[21]等.由此所得的有关跃迁能、单重态-三重态振子强度、低阶三重态的数目、以及对ZFS 值的预测等,虽说多数还不能十分信赖,甚至还不能全部测出,但这些计算结果仍对光物理性质变化趋势的了解有所帮助.如果将SOC效应也同时加以考虑,预测将变得更加可信.对这类有重要应用价值复杂分子的理论计算存在一定的困难,如果能找出该类分子的某种结构参数,据此方便地对化合物的物理特性,特别是光物理特性作出某种经验性的次序排列,将大大有利于这类化合物的实际应用.这里指出的ZFS值[ΔE(ZFS)]就是一种可预测有机金属化合物重要光物理行为有价值的参数,它可用以直接显示1,3MLCT(1,3dπ＊)组分在相应三重态中的重要程度.具体地说,如果ΔE(ZFS)值大于1—2 cm-1者,表明该体系三重态亚态波函数与1,3dπ＊组分间存在着一定的关联;特别大的ΔE(ZFS)值则代表在相应三重态中存在重要的1,3MLCT组分.这种不同的关联或混合程度将大大影响三重态的发光,以及其它的光物理行为.图7列出的是处于高阶能态的MLCT对三重态的影响.这里所讨论的有机-过渡金属化合物的发光都是从最低激发三重态T1到电子基态S0跃迁产生的发光,在无自旋-轨道偶合SOC存在时,该跃迁是高度禁阻的,由于第三周期过渡金属化合物的存在,通过SOC作用使最低三重态到基态的跃迁成为可能.SOC作用还能诱导一些其他的重大效应,如三重态分裂为三个亚态,以及提高辐射衰减的速度等,这些后继效应的出现使化合物的磷光量子产率可达100%,而且使化合物的某些其他光物理性质也产生明显的变化.有机-过渡金属配合物最低三重态的发光,取决于三重态T1亚态I、II、III与基态S0间跃迁的特征和允许程度,而这种允许度又受控于处在高阶的1MLCT单重态的参与与否.图7中列出的1MLCT与T1亚态II、III间的短虚线表示其间的关联,而正是这种关联使三重态的两个高位亚态II、III有着较高的单重态混合程度,而最低三重态亚态I 由于不含明显的单重态组分,通常表现为“纯”的三重态特征,于是也就有着较长的寿命[22-24].十分有趣的是,只要有少量的单重态混入3LC(3π π＊)态,更准确地说是有单重态混入到三重态亚态,就可增大后者的辐射跃迁几率.例如配合物Pd(thpy)2的发光衰减时间就可缩短到235μs(平均寿命),其中的τI=1200μs,τII=235μs,和τIII=130μs[25].对于Pt(thpy)2,因它有较大的MLCT混入最低3LC态,致使其衰减时间相对于纯的有机化合物可小6到7个数量级,其发光寿命短到1μs[10].图8中列出了一系列过渡金属配合物的ZFS值,它们相应的化学结构也列出于图9中[19,26,27].从图8所列不同-过渡金属配合物的ZFS值可以看出,配合物ZFS值的变化范围从最小到最大可跨越3—4个数量级.应当指出,图中所列不同配合物的ZFS序列与发光三重态中MLCT组分的增大有着密切关系,亦即配合物的ΔE(ZFS)值小于1 cm-1时,体系主要是以配体为中心的3LC(3π π＊)发光态;而ZFS值处于中间范围时的配合物,其三重态就不再看作为“纯”的3LC态,其原有三重态特征3LC(3π π＊)已显著地被1,3dπ＊的混入所扰动;至于那些ZFS值大于50 cm-1的配合物,通常可被称为3MLCT发光化合物.常见的MLCT发光化合物有在上面列出的诸多配合物中可发现一个有趣的事实,即在含Pt(II)的准-平面四方形构型的有机金属化合物中,未发现具有大的ΔE(ZFS)值的(如大于40 cm-1)配合物,而对于准-八面体,如Re(I)、Os(II)、Ir(III),甚至第二周期过渡金属Ru(II)的配合物,它们都有很大的ΔE(ZFS)值,这一现象可以用后者易于发生强的SOC效应加以解释.对于准-八面体的配合物,如图9中所列出的配合物[31],其最低三重态3MLCT(3dπ＊)可以和t2g系列中不同d-轨道电子跃迁形成的单重态1MLCT(1dπ＊)间经历强的SOC作用,同时也与那些具有扭曲Oh对称的化合物最终轨道能量相接近.但对于准-平面四方形构型的Pt(II)配合物,其最低1MLCT和3MLCT态均来自相同的dz2→π＊激发,而这些有着相同起始态间的SOC作用通常可以忽略.这是由于发生这种有效SOC的一个重要条件是在作用的二态之间需有不同的起始d-轨道存在,对于平面四方型的配合物,如不考虑处于高能位的dz2为起始激发的能量轨道,其候选者应是dxz和dyz轨道,它们在能量上则与dz2相远离,如从轨道的能量上加以估计,其间的差可以达到4000 cm-1(0.5 eV).因此,这一用于支配SOC有效性的能量分母,就要比八面体化合物的大许多,致使SOC的作用效果变差.对于这些有关八面体以及平面四方形构型的1,3MLCT相互作用的内容,均列于前面的图5中.另一点值得注意的是:MLCT与LC的混合途径,除了SOC外,还有所谓的构型相互作用(CI)作用途径.这种CI也是一种电子-电子间的相互作用,它能诱导3MLCT(3dπ＊)与3LC(3π π＊)的混合,而这种混合还可修饰最低的LC三重态(3π π＊),使它能与3dπ＊间发生间接的混合.因此,准-八面体的SOC途径与准-四面体配合物间的差别不仅只是3MLCT(3dπ＊)态所表现的,还在3LC(3π π＊)态上有所反映,准-八面体的ΔE(ZFS)值和辐射衰减速度都比准-平面四方形大.这种特殊的偶合途径使准-八面体发光物种有着相对短的发光衰减时间,使它比平面四方形材料能更好地应用于OLED之中.从前面列出的大量不同有机-过渡金属配合物的ZFS值可以看出,ZFS参数的大小范围可有2000倍之差,应当说这是由于LC的最低三重态3π π＊与MLCT单重态和三重态间的SOC相互作用而引起最低三重态亚态波函数发生了重要变化的结果.对于多数化合物来说,其最低的发光三重态都是以LC(π π＊)为其“原始能态”,而其ZFS值的增大则是上述不同相互作用的影响使三重态不断增大了与MLCT组分间关联的结果.大的ZFS值还可使原来简并的三重态发生较大的分裂,使共振式的转移成为可能,进一步提高了跃迁的允许程度.从图8中还可看到,准-平面四方形构型的金属配合物(如含Pt(II)配合物)的ZFS值均小于40 cm-1,有关它们的发光问题,可结合下列Pd(thpy)2和Pt(thpy)2配合物的发光状况加以说明,二者显示出十分不同的T1态与MLCT态的特征结合.上面指出的所谓SOC有效性,对于这类化合物的光物理性质十分重要,有效的SOC对增大态与态间的扰动起到重要的作用.Pd(II)和Pt(II)化合物所涉及的4dπ＊和5dπ＊SOC常数不同,因此,两种化合物的光物理行为有明显差别[10].图11中列出了这些化合物的能态变化特征,并与典型的有机分子的低阶3π π＊和1π π＊态相比较. 从图11可以清楚地看出,与纯的有机化合物相比较,配合物因MLCT的混入使单重态-三重态的分裂变小.即从配体有机分子的ΔE(S1-T1)～104cm-1量级(约1.24 eV)减小到有机-金属化合物Pd(thpy)2的5418 cm-1,其主要原因可认为是有小量MLCT(4dπ＊)混入到LC(π π＊)所致.对于有重要MLCT(5dπ＊)混入3LC(π π＊)态的Pt(thpy)2配合物,其电子波函数可扩展到配合物所涉及的配体与金属两者较大的空间中,因此,其ΔE(S1-T1)值降低到更低的3278 cm-1水平.从图11还可以看到,随着SOC诱导所引起的MLCT扰动的增大,三重态的零场-分裂(ZFS)从有机配体分子的0.1 cm-1增大到Pd(thpy)2的0.3 cm-1,到Pt(thpy)2增大至16 cm-1;相应的磷光发射寿命也从有机化合物的10 s减小到Pd(thpy)2的200μs,再到Pt(thpy)2的1μs;而系间窜越(ISC)寿命也同样从100 ns降低到800 fs,再到50 fs.所有这些光物理行为的变化都与“旋-轨偶合”的诱导增大了最低三重态中MLCT的扰动有关,而其中ZFS的数值变化则为一最直观的指标,可用于表示有机-过渡金属配合物作为三重态发光材料的优劣程度.最后要提到的是有关ZFS值的测定,除ESR方法外,最常用的方法是采用低温下激光激发的光学测定法,采用低温与激光的目的是为了消除光谱的不均匀加宽.图12列出的是在不同温度下所测得的结果[32].在常温下测定时,会因声子效应而引起对光谱的掩盖.从图12可以看到,随着温度的下降,这种掩盖效应可不断减小,图左侧的ZPL为零声子线(Zero Phonon line,ZPL),因此,一般的测定均应在零声子线的温度以下进行.光学法测定的装置[33]如图13所示.图中1为样品,2为样品的氦冷冻装置,3为氩离子激光器,4为压力扫描Fabry-Perot干涉仪,5为DFS-12光谱仪,6为光电倍增管,7为光子计数装置,8和9均为电磁快门,10为电子快门的控制系统,11为频率选择干涉仪.有机分子三重态能级的三重简并,严格地讲,在无外磁场存在下因自旋-自旋及自旋-轨道相互作用以及周围晶体场的影响而消失.在零场下自旋亚层(sublevel)的分裂可通过ZFS参数的D和E加以表征,但分子三重态的主要参数ZFS值很小,通常在0.01—0.1 cm-1量级,它可通过ESR法予以测定.采用光学光谱法来测定ZFS时,会因这种光谱的带宽大于所测定的ZFS值约几个数量级而存在困难,因此用光谱法来观察ZFS,直到上一世纪的70年代才得以实现.从图14中可以看到,只有当温度下降到1.35 K时方能对三重态亚态I和II加以分辨,并测出其能差[34].在前言中已经指出,近年来随着电致发光器件的长足发展,有关三重态发光问题得到广泛关注,一系列高水平的综述性论文相继出现,如文献[3]和[35]等.本文就是在这些文章的基础上对有关有机-过渡金属配合物的三重态发光问题,特别是有关三重态的零场-分裂(ZFS)与化合物光物理性质的关系进行简要的介绍.采用这种以ZFS值的大小排列的方法(见图8),可对在不同场合下选择应用的有机-金属发光化合物带来很大的方便,而且这种似乎是经验性的方法事实上也存在着深刻的理论依据.文章还对有关ZFS值的测定方法做了简单的介绍.需要特别指出的是,在有机-金属配合物的三重态发光问题中,尚有许多不够清晰的问题,需要我们进一步的努力.【相关文献】[1] Baldo M A,Thompson M E,Forrest S R.Phosphorescent materials for application to organic light emitting devices[J].Pure A ppl.Chem.,1999,71:2095.[2] Adachi C,Baldo M A,Thompson M E,Forrest S R.Nearly 100%internal quantum efficiency in an organic light-emitting device[J].J.A ppl.Phys.2001,90:5048.[3] Yersin H,Finkenzeller W J.Triplet emitters for organic light-emitting diodes:basic properties,inHighly Ef f icient OL EDs with Phosphorescent Materials[M].Ed.Hartmut Yersin,WILEY-VCH Verlag GmbH&Co.Weinheim,2008.[4] Klessinger M.Elektronenstruktur Organischer Molekule[M].VerlagChemie,Weinheim,1982.[5] McGlynn S P,Azumi T,Kinoshita M.Molecular S pectroscopy of the TripletState[M].Prentice-Hall,Englewood Cliffs,New Jersey,1969.[6] Turro N J.Modern Molecular Photochemistry[M].Benjamin-Cummings,MenloPark,Calif.1978.31.[7] Mataga N,Kubota T.Molecular Interactions and Electronic S pectra[M].Marcel Dekker,NewYork,1970.187.[8] Kohler A,Bassler H.Triplet states in organic semiconductors[J].Materials Science and Engineering R,2009,66:71-109.[9] Maestri M,Sandrini D,Balzani V,Chassot L,Jolliet P,A.von Zelewsky.Luminescence of ortho-metallated platinum(ii)complexes[J].Chem.Phys.Lett.,1985,122,375.[10] Yersin H,Donges D.Low-lying electronic states and photophysical properties of organometallic Pd(II)and Pt(II)compounds.Modern research trends presented in detailed case studies in:Transition Metal and Rare Earth Compounds.Excited States,Transitions and Interactions,Vol.II S pringer-Verlag Berlin,ed.Yersin H.,Top.Curr.Chem.2001,214:81.[11]Jolly W L.Modern Inorganic Chemistry[M].McGraw-Hill,New York,1984.[12]Yersin H,Humbs W,Strasser J.Characterization of excited electronic and vibronic states of platinum metal compounds with chelate ligands by highly frequency-resolved and time-resolved spectra.Electronic and Vibronic S pectra ofTransition Metal Complexes,Vol.II S pringer-Verlag Berlin,ed.Yersin H.,Top.Curr.Chem.1997,191:153.[13] Yersin H,Humbs W.Spatial extensions of excited states of metal-organicPt(II)compound in a Shpolskii matrix[J].Inorg.Chem.,1999,38:5820.[14]Glasbeek M.Excited state spectroscopy and excited state dynamics of Rh(III)andPd(II)chelates as studied by optically detected magnetic resonancetechniques[J].Top.Curr.Chem.,2001,213:96.[15] Komada Y,Yamauchi S,Hirota N.Phosphorescence and zero-field optically detected magnetic resonance studies of the lowest excited triplet states of organometallic diimine complexes.1.Rhodium bipyridine and rhodium phenanthrolinecomplexes[Rh(bpy)3]3+and[Rh(phen)3]3+[J].J.Phys.Chem.,1986,90:6425.。
