| 查看: 2541 | 回复: 8 | |||
[交流]
【求助】电子态1Δg，1∑+g，2p等怎么定义的，
|
|
我最近看文献，一直看到这个。实在有点不明白这些电子态是什么意思。只知道它是电子态。望大侠们给我解析一下，必有重金酬谢 其他电子态的说明也可以在下面留言，与前几个电子态一视同仁，金币不是问题 求讲解 越详细越好 |
回复此楼» 猜你喜欢
调剂招生
已经有0人回复
-
调剂招生
已经有0人回复
-
物理化学论文润色/翻译怎么收费?
已经有200人回复
-
调剂招生
已经有0人回复
-
调剂招生
已经有0人回复
-
调剂招生
已经有1人回复
-
实际气体内压强的微观机制或将改写--------从一个基本的力学佯谬说起
已经有1人回复
-
调剂招生
已经有0人回复
-
调剂招生
已经有0人回复
-
调剂招生
已经有5人回复
-
招收0703开头的学硕调剂生 线上复试
已经有5人回复
» 本主题相关价值贴推荐，对您同样有帮助:
- 百鲜美食谱精典【转载】
已经有26人回复
- 罪与罚【陀思妥耶夫斯基】【已搜索无重复】
已经有37人回复
- 中外名人格言钢笔字帖(赵忱)【转载】
已经有61人回复
- 怎么根据态密度图积分算区间的电子数
已经有8人回复
- 金与什么有机物可以配合，且配合物整体呈正价态？
已经有4人回复
- 请教vulcanized rubber的定义
已经有6人回复
- flory分子量分布函数中定义t时基团反应概率为反应程度P，此处不懂，求助
已经有7人回复
- 脉冲筛板萃取柱中30块塔板可用周期边界条件简化定义边界么
已经有5人回复
- fluent中怎样定义边界层厚度和动量层厚度
已经有5人回复
- 晶界的表示：“Σ3”怎么定义的
已经有19人回复
- 等效位置的态密度分析
已经有9人回复
- ansys 13.0 网格划分和边界定义怎么设置，拜求高手
已经有13人回复
- 机械振动中的模态是怎么定义的
已经有7人回复
- 【求助】分子中是怎么定义成键态和反键态的
已经有18人回复
» 抢金币啦！回帖就可以得到:
-
诚邀申报 | 潍坊学院“绿色催化新材料与光化学转化山东省工程研究中心“开放课题
+2/132
-
2026年手套箱应该怎么选？
+1/90
-
深圳湾实验室招聘电镜运维工程师
+1/84
-
26年秋入学博士招生【二批】
+1/78
-
94年大龄博士工作选择
+1/75
-
昆明理工大学冶能院离子液体冶金课题组招收博士
+1/72
-
深圳89高中男老师，诚征女友
+1/69
-
清华大学化学系张韶光研究室招收研究助理/交换生/联培学生
+1/58
-
俄克拉荷马大学斯蒂芬森生物医学工程学院赵建实验室招收 2027 级博士研究生
+1/36
-
上海交通大学 离子传导膜-纳流控-限域传质课题组招收博士、硕士研究生和博士后
+1/34
-
清华大学招聘环境科学与工程/水文地质方向科研助理/工程师
+1/31
-
桂林理工大学物理学专业招收调剂，还有三个名额！！！
+1/28
-
爱尔兰 - 可持续金融+航空方向 全奖博士 (2个名额)
+1/14
-
急聘！中国农科院兰州牧药所兽药创新与耐药性科研团队聘科研助理
+1/8
-
暨南大学招超表面方向博士后
+1/7
-
南开大学齐迹课题组招收有机分子合成、免疫学、分子生物学相关方向的博士研究生
+1/6
-
北京理工大学（珠海）招收智能科学与技术方向26级博士
+1/4
-
2026年博士招生—中国林业科学研究院---土壤微生物生态学方向
+1/4
-
燕山大学理学院 2026 博士招生 | 报名 4.22-5.22 考核 5.30-31
+1/3
-
北京理工大学（珠海）招收智能科学与技术方向26级博士
+1/2
2楼2011-03-31 11:39:19
3楼2011-03-31 15:37:45
★ ★
zhang302(金币+10): 很感谢呀，我是不太会用度娘 2011-04-01 09:11:58
小红豆(金币+2): 谢谢分享你的看法 2011-04-16 14:06:39
zhang302(金币+10): 很感谢呀，我是不太会用度娘 2011-04-01 09:11:58
小红豆(金币+2): 谢谢分享你的看法 2011-04-16 14:06:39
|
其实度娘真的很有用，动动手啥都有了 http://good.gd/1081561.htm |
4楼2011-03-31 19:51:38
★ ★ ★ ★ ★
zhang302(金币+10): 2011-04-01 09:10:58
小红豆(金币+5): 谢谢分享你的看法 2011-04-16 14:07:04
zhang302(金币+10): 2011-04-01 09:10:58
小红豆(金币+5): 谢谢分享你的看法 2011-04-16 14:07:04
|
In molecular physics, the molecular term symbol is a shorthand expression of the group representation and angular momenta that characterize the state of a molecule, i.e. its electronic quantum state which is an eigenstate of the electronic molecular Hamiltonian. It is the equivalent of the term symbol for the atomic case. However, the following presentation is restricted to the case of homonuclear diatomic molecules, or symmetric molecules with an inversion centre. For heteronuclear diatomic molecules, the u/g symbol does not correspond to any exact symmetry of the electronic molecular Hamiltonian. In the case of less symmetric molecules the molecular term symbol contains the symbol of the group representation to which the molecular electronic state belongs. It has the general form:  where * S is the total spin quantum number * Λ is the orbital angular momentum along the internuclear axis * Ω is the total angular momentum along the internuclear axis * u/g is the parity * +/− is the reflection symmetry along an arbitrary plane containing the internuclear axis For atoms, we use S, L, J and MJ to characterize a given state. In