# Gaussian 09 Geometry Optimization: Identical energies printed in output

This question may be slightly off-topic for this site, but since Gaussian is the "calculator" most often used by computational chemists, perhaps it is relevant still.

I have performed a transition state optimization, trying to tightly converge to the TS. I have used the following keywords in my Gaussian 09 rev D.01

# P opt=(calcall,tight,ts,noeigentest)
# freq=noraman
# pbepbe/def2svp
# scf=(MaxCycle=1000,tight)
# int=ultrafine
# EmpiricalDispersion=GD3
# geom=(ModRedundant,Checkpoint)
# NoSymm


The final SCF eneriges in the output are as follows ($grep "SCF Done" output.out):  SCF Done: E(RPBE-PBE) = -3985.31026080 A.U. after 16 cycles SCF Done: E(RPBE-PBE) = -3985.31003619 A.U. after 13 cycles SCF Done: E(RPBE-PBE) = -3985.31009833 A.U. after 11 cycles SCF Done: E(RPBE-PBE) = -3985.31007900 A.U. after 11 cycles SCF Done: E(RPBE-PBE) = -3985.31002766 A.U. after 11 cycles SCF Done: E(RPBE-PBE) = -3985.30992366 A.U. after 12 cycles SCF Done: E(RPBE-PBE) = -3985.30988992 A.U. after 11 cycles SCF Done: E(RPBE-PBE) = -3985.30987787 A.U. after 11 cycles SCF Done: E(RPBE-PBE) = -3985.30987912 A.U. after 10 cycles SCF Done: E(RPBE-PBE) = -3985.30987915 A.U. after 5 cycles SCF Done: E(RPBE-PBE) = -3985.30987916 A.U. after 4 cycles SCF Done: E(RPBE-PBE) = -3985.30987916 A.U. after 4 cycles SCF Done: E(RPBE-PBE) = -3985.30987916 A.U. after 4 cycles SCF Done: E(RPBE-PBE) = -3985.30987917 A.U. after 4 cycles SCF Done: E(RPBE-PBE) = -3985.30987917 A.U. after 4 cycles SCF Done: E(RPBE-PBE) = -3985.30987917 A.U. after 4 cycles SCF Done: E(RPBE-PBE) = -3985.30987918 A.U. after 4 cycles SCF Done: E(RPBE-PBE) = -3985.30987918 A.U. after 4 cycles SCF Done: E(RPBE-PBE) = -3985.30987918 A.U. after 4 cycles SCF Done: E(RPBE-PBE) = -3985.30987918 A.U. after 4 cycles SCF Done: E(RPBE-PBE) = -3985.30987918 A.U. after 4 cycles SCF Done: E(RPBE-PBE) = -3985.30987918 A.U. after 4 cycles SCF Done: E(RPBE-PBE) = -3985.30987918 A.U. after 4 cycles SCF Done: E(RPBE-PBE) = -3985.30987918 A.U. after 4 cycles SCF Done: E(RPBE-PBE) = -3985.30987918 A.U. after 4 cycles SCF Done: E(RPBE-PBE) = -3985.30987918 A.U. after 4 cycles SCF Done: E(RPBE-PBE) = -3985.30987918 A.U. after 3 cycles SCF Done: E(RPBE-PBE) = -3985.30987918 A.U. after 4 cycles SCF Done: E(RPBE-PBE) = -3985.30987918 A.U. after 2 cycles SCF Done: E(RPBE-PBE) = -3985.30987918 A.U. after 2 cycles  Notice that many of the converged SCF energies are identical. My question is of course why has this happened, and is this a valid result? Am I converging so tightly that the energy change is simply in the decimals that Gaussian has left out? The predicted energy changes are as follows ($ grep "Predicted change in Energy" output.out):

 Predicted change in Energy= 3.362413D-05
Predicted change in Energy=-6.527689D-05
Predicted change in Energy= 1.690958D-05
Predicted change in Energy= 5.120292D-05
Predicted change in Energy= 1.023774D-04
Predicted change in Energy= 3.449328D-05
Predicted change in Energy= 1.361217D-05
Predicted change in Energy=-1.264148D-06
Predicted change in Energy=-9.312661D-09
Predicted change in Energy=-7.213572D-09
Predicted change in Energy=-5.808562D-09
Predicted change in Energy=-4.708143D-09
Predicted change in Energy=-3.818469D-09
Predicted change in Energy=-3.094391D-09
Predicted change in Energy=-2.512754D-09
Predicted change in Energy=-1.889480D-09
Predicted change in Energy=-1.661426D-09
Predicted change in Energy=-1.361766D-09
Predicted change in Energy=-1.110023D-09
Predicted change in Energy=-8.605687D-10
Predicted change in Energy=-7.281627D-10
Predicted change in Energy=-5.759861D-10
Predicted change in Energy=-4.835488D-10
Predicted change in Energy=-3.940408D-10
Predicted change in Energy=-3.130737D-10
Predicted change in Energy=-2.602865D-10
Predicted change in Energy=-2.368678D-10
Predicted change in Energy=-1.560729D-10
Predicted change in Energy=-1.408281D-10
Predicted change in Energy=-1.448954D-10


Seeing as these values quickly drop to 1e-9 and 1e-10, perhaps I am right in assuming that the identical energies printed in the output are identical only due to rounding the energy to 8 decimals?

• Your SCF energies are only identical to eight decimal places! – LordStryker Sep 17 '18 at 12:37
• That was my suspicion. – Yoda Sep 17 '18 at 15:27