基于CASSCF参考函数的块相关耦合簇方法对烷烃中单键解离势能面研究
联系人简介 ：黎书华 ，男，博士，教授，博士生导师 ，主要从事理论与计算化学研究．Ｅ ｍ ｉ ｓｕ ｕ＠ｎｕｅ ｕｃ － ａｌ ｈ ｈａ ｊ．ｄ ．ｎ ：
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不同计算模型方法比较
性能： HF << MP2 < CISD< MP4(SDQ) ~CCSD< MP4 < CCSD(T)MNDO:低估了激发能，活化能垒太高。
键旋转能垒太低。
超价化合物以及有些位阻的体系算出来过于不稳。
四元环太稳定。
过氧键太短，C-O-C醚键角太大，负电型元素间键长太短，氢键太弱且太长。
PRDDO:参数化到溴和第三周期金属。
适合无机化合物、有机金属化合物、固态计算、聚合物模拟。
目标数据是从头算结果。
整体结果不错，偶尔碱金属的键长有误。
AM1:不含d轨。
算铝比PM3好，整体好于MNDO。
O-Si-O不够弯、旋转势垒只有实际1/3，五元环太稳定，含磷化合物几何结构差，过氧键太短，氢键强度虽对但方向性错，键焓整体偏低。
SAM1:开发AMPAC公司的semichem公司基于AM1扩展出来的，明确增加了d轨道。
由于考虑更多积分，比其它半经验方法更耗时。
精度略高于AM1和PM3。
振动频率算得好，几乎不需要校正因子。
特地考虑了表达相关效应。
PM3:比AM1整体略好一点点。
不含d轨。
氢键键能不如AM1但键角更好，氢键过短，肽键C -N键旋转势垒太低，用在锗化合物糟糕，倾向于将sp3的氮预测成金字塔形。
Si-卤键太短。
有一些虚假极小点。
一些多环体系不平，氮的电荷不对。
PM3/MM:PM3基础上加入了对肽键的校正以更好用于生物体系。
PM3(TM):PM3加了d轨，参数是通过重现X光衍射结构得到的，因此对其它属性计算不好，几何结构好不好取决于化合物与拟合参数的体系是否相似。
PM4:没做出来或者没公布。
PM6:可以做含d轨体系。
最适合一般的优化、热力学数据计算。
Bi及之前的元素都能做。
比其它传统和新发展的半经验方法要优秀。
但也指出有不少问题，比如算P有点问题，算个别势垒有时不好，JCTC,7,2929说它对GMTKN24测试也就和AM1差不多，卤键不好。
PM6-DH1/DH2:PM6基础上加了色散、氢键校正项，适合弱相互作用体系。
基于自洽聚类分析的复合材料及结构多尺度力学行为
•引言•自洽聚类分析方法•复合材料多尺度力学行为目录•复合材料结构设计•工程应用案例分析•研究结论与展望复合材料与结构在工程领域的应用日益广泛，如航空航天、土木工程和生物医学等。
针对复合材料及结构的力学行为进行准确预测和理解具有重要价值。
多尺度分析方法能够综合考虑微观到宏观的尺度效应，为复杂材料和结构的性能预测提供有效途径。
研究背景与意义3. 如何实现大规模计算的高效算法。
2. 如何处理不同尺度之间的耦合效应；1. 如何建立准确的材料和结构模型；自洽聚类分析(SCCA)是一种先进复杂材料的不均匀性和各向异性。
SCCA在复合材料和结构多尺度分析中的应用已取得了一些成果，但仍存在以下挑战研究现状与挑战30203011. 针对复合材料，建立精确的SCCA模型，并开发高效算法实现大规模计算；022. 结合实验研究，对所建立的模型进行验证和修正；033. 将建立的模型应用于实际工程结构的多尺度分析，探讨其力学行为和失效机制；044. 通过对比分析，评估所提出方法的优势和局限性。
方法原理与流程聚类分析原理01方法流程02适用范围03算法框架针对算法性能和精度问题，可采用以下优化措施，包括选择合适的距离度量方法、优化迭代算法、引入正则化项等。
算法优化编程实现算法实现与优化验证方法应用领域实际应用案例方法验证与应用201401030204复合材料细观结构与性能关系基于连续介质力学理论和有限元方法，可以对复合材料宏观尺度模拟可以揭示复合材料的整体变形、损伤和破复合材料宏观尺度力学行为模拟1复合材料跨尺度力学行为耦合分析增强相选择界面优化层叠结构030201结构设计原理与方法材料组合优化根据不同材料的性能特点，进行合理搭配和优化，以实现整体性能的提升。
多尺度结构设计从细观、宏观等多尺度角度出发，对结构进行优化设计，提高复合材料的综合性能。
实验研究通过实验验证和反馈，对结构设计进行修正和完善，实现性能的最佳化。
结构优化与性能提升01功能导向设计02多学科交叉03系统性优化结构功能一体化设计总结词广泛用于航空航天领域，具有高强度、轻质、耐高温等优点，有效提升航空器的性能和安全性。
量子化学
量子化学简介量子化学基于非相对论薛定谔方程,作了博恩－奥本海默近似.薛定谔方程是H totalΨtotal=EΨtotal其中E=系统的容许能(系统通常是一个分子).Ψtotal=所有电子和原子核以及它们自旋位置的函数.H total=一个微分运算符,它源于经典哈密顿函数H(p,q)=E,函数中所有的动量p i用(h/2πi)∂/∂q i 替代,只要p和q在直角坐标系中.如果你不喜欢用直角坐标系,那么您可以构造一个矫正的量子力学H.标准的方法是用"波多尔斯基法"在任意坐标系统中构造哈密顿函数.在一个无外磁场的真空条件下,一个原子核和电子系统忽略磁场相互作用,用原子单位:H total=-1/2∑i2/M i-1/2∑n2＋∑Z i Z j/︱R i-R j︱-∑Z i︱R i-r n︱+∑l/︱r m-r n︱∇∇博恩－奥本海默近似值忽略了一些电子和原子耦合的条件,所以可以写成:Ψtotal(R,r)=Ψnuclei(R)Ψelectrons(r;R)≅H total T nuclei(P,R)+H electrons(p,r;R)(忽略了在原子核的动量P和H electrons的关系)然后解薛定谔方程求电子(固定原子核).我们根据这些固定的原子核的位置R来计算能量,就是V(R):H electrons(p,r;R)Ψelectrons(r;R)=V(R)Ψelectrons(r;R)现在我们回到总哈密顿函数,对所有电子的位置r积分,忽略所有f复杂的条件,从而得到了一个关于原子核的近似薛定谔方程:≅<Ψelectrons(r;R)︱H total︱Ψelectrons(r;R)>H nuclei=T nuclei(P,R)+V(R)两个近似薛定谔方程都还很难得到准确的解(两个方程是在3N particles坐标中的偏微分方程),所以我们构造更加近似的方程.V nuclei通常被展开到关于一个固定值R o的R的二阶偏导:≅+1/2ΣΣ(∂2V/V/∂∂R i∂R j)(R i-R oi)()(R R j-R oj)V nuclei V nuclei(R o)+1/2然后分别处理平动,转动,和振动条件下的数据,忽略结合不同坐标中复杂的条件.在这种著名的"刚性转子谐振子(RRHORRHO)")"近似值中,解析式就是所谓的能量本征值相应的配分函数Q,在P.Chem.text文件查找.近似值法有一个重要的优点就是我们解薛定谔方程不需要在意电子有很多R:我们只需要找到一个固定值R o,然后在R o点计算能量和二阶导数.很多计算程序大都能在算出V的同时就10=3030能计算V的一阶导数和二阶导数.例如,一个最大的计算包含3个问题,10个原子和3*10=的坐标R i,在Athena机上算V nuclei(R o)花了大约半分钟,算30*30=900二阶导数(∂2V/V/∂∂R i∂R j)只花了13分多.如果你想简单地通过有限差分法来算的话,得到同样的结果可能需要15个小时(而且可能因为有限差分法的数值错误,造成结果偏差更大).以前分析一阶导数是用来加速求固定值R o(例如,平衡结构).结构和二阶导数通常都是用某一个近似值算出的,但是最终能量V(R o)是更精确的(因为热数据和速率数据对V(R o)中的错误是最敏感的,即使很差的近似值通常也会得到接近于正确的结构图和频率).所以...只要有一个合适的V的二阶泰勒展开式近似,就能得到不错的效果."大振幅位移"的分子和过渡态(例如,泰勒展式不充分)问题就比较多了,要在一个灵活的研究范围里处理它们.幸好有很多常规的二级V系统,它们的RRHO近似是精确的.但是我们怎样在任意几何结构R中计算V(R)呢？我们想解H electrons(p,r;R)Ψelectrons(r;R)=V(R)Ψelectrons(r;R)在真空,无电场,忽略磁场效应的条件下H electrons=-1/2∑n2＋∑Z i Z j/︱R i-R j︱-∑Z i︱R i-r n︱+∑l/︱r m-r n︱因为电子是不可区别的费密子,任意两个电子的置换必须改变Ψelectrons的符号(由于元素周期的原因,这是一个非常重要的约束条件叫作泡利不相容原理,)再加上由于自旋有一不错的量子数所以我们得到更多的系统规定参数:S2|Ψelectrons>=S(S+1)|Ψelectrons>S z|Ψelectrons>=M|Ψelectrons>我们用一种形式写Ψelectrons以保证满足泡利不相容原理:Ψelectrons(x1,x2,x3,…xN)=ΣC m1m2m3…mN|Φm1(x1)Φm2(x2)Φm3(x3)…ΦmN(x N)|符号|….|意思是构造校正反对称"斯莱特行列式"."分子轨道"Φm(x1)是一个电子的自旋坐标和位置的标量函数.通常被写作"原子轨道"的和χ:Φm(x,y,z,s)=|S z>ΣD mnχn(x,y,z)在和原子有关的电子坐标系中原子轨道大多数总是高斯型和的形式位于多项式中一个原子的中心:χn(r)=ΣN n1exp(-αn1|r-R i(n)|2)P1(r-R i(n))这里应用了一些原子轨道的常规组,把多项式隐藏成某些选择α的命令；这些叫做"基组",像"6-31G*","TZ2P","cc-pVQZ".一般的程序是挑选基组中的一个,然后改变C和D来找到一个Ψelectrons的近似值尽可能接近的解薛定谔方程.如果你的基组与真实情况的重叠度很好,那么只要改变一点C和D你将得到精确的结果.否则,有一个经典的变化定理说可以通过一个估算的(很复杂的多维)积分来计算E相应的任意Ψelectrons近似值,一直算到最低的E.所以关键就是使C和D最小化:E[Ψ]=E(C,D)=<Ψelectrons|H electrons|Ψelectrons>/<Ψelectrons|Ψelectrons>积分的估值需要O(N basis3)操作.(因为高斯型函数允许积分被分析计算,所以在这里可以应用)标准状况下基组的每个原子可以包含15个原子轨道(除了H原子不需要这么多以外),可以改变(15*N atoms)2的系数D mn.可能系数C的数特别大,像N basis和N electrons相乘,所以完整的展开几乎不可能.通常人们不是不愿意改变C,而仅是不愿意独自改变一小部分C,来减少参数的数量.但是在允许改变C的同时,应该说明事实上不同的电子之间也是相互影响的:当一个电子靠近原子核,其它的电子可能要远离原子核.关键的问题是我们要找到一个3*N electrons变量的近似函数.为了解决这个问题人们提出了"密度泛函理论(DPF)",其中用电子密度的近似函数来代替波函数Ψ.这种泛函数的本质是从电子的相互作用中获得最大的影响.大多数常见的密度泛函理论解到最后方程中不存在变量C,所以只需要改变D来进行函数值最小化:E[ρ]=E(D)密度泛函理论计算法通常很经济,计算中用到的E[ρ]仅是近似值,是限制计算结果精确度的主要原因.幸好我们用的现代泛函数已经十分的精确了(标准错误～4kcal/mole).前不久Kohn因为发现了密度泛函理论获得了诺贝尔奖.近似值都有名字,下面是一个术语表:半经验(MOPAC,MNDO,AM1,PM3):改变D,只用经验的估值而不是真的去积分.非常经济,但是只对于一部分分子才够精确,而且这部分分子必须与得到经验估值的分子相似才行.密度泛函理论(B3LYP,BLYP,PW91):经验值用得少,要比半经验法更可靠.CPU:经济的,和HFO(N3)一样.出错～4kcal/mole(精确度可以和MP2媲美而且更经济).对于结构学,二阶导数来说更好的方法是先试V(R o).HF(aka Hartree-Fock,SCF):只有一个C非零,改变D CPU:经济的O(N3)出错～15kcal/mole MP2,MP4(aka Moller-Plesset,MBPT):先改变D,然后通过微扰理论调整C得到数值(为了节省CPU,不要随意改变C的).MP2:中等CPU:O(N5),出错～5kcal/moleCI,CISD(组态相互作用):先改变D,固定D不变,然后改变C的多一点.昂贵的,不处理更多任务的话,CCSD法更好.MCSCF,CASSCF:同时改变一个C和所有D的有限组.昂贵的,更好的帮助我们了解能量有可比性的几个电子的状态.专业用户需要选择哪个C改变.CAS-PT2:用CASSCF来确定D和一部分C,然后微扰理论确定更多的C.