linear molecules, however, the lack of spherical symmetry destroys the relationship [\hat\mathbf L^2, \hat H]=0, so L ceases to be a good quantum number. A new set of operators have to be used instead: \{\hat \mathbf S^2, \hat\mathbf{S}_z, \hat\mathbf{L}_z, \hat\mathbf{J}_z=\hat\mathbf{S}_z + \hat\mathbf{L}_z\}, where the z-axis is defined along the internuclear axis of the molecule. Since these operators commute with each other and with the Hamiltonian on the limit of negligible spin-orbit coupling, their eigenvalues may be used to describe a molecule state through the quantum numbers S, MS, ML and MJ. The cylindrical symmetry of a linear molecule ensures that positive and negative values of a given ml for an electron in a molecular orbital will be degenerate in the absence of spin-orbit coupling. Different molecular orbitals are classified with a new quantum number, λ, defined as λ = |ml| Following the spectroscopic notation pattern, molecular orbitals are designated by a smallcase Greek letter: for λ = 0, 1, 2, 3,… orbitals are called σ, π, δ, φ… respectively. Now, the total z-projection of L can be defined as M_L=\sum_i {m_l}_i. As states with positive and negative values of ML are degenerate, we define Λ = |ML|, and a capital Greek letter is used to refer to each value: Λ = 0, 1, 2, 3… are coded as Σ, Π, Δ, Φ… respectively. The molecular term symbol is then defined as 2S+1Λ and the number of electron degenerate states (under the absence of spin-orbit coupling) corresponding to this term symbol is given by: * (2S+1)×2 if Λ is not 0 * (2S+1) if Λ is 0. Ω and spin-orbit coupling Spin-orbit coupling lifts the degeneracy of the electronic states. This is because the z-component of spin interacts with the z-component of the orbital angular momentum, generating a total electronic angular momentum along the molecule axis Jz. This is characterized by the MJ quantum number, where MJ = MS + ML. Again, positive and negative values of MJ are degenerate, so the pairs (ML, MS) and (−ML, −MS) are degenerate: {(1, 1/2), (−1, −1/2)}, and {(1, −1/2), (−1, 1/2)} represent two different degenerate states. These pairs are grouped together with the quantum number Ω, which is defined as the sum of the pair of values (ML, MS) for which ML is positive. Sometimes the equation Ω = Λ + MS is used (often Σ is used instead of MS). Note that although this gives correct values for Ω it could be misleading, as obtained values do not correspond to states indicated by a given pair of values (ML,MS). For example, a state with (−1, −1/2) would give an Ω value of Ω = |−1| + (−1/2) = −1/2, which is wrong. Choosing the pair of values with ML positive will give a Ω = 3/2 for that state. With this, a level is given by 2S + 1ΛΩ Note that Ω can have negative values and subscripts r and i represent regular (normal) and inverted multiplets, respectively.