# T1 Diagnostic for Coupled-Cluster method

Hello,
After running CCSD(T) calculation for H2O molecule, I was looking into the output file to find T1 diagnostic value. Can anyone show me where to look? There is only T1^2 value after reporting energies and I don’t know what is referring to.

Input file:

$molecule 0 1 H -2.3527135 2.2827770 0.4401250 O -3.1357501 2.2827770 -0.1660574 H -3.9187867 2.2827770 0.4401250$end

$rem jobtype = sp method = ccsd(t) basis = def2-SVP n_frozen_core = fc ccman2 = true$end

Output file:

Starting (T) calculation…
Using double precision libpt code
Running restricted (T) code
Using 1 integral batch

(T) calculation completed in 0.01 sec
(T) energy is -0.0031326630

SCF energy = -75.95721338
MP2 energy = -76.16060275
CCSD correlation energy = -0.21302039
CCSD total energy = -76.17023378
CCSD(T) correlation energy = -0.00313266
CCSD(T) total energy = -76.17336644

CCSD T1^2 = 0.0007 T2^2 = 0.0588 Leading amplitudes:

Amplitude Orbitals with energies
0.0097 3 (A1) A → 4 (A1) A
-0.5621 0.1710
0.0097 3 (A1) B → 4 (A1) B
-0.5621 0.1710
0.0075 1 (B1) A → 6 (B1) A
-0.6863 2.4830
0.0075 1 (B1) B → 6 (B1) B
-0.6863 2.4830

Amplitude Orbitals with energies
-0.0512 1 (B2) A 1 (B2) B → 2 (B2) A 2 (B2) B
-0.4957 -0.4957 1.2016 1.2016
0.0512 1 (B2) A 1 (B2) B → 2 (B2) B 2 (B2) A
-0.4957 -0.4957 1.2016 1.2016
0.0512 1 (B2) B 1 (B2) A → 2 (B2) A 2 (B2) B
-0.4957 -0.4957 1.2016 1.2016
-0.0512 1 (B2) B 1 (B2) A → 2 (B2) B 2 (B2) A
-0.4957 -0.4957 1.2016 1.2016

You can calculate the T1 diagnostic by taking the square root of that number and dividing it by $\sqrt{2 * (N_{\alpha} + N_{\beta})$. In Python it might look like

t1_diagnostic = math.sqrt(t1_squared) / math.sqrt(2 * (nalpha_elec + nbeta_elec))


Thank you ericb.
As you helped, I calculated T1 value (T1= 0.00591608) which is really close the value I got it from Molpro software with the same geometry coordinate (T1 diagnostic: 0.00653054).
However, in references, I cannot see multiplier 2 in denominator of T1 formula and I guess this was the reason I got wrong answers.
t1_diagnostic = math.sqrt(t1_squared) / math.sqrt(2 * (nalpha_elec + nbeta_elec))

Thank you again!

Apologies, the factor of two in the denominator is only for a RHF reference. It is not there for UHF; it is related to the number of doubly-occupied orbitals.