没有CASSCF的昂贵.有时效果很好,但不稳定.MRCI(多方面参考CI):通过CASSCF或MCSCF来确定D和一部分C,固定它们不变,然后让许多的C改变.很昂贵,对小的系统来说非常精确.CCSD,CCSD(T),QCISD(耦合簇)改变D,固定它们,然后改变很多C,但是约束某些C之间的联系.也就是有效地用一个更长的展式,而不是增加可校正参数的数量.这种约束迫使结果"量值一致".也就是,被同时计算的两个分子与被分别计算的两个分有相同的能量.昂贵,通常很精确.外推法("合成法"):G2,G3,CBS-q,CBS-Q,CBS-QB3,CBS-RAD根据一些方案,用不同量值的基组运行一系列以上计算.所有计算的结果被外推成一个真实V(R)的估值.这种方法比CCSD或MRCI用的CPU时间更少,同时也有极好的精确度.但是,多重的步骤也为出错提供了更多的机会.现在我最喜欢的方法是CBS-QB3,我急切地期待卫斯里的彼得森组对CBS-QB3下一代的开发.精确度:通常为1-2kcal/mole符号方法1/基组1//方法2/基组2意思是"用方法2和基组2计算几何结构,然后在此基础上用方法1和基组1计算能量."如果没有说明,二阶导数的计算也用方法2和基组2.当你在解释说明你做的数据时,所用的方法(例如,B3LYP,MP2,CCSD(T))和基组都必须详细说明.使所有看到说明的人都能重复你的计算并且得到相同的的结果.等键反应可以看到,计算中用了很多近似值,导致计算结果与实验结果不同,绝对能量的计算也经常出现严重的错误.但是,计算相似分子的差分要比算绝对能量更精确了.所以如果你想得到某种物质X精确的焓值,那么用这种方法:1)找到一个反应X+A=B+C A,B,C的焓已知,而且反应物和产物相似(例如,化学键类型的数量).反应式两边的物质越相似,得到的结果越精确,理想的反应热将是零.2)在X,A,B,C的平衡几何结构上,用同样的量子化学方法和基组计算能量.由此继续计算理论ΔH rxn3)ΔH f(X)isodesmic=Hf(B)expt+Hf(C)expt-ΔH f(A)expt–ΔH rxn theor遗憾的是,用同样的方法改善过渡态能量的精确度是困难的,因此很少用公认的系统来比较.一些注意事项1)优化(SCF/HF/DFT/CASSCF/MRSCF)问题需要解D,解是非线性的而且有多重解,只有一个是我们想得到的(通常想要得到最低能量的解).所以可能解到最后剩下一个不正确的波函数,也可能它符合一个电子的存在态.如果这种情况发生,在高斯型中有很多工具会帮你指出来.2)存在低态电子(接近于基态)的系统中,大多数的量子化学方法有问题(收敛,精确性).在这些情况下,有时计算出的数是完全对的,有时是错的.尤其对于过渡态来说这是一个问题,在系统中存在一些孤对电子.如果必须研究这些系统的话,应该寻求专家的帮助.3)很多分子本身有多重的构造(V(R)中的局部最小值),有时存在多重鞍状点可能与过渡态混淆.看一看你的结构,如果不是你所期望的,继续研究.在一个足够好的分子结构中即使在确定初值上多做一些努力也是值得的.另外结构－优化算法可能占用和浪费很多CPU的时间去作无用功.如果你遇到这方面的问题,可以约束一些坐标使得优化更容易.4)对于基本系统和开放系统,比较计算结果<S2>和理论值S(S+1).如果差距很大,可能还有其他的问题没有考虑到.有时你可以用"限制"法像ROHF和RMP2,或者自旋投影法来解决"自旋混乱"问题.5)同一个问题有很多不同的解法,有时结果也是很微妙的.把你自己算法的计算结果和其他人不同算法的结果核对是一个好主意.如果结果相同,那么你就应该确信你的结果是正确的.。
CASSCF活性空间的选择-How to Select Active Space for Multiconfigurational Quantum Chemistry
How to Select Active Space for Multiconfigurational Quantum Chemistry?V ALERA VERYAZOV,PERÅKE MALMQVIST,BJÖRN O.ROOS Department of Theoretical Chemistry,Lund University,P.O.B124,S-22100Lund,SwedenReceived8November2010;accepted17January2011Published online25April2011in Wiley Online Library().DOI10.1002/qua.23068ABSTRACT:Björn Roos is one of the pioneers in the development and usage of multiconfigurational methods,in particular,the complete active space self-consistentfield method and the perturbational complete active space perturbation theory through second order.To perform multiconfigurational calculations using these methods,a set of active orbitals must be selected,and the success of the methods depends on the choice of this set. This is not only sometimes easy but also sometimes difficult,especially for use of the more recent RASSCF and RASPT2methods(which use a“restricted active space”rather thanthe complete one).Although an automated procedure for selecting the active orbitalswould be a preferable solution,this does not seem feasible yet.An account of the problemis given,with examples and some approaches that usually work.©2011Wiley Periodicals, Inc.Int J Quantum Chem111:3329–3338,2011Key words:ab initio quantum chemistry;multiconfigurational methods;RASSCF; RASPT2;active orbitals1.IntroductionF or realistic modeling of chemical system,elec-tron correlation is usually important.For ground state systems,modern density functional theory(DFT)is not very demanding on computer resources and can give good accuracy in many cases.Correspondence to:V.Veryazov;e-mail:valera.veryazov@ teokem.lu.seContract grant sponsor:Swedish National Science Foundation (VR).Contract grant numbers:621-2010-5008,239-2009-6797.However,molecules including transition metals, lanthanides,and actinides usually require a mul-ticonfigurational treatment.Also bond dissociation and processes involving excited states and radicals usually need such methods,and the additional com-plexity of codes and computations not only increase the amount of computer time and other resources but also make the preparation of the calculation much more difficult for the user.Björn Roos not only pioneered several of the most used computational methods of this sort but also tried to formulate rules and approaches that alleviated the task of performing such calculations.VERYAZOV,MALMQVIST,AND ROOSThis work is written by two of us(P.Å.M and V.V) based on previous work in collaboration with Björn before his death,and we thereforefind it proper to include his name in the list of authors.2.The CASSCF and CASPT2MethodsThis article concerns the proper selection of active space in the methods complete active space self-consistentfield(CASSCF),the extension RASSCF (same,with restricted rather than complete active space),and CASPT2and RASPT2,which adds dynamic correlation lacking in the CASSCF or RASSCF calculation,computed by second-order per-turbation theory using a CAS(or RAS)wave function as the unperturbed wave function.These methods are assumed familiar to most read-ers,and we will describe only such aspects that are pertinent to the discussion.For details,please refer to the original publications[1–4].We use the Molcas program package[5],but the discussion is expected to be relevant also when these methods are used in other program packages.Alternative methods, for example,the multiconfigurational perturbation methods[6],are not used by our group,but are sim-ilarly dependent on selection of a good set of active orbitals.There are emerging methods that can extend considerably the size of the active space,such as the density matrix renormalization group(DMRG) method[7],where the selection of active orbitals may become redundant,but which are still at an experimental stage,and little is known about their usefulness.The CASSCF method is an multiconfigurational SCF(MCSCF)method,which implies that the wave function contains terms,which are configuration state functions obtained by populating the orbitals in different ways.In CASSCF,the user specifies the number of inactive and active orbitals,the number of electrons,and total spin of the wave function.The wave function will contain all possible configuration functions generated by keeping the inactive orbitals fully occupied and distributing the remaining elec-trons in all possible ways that are consistent with the specified spin(and possibly spatial)symmetry. If there are N I inactive orbitals,these are obviously populated by2N I electrons,which are not treated