TDA with RSH giving negative triplet excitation

Questions
#1

Hello,
I am trying to obtain the singlet and triplet excitation energies for some molecules using the LCwPBE functional, with TDA. But I am actually getting the first triplet excitation with a negative value. What should I do?
Here is the input for your reference:

$comment
B_B_O
$end

$molecule
0 1
C -3.62650271490383 1.84809387627588 -0.20031656213029
C -2.64494069627883 0.80030371330622 -0.08162422772159
C -3.09391738265105 -0.54955436924551 0.05245182734149
C -4.46254990461043 -0.80368078435983 0.06314441793440
C -5.43893151762219 0.24674346719975 -0.05638036624317
C -4.99155270557869 1.58326746812945 -0.18868134819704
H -3.28702959644124 2.88664438540846 -0.30394402913536
H -2.35083324275376 -1.35331395805396 0.14344158701062
H -5.71697231591678 2.40462920549294 -0.28155352507590
H -4.69287976475051 -2.92558712482248 0.27819033350270
C -6.50714977773098 -1.79251485989195 0.14082128849821
C -7.56916632380000 -2.71094900582880 0.22247492020827
C -8.87183418711502 -2.19957287166716 0.15365683302839
C -9.12036185562526 -0.81069667829129 0.00713195615462
C -8.06395620599324 0.10100657969699 -0.07386140307076
C -6.73715449439281 -0.38137351978382 -0.00732659778693
H -7.38709794106071 -3.78948231504478 0.33566398598005
H -9.72228355393836 -2.89453382931922 0.21477345559173
H -10.15817247303870 -0.45160493118630 -0.04298811965658
H -8.25947890261030 1.17722994523906 -0.18811797901953
N -5.13866914349988 -2.01511477792599 0.18009201468675
C 3.11295779911888 2.32598459388954 -0.18885586252162
C 2.55109930417773 0.98495320653462 -0.05955917289506
C 1.17156686088761 0.89607101594266 -0.05814102924566
C 0.72008448755898 2.38464647248100 -0.20867341196515
C -1.22490882475195 1.06051449874251 -0.09360532621292
C -0.65663575819545 2.40943035271198 -0.22269063522767
H -1.24674894762253 3.33329237884800 -0.31920926278574
C 4.51090775915446 2.12524575246898 -0.16286754731462
C 4.73798238038922 0.74192552179673 -0.02607657321404
H 5.31133428848113 2.87130403440627 -0.23280085207310
C 5.97608043399304 0.05380505971443 0.04637083264142
C 6.22404824855486 -1.30149341693661 0.18030662069639
H 6.87847916817281 0.68249877617629 -0.01196300429076
C 5.22365630683594 -2.31392536166448 0.27670365049823
C 7.66559419718402 -1.70879656244673 0.22503103488005
N 4.43439421754876 -3.18636680640678 0.36045412283851
O 8.60719757883900 -0.92805352222971 0.15139322571677
O 7.81365151738357 -3.05368556239202 0.35800529304992
H 8.78718620624828 -3.20169704061255 0.37638767673721
H -0.13807650798141 -1.18028169846188 0.13875780994923
B 1.93973716790025 3.33358719352677 -0.29426288674738
H 1.97116436517001 4.53647496472876 -0.41233586348121
B -0.05107044808928 0.02074461705129 0.01986763010933
O 3.54155289935468 0.03598891680328 0.03823106895776
$end

$rem
SCF_CONVERGENCE 6
MAX_SCF_CYCLES 100
EXCHANGE gen
LRC_DFT = true
omega = 219
CIS_N_ROOTS 10
CIS_SINGLETS true
CIS_TRIPLETS true
RPA FALSE
BASIS def2-TZVPD
XC_GRID = 000099000590
MEM_TOTAL 2000000
THRESH 14
SYM_IGNORE TRUE
SYMMETRY FALSE
$end

$xc_functional
C PBE 1.00
X wPBE 1.00
$end

#2

Probably an instability in the reference state. Try a stability analysis (INTERNAL_STABILITY = TRUE).

#3

Hi John, I tried using this “INTERNAL_STABILITY = TRUE”, but still obtained a negative triplet excitation energy.

#4

What did the stability analysis say? If the solution is unstable, that code is set up to perturb the MOs in the direction of the downward curvature and leave them on disk, so that a subsequent job can read in the perturbed MOs (SCF_GUESS = READ) and try to find a stable solution.

#5

I went ahead and ran this. (Side note: for TDDFT or other calculations that require the wave function and not just the energy, we set SCF_CONVERGENCE = 8 by default so you’re loosening the convergence. Also, PBE doesn’t require a grid that’s nearly so dense; the default works just fine. Neither of those choices affects the specific issue at hand, however.)

What this is telling you is that the triplet state is slightly lower in energy than the singlet state, at this geometry and for this particular functional and basis set.

#6

here is what i got in the output

===================================================
Beginning Test for Internal Stability

generating davidson guess vectors based on koopmans excitations
1 8.55e-01 00000 Davidson Iteration
2 2.63e-01 00000 Davidson Iteration
3 2.31e-01 00000 Davidson Iteration
4 1.42e-01 00000 Davidson Iteration
5 8.69e-02 00000 Davidson Iteration
6 4.95e-02 00000 Davidson Iteration
7 4.36e-02 00000 Davidson Iteration
8 3.50e-02 00000 Davidson Iteration
9 1.55e-02 00000 Davidson Iteration
10 7.57e-03 00000 Davidson Iteration
11 4.54e-03 00000 Davidson Iteration
12 2.06e-03 00000 Davidson Iteration
13 8.45e-04 00000 Davidson Iteration
14 5.02e-04 00000 Davidson Iteration
15 2.01e-04 00000 Davidson Iteration
16 7.49e-05 00000 Davidson Iteration
17 1.76e-03 00000 Davidson Iteration
18 1.05e-03 00000 Davidson Iteration
19 4.90e-04 00000 Davidson Iteration
20 3.56e-04 00000 Davidson Iteration
21 2.28e-04 00000 Davidson Iteration
22 1.19e-04 00000 Davidson Iteration
23 7.81e-05 00000 Davidson Converged
converged_eigenvalues
0.1767
0.3162
Threshold for negative eigenvalues: -1.0e-05
solution was a local minimum (stable)

End Test for Internal Stability

#7

Hi, maybe to add to this.

From a physial point of view, if your first triplet excitation energy is below the closed shell, then this means that you have a diradical. This simply means that in your system the T1 happens to be below S0.

From a methodological point of view, this situation means that the single reference DFT framework might break down. So, in such a case, you might have to go for a multireference method, spin-flip, etc.

As some further reading if you are interested
http://dx.doi.org/10.1002/jcc.70072

#8

Thanks for the insight. I shall surely explore the literature.

#9

You might see this paper about triplet energies with LRC-DFT:

https://doi.org/10.1063/1.3656734

1 Like
#10

Thanks so much, John.

#11

What is still interesting is the claim in the paper that TDA removes instabilities, which is incorrect in our case. The extract from the paper “the presence of these instabilities or nearby instabilities in the ground-state wavefunction leads to a possible divergence of the TDDFT excitations for the lowest triplet states and a strong sensitivity to the exact value of the range-separation parameter. The Tamm-Dancoff approximation is shown to remove this sensitivity completely, as is the SCF approach.” I do understand the role of HF contribution in the LRC functional, which causes these instabilities. However, I am still curious if this can be improved in some way.

#12

It doesn’t need to be an instability to get the behavior that you are seeing. It can simply be that the singlet/triplet gap is not large and TDDFT with this particular functional gets the state ordering wrong.

1 Like