[1] For a 4Π term there are four degenerate (ML, MS) pairs: {(1, 3/2), (−1, −3/2)}, {(1, 1/2), (−1, −1/2)}, {(1, −1/2), (−1, 1/2)}, {(1, −3/2), (−1, 3/2)}. These correspond to Ω values of 5/2, 3/2, 1/2 and −1/2, respectively. Approximating the spin-orbit Hamiltonian to first order perturbation theory, the energy level is given by E = A ML MS where A is the spin-orbit constant. For 4Π the Ω values 5/2, 3/2, 1/2 and −1/2 correspond to energies of 3A/2, A/2, −A/2 and −3A/2. Despite of having the same magnitude, levels of Ω = ±1/2 have different energies associated, so they are not degenerate. With that convention, states with different energies are given different Ω values. For states with positive values of A (which are said to be regular), increasing values of Ω correspond to increasing values of energies; on the other hand, with A negative (said to be inverted) the energy order is reversed. Including higher order effects can lead to a spin-orbital levels or energy that do not even follow the increasing value of Ω. When Λ = 0 there is no spin-orbit splitting to first order in perturbation theory, as the associated energy is zero. So for a given S, all of its MS values are degenerate. This degeneracy is lifted when spin-orbit interaction is treated to higher order in perturbation theory, but still states with same |MS| are degenerate in a non-rotating molecule. We can speak of a 5Σ2 substate, a 5Σ1 substate or a 5Σ0 substate. Except for the case Ω = 0, these substates have a degeneracy of 2. Reflection through a plane containing the internuclear axis There are an infinite number of planes containing the internuclear axis and hence there are an infinite number of possible reflexions. For any of these planes, molecular terms with Λ > 0 always have a state which is symmetric with respect to this reflection and one state that is antisymmetric. Rather than labelling those situations as, e.g., 2Π±, the ± is omitted. For the Σ states, however, this two-fold degeneracy disappears, and all Σ states are either symmetric under any plane containing the internuclear axis, or antisymmetric. These two situations are labeled as Σ+ or Σ−. Reflection through an inversion center: u and g symmetry Taking the molecule center of mass as origin of coordinates, consider the change of all electrons’ position from (xi, yi, zi) to (−xi, −yi, −zi). If the resulting wave function is unchanged, it is said to be gerade (German for even); if the wave function changes sign then it is said to be ungerade (odd). For a molecule with a center of inversion, all orbitals will be symmetric or antisymmetric. The resulting wavefunction for the whole multielectron system will be gerade if an even number of electrons is in [[ungerade orbitals]], and ungerade if there is an odd number of electrons in ungerade orbitals, independently of the number of electrons in gerade orbitals. [ Last edited by jmlong on 2011-4-1 at 06:09 ] |
5楼2011-04-01 06:01:35
6楼2011-04-01 16:23:40
7楼2011-04-16 10:07:49
8楼2011-04-16 13:35:18
★
小木虫(金币+0.5):给个红包，谢谢回帖
小木虫(金币+0.5):给个红包，谢谢回帖
|
2p：2为主量子数，p为轨道量子数。在任何一本原子物理（以及原子光谱学、结构化学，量子化学）书里都能找到。 1Δg，1∑+g： 1为自旋多重度； Δ，∑+仅用于线形分子（非线性分子需要查群表），表示轨道量子数在分子轴上的投影。例如d=2的投影，按照轨道磁量子数可以分为-2/+2，-1/+1，0三类，分别用Δ，Π，∑描述，显然除了∑以外都是二重简并的。至于∑+中的+号和∑-中的-号，分别表示0投影是对称的还是反对称的（也就是说，0有+0和-0两种）。在线性分子的轨道中，只能出现σ+（按照分子光谱学中的约定，这里用小写符号表示轨道，电子态用大写）；而在线性分子的电子态中，∑+和∑-都可以出现，但∑+个数往往更多。 g：正宇称对称性。相对应的还有u：反宇称对称性。在具有D∞h对称性的线性分子中会出现g/u对称性，例如同核双原子分子。原子是特殊情况：所有的s,d,g,...轨道（不是电子态）都是g对称性，所有的p,f,h,...都是u对称性。 |
9楼2011-04-18 03:53:08