as correlated.Assume there are N A active orbitals to be populated by the remaining n A electrons.The configuration state functions(CSFs)are,in our pro-grams,spin-coupled according to the prescriptions laid down by Shavitt[8]in the so-called graphi-cal unitary group approach(GUGA).The number of such configuration functions is given by Weyl’s formula,N CI=2S+1N A+1N A+1n A2−SN A+1n A2+S+1This number is a polynomial in N A of degree n A, for N A>n ually n A is chosen to be roughly equal to N A,and the number of terms in the CI expansion is growing very rapidly beyond the correlation of12 electrons in12orbitals,even if larger expansions can sometimes be tolerated.Not only for transition metal complexes,in par-ticular,with more than one metal ion,but also for large organic molecules,with many multiple bonds and/or several,aromatic rings,one prefers to have active spaces much larger than could be afforded in a CASSCF.A way to accomplish this is to introduce restrictions in the allowed occupation of selected sets of orbitals.Arbitrary restrictions on the configura-tions included in the CI expansion can in principle be allowed,but the efficiency of the CI solver would go down drastically,and the coupled problem of opti-mizing the orbitals and the CI coefficients is known to become very difficult,and often impossible in practice.In recent years,a bottleneck to the multiconfig-urational approach to quantum chemistry has been removed with the use of so-called Cholesky decom-position,replacing the earlier use of explicitly com-puted integrals on disk[9].For such systems,our earlier approaches in the selection of active spaces can become untenable.The programs can easily han-dle CI expansions with up to a few million terms, but this still allows only around14active orbitals, if the preferred choice is to be followed,namely to have most of the active orbitals paired,where each pair consists of one strongly occupied orbital and one correlating,almost empty one.Typical exam-ples would be fairly extended systems with many rings or conjugated bonds,or complexes,for exam-ple,enzyme models with more than one transition metal atom.3.The RASSCF and RASPT2 ExtensionsSometimes we and others have experimented with restrictions based on a division of active orbitalsSELECTION OF ACTIVE SP ACE FOR MULTICONFIGURA TIONAL METHODSinto a few subspaces,in particular the so-called RASSCF approach[2,10].The active orbitals are then classified as“RAS1”orbitals,which are fully occupied in all the CI terms with the exception that at most a predefined maximum number of elec-trons can be excited out from these orbitals;“RAS3”orbitals that are always empty except for a prede-fined maximum number of electrons being allowed to use these orbitals.The“RAS2”orbitals are those where no additional restrictions have been made. Such a calculation defines a fairly large number of possible CI expansions,including,for example, the conventional multireference configuration inter-action with single and double replacements(MR-CISD)from a complete reference but with orbital optimization.The hope is that such orbital-based restrictions will allow calculations with less capri-cious convergence properties than a completely general MCSCF.In this article,we will note the shorthand“/N1/N2/N3/”for a RASSCF calcula-tions having N1orbitals in the RAS1space,and so on.Most calculations would then fall into the cat-egory of allowing at most two holes in RAS1and two electrons in RAS3is and called an“SD”-type RASSCF.More elaborate notation may be needed in general,but this will do for the majority of calculations.The larger active space admitted by the RASSCF is not enough to be able to dispense with dynamic correlation,and so the RASSCF calculation would usually not be worthwhile unless the wave func-tion could be used as starting point of a perturbative correction,similar to the way CASPT2is used“on top of”a CASSCF reference wave function.With the RASPT2method[11],we have tried to do this using precisely the same type of approach as for CASPT2. However,it should be noted that CASPT2excludes double excitations within the active space.This is justified since the excluded terms do not interact with the root function.However,in RASPT2such terms should generally be included.To do so not only would take some quite complicated programming but also would add a lot of computational burden to the RASPT2,which would negate the intended improvements.Such terms have therefore been left out,and this is reasonable only if the RASSCF wave function is a good approximation to the unre-stricted CASSCF.In other words,the RAS restrictions should only act to discard what has been termed the “deadwood”of the complete active space.A sim-ilar method,described by Celani and Werner[12], includes such terms.4.Björn’s Rules:Advice on Selecting Active SpaceThere are two problems to solve:to decide on how many active orbitals to have in each symmetry and then to select a good set of actual starting orbitals.In recent Molcas workshops,Björn Roos formulated a set of general advices on what could be called prime candidates for active orbitals.4.1.MAIN GROUP ATOMS•For each Li,B,and C atom,choose2s and2pactive(four orbitals).For N,O,and F,choose2p(three orbitals).•A molecule,such as S3O,which has manylow-energy conformations,may need12activeorbitals(16electrons in12orbitals).•CH bonds can often be left inactive.A moleculesuch as butadiene will need12electrons in12active orbitals,if all CC bonds could be broken.•A long alkyl chain with an active end groupneeds active orbitals only at the active end.4.2.EXCITED STATES OF PLANARUNSATURATED MOLECULES•For eachπbond,use twoπ-orbitals active,ifpossible.Else,select by energy.The necessaryorbitals also depends on how many valencestates to compute.•A set of Rydberg orbitals is needed,if any statesof Rydberg character are included.In general,a single set of specially devised basis func-tions is preferable,rather than additional basisfunctions on each atom.4.3.TRANSITION METAL COMPOUNDS•For the atoms from Cr to Cu,one needs toaccount for the double shell effect,at least ifthe d-orbital occupation changes in the processstudied.