高斯的TD频率计算

ter20

我发现高斯TD计算频率时，也会有很多激发态计算，就是优化时那些，比如：
Excited State   1:      Singlet-A"     4.3748 eV  283.40 nm  f=0.0003  <S**2>=0.000
      21 -> 22         0.69492
      21 -> 23        -0.11452
This state for optimization and/or second-order correction.
Total Energy, E(TD-HF/TD-KS) =  -264.405092706   
Copying the excited state density for this state as the 1-particle RhoCI density.

Excited State   2:      Singlet-A"     5.2320 eV  236.97 nm  f=0.0047  <S**2>=0.000
      21 -> 22         0.10895
      21 -> 23         0.69029

Excited State   3:      Singlet-A'     5.8057 eV  213.56 nm  f=0.0991  <S**2>=0.000
      19 -> 23         0.24243
      20 -> 22         0.65217
。。。。

不知道为何是这样，不该直接进行振动分析吗？而且优化时还会有对称性的归属，频率计算一步之后，对称性就变为?了（Singlet-?Sym）

另外之前我问过关于虚频总是消不掉的问题，后来我问了高斯公司的工程师，问题和回复如下，我有些不确定，请Sob鉴定(附件是我的结果文件)：我的问题如下：

I am doing excited state geometry optimizations with TD-DFT methods. I got a structure with 1 imaginary frequency and I tried tons of stragegies but still failed in eliminating it. The stragegies include modifying the geometry along the imaginary vibrational mode, read force constant of frequency calculation, add “maxstep” keywords in Opt, etc. And I manually scan the energy profile along the imaginary frequency vibrational mode (with very tiny increment in the geometry, 0.0001 Angstrom), but I found the geometry I got was the minimum. So I don’t know why the frequency calculation always gives one imaginary frequency, is it because the frequency calculations were done numerically?
Another question is that can I force Gaussian to calculate force constant in each Opt step using TD-DFT methods? Because I see simply specify “CalcAll” in Opt does not work. I guess there are some keywords in IOP, but I didn’t find it.

回复：

Thank you for giving us a chance to comment. The issue is not in the frequency calculation itself and the force constant is not a problem here, but in following the right excited state.

Note that excited state optimization is not as straightforward (as black-box) as ground state optimization, and it does require careful manual check throughout the optimization. With diffuse functions, small quantities are computed so it is even more sensitive to numerical noise issues. What you have encountered is an illustration about the difficulty.

The program tries to follow the excited state but sometimes it gets degenerate and may even switch orders. In this case you should stop the optimization, choose the correct state, and continue the optimization. In some other cases, the excited state you're studying crosses with the "ground state" (at the initial geometry). If that happens, you cannot use CIS or TD anymore since they are single-determinant; you'll need CASSCF to deal with the conical intersection or avoided crossing of states. For your case, if you search for "Excited State   1:", the first one shows:

Excitation energies and oscillator strengths:                                         
                                                                                       
Excited State   1:      Singlet-B1     2.9627 eV  418.48 nm  f=0.0014  <S**2>=0.000   
      21 -> 22         0.70191                                                         
                                                                                       
Excited State   2:      Singlet-A2     4.5387 eV  273.17 nm  f=0.0000  <S**2>=0.000   
      21 -> 23         0.70466                                                         
                                                                                       
Excited State   3:      Singlet-B2     5.3731 eV  230.75 nm  f=0.1559  <S**2>=0.000         19 -> 23         0.19026                                                               20 -> 22         0.67956                                                          This state for optimization and/or second-order correction.                           
So you're trying to follow excited state 3, with B2 symmetry and an oscillator strength of 0.1559. However, 2 steps later, excited state 3 becomes lower in energy than excited state 2 (Orbital 20 and 21 switched order as well):

Excited State   1:      Singlet-B1     3.9767 eV  311.78 nm  f=0.0026  <S**2>=0.000
      20 -> 22         0.70137

Excited State   2:      Singlet-A2    5.4776 eV  226.35 nm  f=0.0000  <S**2>=0.000
      20 -> 23         0.70442

Excited State   3:      Singlet-B2    4.8186 eV 257.30 nm  f=0.1419  <S**2>=0.000
      19 -> 23         0.15391
      21 -> 22         0.69006

So far the program still managed to follow this "Excited state   3" even if the energy is lower than "Excited State   2". You can see something like:

New state      2 was old state      3 New state      3 was old state      2
However, after 6 more steps, it cannot follow the order any more, and the two states switched order:

Excitation energies and oscillator strengths:

Excited State   1:      Singlet-B1     3.9485 eV  314.00 nm  f=0.0026  <S**2>=0.000
      20 -> 22         0.70139

Excited State   2:      Singlet-B2     4.8017 eV  258.21 nm  f=0.1408  <S**2>=0.000      19 -> 23         0.15267      21 -> 22         0.69038
Excited State   3:      Singlet-A2     5.4955 eV  225.61 nm  f=0.0000  <S**2>=0.000
      20 -> 23         0.70440
This state for optimization and/or second-order correction.

From this point above the geometry optimization on "Excited State   3" is the wrong state; therefore please stop the calculation, choose the right excited state (here "root=2"), and continue the optimization. Again please keep checking the states in each steps.

As we can see above, part of the difficulty comes from that the energy differences among excited states are typically smaller than between the ground state and the first excited state. Thus, it is helpful to use smaller geometry optimization steps (with the option "maxstep=N") when optimizing an excited state than in the ground state. As a first measure to increase the reliability of the geometry optimization of excited states, I recommend to reduce the maximum allowed step size during geometry optimizations. Try "Opt=(MaxStep=10)" or "Opt=(MaxStep=5)" to set this value to 0.10 Bohr, or a smaller value if you still have problems. The default value is 0.30 Bohr (MaxStep=30). Reducing the maximum allowed step size will result in the geometry optimization taking more steps to reach convergence than with the default value. This will be true obviously for well-behaved geometry optimizations, but for problematic cases it will be the other way around, i.e. it will take fewer steps (and may even be impossible with the default step size) because it will be easier for the optimizer to follow a particular electronic state if the changes from step to step are not very drastic.

Finally, (not in this case but could be helpful for future excited state optimizations) that sometimes an excited state may be described by several orbital transitions (matrix) with comparable coefficients, so it's helpful to view the "natural transition orbitals" to learn about the nature of the excited state

sobereva

做振动分析前程序肯定得先做一次电子激发计算才行，所以会输出那些

至于虚频之类的，之前已经讨论过了，高斯客服说的都比较靠谱。由于最近太忙没时间给你细看

ter20

我发现在优化没有得到minimum的结构的频率计算中，优化部分的激发态顺序是正确的，但是频率部分的激发态顺序很多都发生了改变，按照他的建议，我也不存在停掉优化过程这一措施了，就是接着该结构，把root=3改为root=2继续做优化，可是我试了，目前还是不行，还出现了很多奇怪的轨道跃迁贡献，总觉得这么做不太可靠，但是对TD的本质和高斯中的算法不是很了解，请Sob指教，多谢！