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【求助】電子態(tài)1Δg，1∑+g，2p等怎么定義的，
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我最近看文獻(xiàn)，一直看到這個。實在有點不明白這些電子態(tài)是什么意思。只知道它是電子態(tài)。望大俠們給我解析一下，必有重金酬謝 其他電子態(tài)的說明也可以在下面留言，與前幾個電子態(tài)一視同仁，金幣不是問題 求講解 越詳細(xì)越好 |
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2樓2011-03-31 11:39:19
3樓2011-03-31 15:37:45
★ ★
zhang302(金幣+10): 很感謝呀，我是不太會用度娘 2011-04-01 09:11:58
小紅豆(金幣+2): 謝謝分享你的看法 2011-04-16 14:06:39
zhang302(金幣+10): 很感謝呀，我是不太會用度娘 2011-04-01 09:11:58
小紅豆(金幣+2): 謝謝分享你的看法 2011-04-16 14:06:39
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其實度娘真的很有用，動動手啥都有了 http://good.gd/1081561.htm |
4樓2011-03-31 19:51:38
★ ★ ★ ★ ★
zhang302(金幣+10): 2011-04-01 09:10:58
小紅豆(金幣+5): 謝謝分享你的看法 2011-04-16 14:07:04
zhang302(金幣+10): 2011-04-01 09:10:58
小紅豆(金幣+5): 謝謝分享你的看法 2011-04-16 14:07:04
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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樓2011-04-01 06:01:35
6樓2011-04-01 16:23:40
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2p：2為主量子數(shù)，p為軌道量子數(shù)。在任何一本原子物理（以及原子光譜學(xué)、結(jié)構(gòu)化學(xué)，量子化學(xué)）書里都能找到。 1Δg，1∑+g： 1為自旋多重度； Δ，∑+僅用于線形分子（非線性分子需要查群表），表示軌道量子數(shù)在分子軸上的投影。例如d=2的投影，按照軌道磁量子數(shù)可以分為-2/+2，-1/+1，0三類，分別用Δ，Π，∑描述，顯然除了∑以外都是二重簡并的。至于∑+中的+號和∑-中的-號，分別表示0投影是對稱的還是反對稱的（也就是說，0有+0和-0兩種）。在線性分子的軌道中，只能出現(xiàn)σ+（按照分子光譜學(xué)中的約定，這里用小寫符號表示軌道，電子態(tài)用大寫）；而在線性分子的電子態(tài)中，∑+和∑-都可以出現(xiàn)，但∑+個數(shù)往往更多。 g：正宇稱對稱性。相對應(yīng)的還有u：反宇稱對稱性。在具有D∞h對稱性的線性分子中會出現(xiàn)g/u對稱性，例如同核雙原子分子。原子是特殊情況：所有的s,d,g,...軌道（不是電子態(tài)）都是g對稱性，所有的p,f,h,...都是u對稱性。 |
9樓2011-04-18 03:53:08
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