•Second and third row atoms do not need anextra d-shell.•Generally,all orbitals of d-character should beincluded.For example,a10-in-10active space isneeded for all the molecules Cr(CO)6,Fe(CO)5,and Ni(CO)4.•High oxidation numbers need more activeorbitals,because bonds become very covalentVERYAZOV,MALMQVIST,AND ROOS(large charge transfer):[MnO4]−needs24-in-17(all3d and O(2p)).See also the article byPierloot[13].NTHANIDES AND ACTINIDES•Lanthanides:The4f shell is inert but has to bekept active.•5d,6s(6p)are generally the most importantorbitals.However,strongly ionic complexesneed only4f active.Covalent bonds difficultbecause large demands on the active space.•High spin in the f-shell helps(e.g.,Gd2,S=7),because this keeps the number of configurationstates down.•Actinides:In principle,5f,6d,and7s should beactive(13orbitals).But if highly charged,only5f is needed.Again,covalent bonds requiremore active orbitals.Example:Uranyl,[UO2]2+,needs a12-in-12active space.These rules are not comprehensive but can often serve as a guide.More serious is that they often can-not be followed,because the resulting number of active orbitals would make the calculation impossi-ble in practice.Except for small cases,the position is that we already want more active orbitals than can practically be used,and we need to cut down the number.A common choice is to more or less explic-itly order the orbitals by some perceived importance, keeping the most needed ones.These are the ones that would have fractional occupation,due to quasidegeneracy due to symme-try(exact or approximate),such as in the multiplet states of open shells[Please note:presence of a(for-mal)atomic f3,for instance,does not imply that three f orbitals would be sufficient:all seven must be used],or the bonding and antibonding orbitals of a bond that may become(partially)broken.In multiple bonding,theσcomponent is usually com-pressed,and keep theπorδcomponents at too long a distance for them to fully develop bonding,so they are partially broken.In particular,conjugated and aromatic bonds should be active.However,one should not always use as many active orbitals as is affordable,on the principle that more is better.It is important not to split sets of orbitals that could become symmetry-related,for instance.Obviously,one would not deliberately include one but not the other of twoδorbitals,for instance,if they were exactly or nearly symmetry-related.But similar mistakes are often done and are usually unintentional:the number of active orbitals is reasonable,but the shape of starting orbitals isnot,and the calculation results in a set of unsuitableorbitals[14].The expected delta orbital can come outas an irrelevant sigma orbital,either distorting thestate or breaking an expected symmetry,or appear-ing as a useless,almost uncorrelated orbital withvery small occupation number.The input to the computer code is,thus,notmerely the numbers like“10-in-10”but also the start-ing orbitals must be regarded an important part ofthe input.As in many cases,the shape and local-ization in space of the orbitals can be used as acriteria for the selection,a graphical inspection oforbitals can be useful,and it makes possible to usethe chemical intuition.Using a large basis set from the start merelyintroduces unnecessary details in the shape of occu-pied orbitals andfills the lower part of the virtualspace with a large number of low-lying delocalizedorbitals.Orbital optimization will attempt to createthe correlating active orbitals by linear combinationsof the virtual orbitals.A better approach is to startfrom minimal basis calculations,where the calcula-tion starts from a virtual space built from only theatomic valence shells.The selected active orbitals arethen used(by projection)to create orbitals with thelarger basis.In any orbital optimization procedure,secondaryminima can occur.When compared with generalMCSCF,state-averaged CASSCF is fairly free ofsuch problems.State-specific optimization of excitedstates is however very problem-prone and should beavoided.Occasionally,such problems are also seen,for example,with mixed-valence compounds,andthey sometimes go undetected and are discoveredonly when the electronic structure fails to show someexpected symmetry.In some cases,the best proce-dure is to accept this situation:symmetry-equivalentpairs of symmetry-broken have functions have beenused,for example,in studies of Ni+2[15],O+4[16],andFe2+−Fe3+electron transfer[17],in a post-CASSCF calculation using RASSI[5].However,this is excep-tional situations.For molecules with high symmetry,the another problem may occur.Unless the orbitalsare prepared with good symmetry properties fromthe start,for example,as eigenfunctions of some Fockmatrix with the proper symmetry,the orbitals mayneed many iterations to converge,or it may even fail.Natural orbitals,or approximate natural orbitals,from a correlated calculation provide good startingpoints for CASSCF—much better than the IVO-typevirtuals that are often used for CI.This is an issue,when the CASSCF has initial problems with orbitalSELECTION OF ACTIVE SP ACE FOR MULTICONFIGURA TIONAL METHODSoptimization,and even more so for RASSCF.Such natural orbitals can easily be produced,for exam-ple,by a preliminary calculation with a very small active space followed by ing the natu-ral occupation number to determine the best active orbitals is not quite reliable,however.Obviously, orbitals with very large occupation number for any specific state should be included.However,one must also keep an eye to include orbitals that may be important for other states.There are procedures for averaging natural orbitals from different states,but it may be more convenient to take advantage of the state-average orbital optimization of a prepara-tory RASSCF calculation,as will be seen later in the durene example.Often,one wish to be able to select good active orbitals by hand,and it is then very advantageous to use some localization procedure,which brings out key features of the orbitals.There are several differ-ent schemes described in the literature[18–21],but for this purpose—to easily recognize and identify the relevant orbitals,localized on an atom,or on a bond—any of these schemes is acceptable.The following general advice should always be observed:•First,try to understand the system,to knowwhat to expect.Try a smaller system to checkyour assumptions,read the literature.•Start exploring with a smaller basis set.Thisnot only makes the calculations faster but alsomakes the orbitals visually better defined.•Localize the orbitals.Again,this helps in thevisual identification of which orbitals to select.•Use an orbital viewer to pick out the startingorbitals.•If in doubt,run exploratory calculations withlarger active space.•Ideally,orbitals with natural occupation num-ber in the range of0.02–1.98should be active.Note that the occupation numbers change withgeometry or during reaction.The ideal activespace should contain enough orbitals to staycontinuous during reaction.Finally,also the states to optimize may be an important factor.Of course,if there is a degener-ate or almost degenerate pair of states,it is probable that both should be included or excluded together. If the two states have very different polarity it is dif-ficult to ensure that both are treated in a balanced way.In exceptional cases,the two states prefer dif-ferent active orbitals,and using a too small number of active orbitals may then give rise to hysteresis, where one or the other state can be stabilized depen-dent on optimization history.In cases of symmetry, this usually results in electronic symmetry break-ing.The only good solution is to provide a large enough active space.An inadequate active space causes errors that are not usually compensated by the subsequent CASPT2or RASPT2calculations, which tend to overcompensate,and may even get unnecessary intruder problems.5.Examples5.1.CO2The choice of active orbitals is a compromise between accuracy and expedience,and these can-not be very well defined a priori.The methods described here are used tofind electronic energies in the Born–Oppenheimer approximation,based on the variational principle that these energies are sta-tionary with respect to variations of orbitals and CI coefficients,for any given set of nuclear coordinates. Superficially,it would seem that this would define an accuracy criterion:the best choice of basis and of active orbitals would be that affordable combi-nation,which gives the lowest electronic energies. Obviously,this is not a viable criterion if applied uncritically,because it would lead to correlation of the core,but given a standard basis set,which lacks core correlating basis functions,it can look as a plau-sible choice,and it is often reasonable for small molecules.However,first of all the aim is not to get abso-lute energies right but relative energies for all the electronic states and all geometries.Second,it is important that the electronic states obtained from the CASSCF calculation are suitable for the second-order perturbation calculation.Third,the converged wave functions must be a function of the geome-try:there are cases when the inherently nonlinear optimization can lead to multiple solutions,with noncontinuous states and possibly hysteresis phe-nomena,and this is usually avoidable by a suitable set of active orbitals.The simple problem of studying the photodis-sociation of CO2illustrates the problem.Figure1 shows some of the lowest states,as obtained by a demonstration calculation using an active space of 10electrons in eight orbitals,without any symmetry imposed,with a small basis set(ANO-RCC-VDZP). The same number of active orbitals were used whileVERYAZOV ,MALMQVIST ,ANDROOSFIGURE 1.CASSCF electronic energy curves for linearOC ···O stretch computed without using symmetry.stretching one bond,and each calculation started with converged orbitals from the preceding one.An attempt to fit smooth potential energy func-tions to the points fails for the excited states.This is due to state crossings,which change the selection of states used in the optimization of the orbitals.The singlet ground state is reasonably well described for this range of distances,and perhaps this is all that is needed.The ground state products are CO (1 +)and O (3P e ),whereas at shorter dis-tances,the lowest molecular state is CO 2(1 +),so the dissociation is spin forbidden,and singlet and triplet systems are computed separately.The excited states that cross belong to different irreducible representa-tions of the C ∞v group,so for the linear molecule the excited states can be treated by restricting the sym-metry,which may alleviate the problem of having a discontinuous active space.But probably we need to study both bent and lin-ear conformations.Moreover,in a similar study for a larger molecule,the broken bond may well inter-act with unpaired electrons elsewhere in the system.This produces state crossings that can become arbi-trarily abrupt,as well as problems with multiple solutions and hysteresis.It is then clear that there are always many cases where one cannot devisean active space that allows problem-free CASSCF calculations for all conformations and states studied.5.2.DURENEA common recipe for selection of the active space based on one-electron energies,and so orbitals near HOMO–LUMO gap are included into consideration.However,even in a simple case,this recipe might lead to a wrong conclusion.For durene (1,2,4,5-tetramethylbenzene)mole-cule,the best choice of a small active space will span the six π-type atomic orbitals of the carbon atoms.To obtain one-electron energies one can perform SCF or DFT calculation.In durene molecule,two occupied π-orbitals have the highest one-electron energies.However,the third π-orbital has the energy,which is almost the same as the orbital energy of σ-bond (see Fig.2).The details of SCF calculation,for example different basis set,can change the order of these orbitals.The virtual π-orbitals have orbital energies far away from LUMO orbital.To check how important to include correct orbitals into active space in the beginning of the calculation,we made a numerical experiment.For durene,the calculation was performed as a single job,where in this case the number of inactive and active orbitals in each irreducible representation was predetermined,but the actual orbitals to select were not.In this job,the first step was a CASSCF with a small minimal basis,thus forcing the correlating orbitals to have the character of valence orbitals.The orbitals were then re-expanded in a larger basis and used as start orbitals for a second CASSCF,which converged in a few steps,showing that the orbitals maintained their general shape;and in this calcu-lation,this was followed by yet another expansion to a final basis set of triple-zeta quality,again with no drastic change of the orbitals selected.In fact,we could have done the step from minimal to final basis directly.The final calculation was repeated with the con-verged orbitals as input,which obviouslyconvergedFIGURE 2.Four occupied orbitals in durene with highest one-electron energy.SELECTION OF ACTIVE SP ACE FOR MULTICONFIGURA TIONAL METHODSat once,but this time using the program option to use quasi-canonical orbitals.This was done to get a meaningful set of orbital energies also for the active orbitals.One-electron energies of the active orbitals can be quite far from HOMO or LUMO—in our calculation they are:HOMO,HOMO-1,and HOMO-4(for occupied)and LUMO+14,LUMO+15,and LUMO+43(for virtuals).If the starting guess are any kind of canonical orbitals obtained from,for example,UHF,DFT,or other SCF-like method,and a large basis set is used,the optimal active orbitals will not be present as such among the orbitals but will possibly emerge after a more or less long-winded optimization procedure.Such a procedure will be prone to fail or to give suboptimized orbitals.The best procedure is to start with a very small basis set,and as this example shows,this is often successful even as an automated procedure.In this example,the number of active orbitals was predetermined.This is not always the case,in particular when calculation size forces compromises.5.3.CHLOROIRON CORROLEChloroiron corrole is an example of a rather com-plicated system for multiconfigurational theory.The molecule contains a transition metal atom and many nonsaturated bonds,which makes it impossible to include all potentially interesting orbitals in the active space.A compromise solution must be found. In Ref.[22],a comprehensive study of chloroiron cor-role has been performed and different active space sets were tested to describe the spectroscopy of this molecule.The starting point for the selection was a set of standard rules for transition metal complexes [23].The best choice turned out to be one specific choice of14active orbitals with14electrons.To ver-ify that other orbitals are less important,these were included into a test calculation,but the occupation number of these extra orbitals were very close to unperturbed values.The graphical inspection plays an important role in this case,especially for deciding which orbitals from corrole are localized in the region near the iron atom and thus assumed to be primary choice for active orbitals.On the other hand,graphical inspection of orbitals in this case leads to a very long list of potential can-didates.In this study,we tried tofind another way to pinpoint orbitals,which were found at[22].We used a small RAS2space of6orbitals,and included additional potential orbitals into RAS1and RAS3space,allowing single and double excitations.In this approach(which we can call“RAS probing”), we can perform relatively cheap calculations,which include more orbitals than needed and later elim-inate orbitals with occupation numbers close to0 and2.An initial calculation using four RAS1-,six RAS2-, and four RAS3-orbitals forfive quintet states,started with the orbitals found by the14-in-14CASSCF,con-verged a solution with nearly the same quality as the CASSCF.We denote this as having a/4/6/4/ division of the active space.Up to two holes were allowed in RAS1and up to two electrons in RAS3.With the orbitals obtained,we then optimized the two lowest quintet states with18active orbitals in a/6/6/6/RASSCF.The resulting18active orbitals has two pairs of strongly occupiedσ-orbitals with the corresponding pair of correlating orbitals,with occupation numbers in the range of1.98–0.02.These can be removed from the active space,leaving14 orbitals(See Fig.3).These14orbitals are the same as obtained at[22].The RAS probing technique requires further investigation,but in this complicated case,it found the active space almost automatically.5.4.FORMATION OF APYRIDINE-CYANONAPHTALENE COMPLEXIt has recently been suggested that an exciplex, that is a heterodimer that is bound in an excited state,is formed in the lowest excited state of the complex formed between pyridine and a number of cyanoaromatics[24],such as cyanonaphthalene.Multiconfigurational description of this system is problematic.The total number of nonsaturated orbitals plus lone pairs is23,which is beyond the possibilities of CASSCF approach.Also,differ-ent orbitals can be important in the description of the complex near equilibrium distance and during dissociation.The pyridine–cynaonaphtalene complex has been studied using state-average CASSCF calculations and multistate second-order perturbation theory, MS-CASPT2.In the MS-CASPT2,the Hamiltonian matrix ele-ments of the type(0)I|ˆH| (0)J+ (1)Jare computed for the set of CASPT2wave func-tions,resulting in an effective Hamiltonian matrix, which is symmetrized and diagonalized.(Note that the perturbed states are not orthogonal,and the。
势能面的锥形交叉及其在光化学领域的应用ppt课件
为深入学习习近平新时代中国特色社 会主义 思想和 党的十 九大精 神,贯彻 全国教 育大会 精神,充 分发挥 中小学 图书室 育人功 能
光化学中的地位、意义
• 存在于许多光化学反应体系（涉及多个电子态 的反应）其重要性体现于这个领域
• 连接不同电子态之间的一个快速、有效途径 （漏斗）：激发态——〉基态；
为深入学习习近平新时代中国特色社 会主义 思想和 党的十 九大精 神,贯彻 全国教 育大会 精神,充 分发挥 中小学 图书室 育人功 能
两个势能面的交叉区域
• 两个势能面的交叉区定义：两个势能 面（相同对称性也可）可以相交于一 个n-2 维的超线（曲面）中。（前提： 所画的势能面是 n维核坐标的函数）
Fig. 3 Time-cumulated flux measured on the upper S1 (lines with crosses) and lower S0 (lines with circles) adiabatic dissociation limits, for initial conditions (0,0) (a), (0,1) (b) and (1,0) (c).
为深入学习习近平新时代中国特色社 会主义 思想和 党的十 九大精 神,贯彻 全国教 育大会 精神,充 分发挥 中小学 图书室 育人功 能
Fig. 5 Dissociation probabilities on the upper (black) and lower (grey) adiabatic dissociation limits, for initial conditions (nr , 0), nr = 1,2 (a), (0,ny ), ny= 0,7 (b), and (1, ny), ny = 0,4 (c).
《2024年CASS工艺在国内的应用现状》范文
《CASS工艺在国内的应用现状》篇一一、引言随着国内水污染问题的日益严重，污水处理技术逐渐成为环境保护领域的重要研究方向。
CASS（Cyclic Activated Sludge System，循环活性污泥系统）工艺作为现代污水处理技术的一种，因其高效、节能、操作灵活等优点，在国内得到了广泛的应用。
本文旨在分析CASS工艺在国内的应用现状，以期为未来的污水处理技术研究和应用提供参考。
二、CASS工艺概述CASS工艺是一种基于活性污泥法的污水处理技术，其核心思想是通过周期性循环操作，实现污泥的高效处理。
该工艺具有处理效率高、节能减排、操作灵活等优点，适用于各种规模的污水处理厂。
CASS工艺的运作原理主要包括曝气、沉淀、排水等过程，通过这些过程的循环交替，达到净化水质的目的。
三、CASS工艺在国内的应用现状1. 应用领域CASS工艺在国内的应用领域非常广泛，包括城市污水处理、工业废水处理、农村污水治理等。
在城市污水处理方面，CASS 工艺被广泛应用于大型污水处理厂和小区污水处理站；在工业废水处理方面，CASS工艺能够有效地处理各种工业废水，如造纸、纺织、化工等行业的废水；在农村污水治理方面，CASS工艺因其操作灵活、适应性强等特点，得到了广泛的应用。
2. 应用效果CASS工艺在国内的应用效果显著。
首先，该工艺能够有效地去除污水中的有机物、氮、磷等污染物，使出水水质达到国家排放标准。
其次，CASS工艺具有节能减排的优点，能够降低污水处理厂的能耗和碳排放。
此外，CASS工艺的操作灵活，能够适应不同规模和处理需求的污水处理厂。
3. 发展趋势随着国内对环境保护的重视程度不断提高，CASS工艺在未来的发展前景广阔。
一方面，随着技术的不断进步和优化，CASS 工艺的处理效率将进一步提高，能耗和碳排放将进一步降低。
另一方面，CASS工艺将与其他先进技术相结合，形成更加高效、节能、环保的污水处理系统。
此外，随着国家对污水处理行业的政策支持力度不断加大，CASS工艺将得到更广泛的应用和推广。
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H-P Zhao, D-C Fang, in preparation
计算化学理论与实践
6、计算上的困难
（1）活化空间的选择 （2）收敛问题：不收敛及收敛到不同的态 (3) Size-Consistence, Size-extensivity问题 Davidson, Int. J. Quantum Chem., 8,61(1974)
G3B3 method
Reaction Process
CH2(-O9+2H.2O) 2
k ( T ) ( 5 .1 1 .6 ) 1 1e 0 2 x 2 p 1 8 /( T 0 4 ) k(T )5 .4 1 1 0e 2 x 5 p3 /T ()0
1.91 C A S(7,7)/cc-pV D Z 2.69 C A S(7,7)+1+2/cc-pV D Z
HF没有考虑相关能的原因
Coulom: bJˆi ji
*j ( j) r1ijj ( j)d j
交换算符Kˆi： ji
*j (i) r1iji ( j)d j
2. CASSCF
计算化学理论与实践
MCSCF 波函数的定义
CII CI2 1 I |J IJ
I
I
{ I } 由 { i } 组成
M. J. Frisch, I. N. Ragazos, M. A. Robb and H. B. Schlegel, Chem. Phys. Lett. 189, 524 (1992)
计算化学理论与实践
5、实际应用
Diradical system
CC
C C
+
C O
O
CO
Hale Waihona Puke G-J Chen, D-C Fang, X-Y Fu, Int. J. Quantum Chem. QCS, 23,501(1989).
4、参考文献
计算化学理论与实践
MOLPRO H.J. Werner P.J. Knowles, J. Chem. Phys., 82,5053(1985)
DALTON H.J.A. Jensen, P. JØrgensen, H. Ågren,
J. Chem. Phys., 87, 451(1987) Gaussian
计算化学理论与实践
第七讲:CASSCF 的理论与应 用
方德彩 Email: 2019年4月15日
计算化学理论与实践
1、相关能的定义及计算
“Fermi穴”： 自旋相同的电子之间 “Coulomb穴”： 自旋相反的电子之间 “电子相关”：电子的这种运动的相互关联性 “静态电子相关”： 禁止相同自旋电子进入
计算化学理论与实践
实际应用
光化学 M.A. Robb(London, UK) 刘若庄、方维海、丁万见 主要处理S0, T1,S1等反应，（1）优化反应过渡
态，中间体以及产物等几何构型 （2）优化势能面的交叉点
计算化学理论与实践
实际应用
自由基反应
（1）二重态与单重态
如： H
HH
Cl +C C
C
计算化学理论与实践
HNN+OH
计算化学理论与实践
自由基反应
计算化学理论与实践
(3) 三重态与二重态
如： 3CH2+NO, CH3+3O2 CH+3O2 3C2+NO (4) 三重态与三重态
如： 3CH2+3O2 3C2+3O2 D-C Fang, X.Y. Fu,, J. Phys. Chem. A, 106,
“Feimi穴” “动态电子相关”： 禁止相反自旋电子进入
“Coulomb穴”
计算化学理论与实践
Lowdin（Advan. Chem. Phys.,1959,2,207)
ECo rrEnon rE eH l F
主要考虑相关能的方法: CI, MCSCF(CASSCF),MPn, CC
计算化学理论与实践
H
HH
H
H
H
C +HCl
CC
H C C H+H
H D-C Fang, X-Y Fu, J. Mol. Struc.(Theochem),
310, 23(1994).
计算化学理论与实践
自由基反应 CH3+O3
CH3 + O3
CH2O+HO2 CH3O+O2
L. C. Yang, D-C Fang, J. Mol. Struc.(THEOCHEM), 2019,671, 141
NO2 CAS(7,7) 二重态 NO2 CAS(7,7) 四重态 NO2 CAS(11,10) 二重态 NO2 CAS(7,7) B1 二重态
3、计算程序
计算化学理论与实践
MOLPRO Werner (Germany) and Knowles (United Kingdom)
MOLCAS (Lund Univ., Sweden) DALTON Ruud (Norway) GAMESS Gordon (USA) COLUMBUS Lischka(Austria), Shepard(USA) GAUSSIAN (USA)
0 .0
5 9 .0 5 7 .0
计算化学理论与实践
(2) 二重态与二重态的反应
如： CH+NO, NH2+NO D-C Fang, L.B. Harding, S.J. Klippenstein,
J.A. Miller, Faraday Dissc., 119, 207(2019).
NH2+NO
i |i Cix
计算化学理论与实践
1、 活化轨道和活化电子
活化轨道 活化电子 目前比较常用的组合：
(1) 单重态/三重态 (6,6), (8,6), (8,7), (8,8), (10,8), (12,10), (14,12), (16,14), (16,16), (18,16) (2)二重态/四重态 (7,7), (9,7), (11,9), (11,11), (13,11), (15,13), (17,15)
Relative energy(Kcal/mol)
CH3+O3 (0.0)
TS1 (-55.7)
TS3 (-52.6) TS2 (-57.0)
(T-4S15.+2O) 2
TS4 C(-H424O.4+)H+O2 (-47.1)
INT1 INT2 (-60.7) (-62.3)
C(H-63O3.+6O) 2
计算化学理论与实践
2、活化轨道、活化电子数与组 态数目
nconf (2m)! n!(2mn)!
n: 活化电子数 m：活化轨道数
m=10, n=12, nconf=125970
计算化学理论与实践
考虑自旋多重度的限制
Paldus J., JCP, 61(12),532191974)
n(N,S,m )2 m S 1 1m 1( N 12S)m 1( N 12S)1
2
2
例如:
n 5 , 1 ,10 3300 2
252X6+1848X4+3300X2=
n 5 , 3 ,10 1848
15504
2
n 5 , 5 ,10 252 2
计算化学理论与实践
例子: CAS(2,2)
例子: CAS(4,3)
计算化学理论与实践
Gaussian 计算的例子