The output of a typical ab initio calculation is quite daunting to novices. So many numbers, so many foreign-sounding terms, and then they repeat over nineteen times before the end of the file is reached ... and there is no answer in big bold red letters at the last line of the output. Gaussian at least emits reassuring messages from the past intellectuals, like this one:
"THE TEST OF A FIRST RATE INTELLIGENCE IS THE ABILITY TO HOLD TWO OPPOSED
IDEAS IN THE MIND AT THE SAME TIME, AND STILL RETAIN THE ABILITY TO FUNCTION.
ONE SHOULD, FOR EXAMPLE, BE ABLE TO SEE THAT THINGS ARE HOPELESS AND YET BE
DETERMINED TO MAKE THEM OTHERWISE."
-- F. SCOTT FITZGERALD
Most quantum chemistry calculations that you will be doing fall into one of the two categories: geometry optimization, and single point calculations. The calculation that you did with formaldehyde in the previous tutorial using Opt=CalcAll was an example of geometry optimization involving calculation of the Hessian at every step. In this calculation, a line such as "SCF Done: E(RHF) = -113.873389817 A.U. after 11 cycles" reports on the molecular energy in Hartree-Fock approximation at each step in optmization. You could use Unix command grep to see how the energy decreases during optimization:
grep 'SCF Done:' formaldehyde.out
SCF Done: E(RHF) = -113.873389817 A.U. after 11 cycles SCF Done: E(RHF) = -113.874554607 A.U. after 12 cycles SCF Done: E(RHF) = -113.874558296 A.U. after 12 cycles
To confirm that the calculation really converged, you would look also at the forces, which should become close to zero, and the size of structural changes from step to step (displacements), which should also be close to zero. These are reported at the end of each geometry optimization ctycle in a block like this:
Item Value Threshold Converged?
Maximum Force 0.033774 0.000450 NO
RMS Force 0.013621 0.000300 NO
Maximum Displacement 0.044624 0.001800 NO
RMS Displacement 0.022543 0.001200 NO
You can use grep 'Maximum Force ' formaldehyde.out to monitor the convergence. The convergence of energy, forces, and displacements is graphically shown by MOLDEN and other programs for the visualization of results from electronic structure calculations.
The calculations of hydrogen atom that you did with Mathematica, or of neon that you did with Gaussian were examples of single point calculations. The hallmark of a single point calculation is that you are not altering the positions of nuclei in the calculation. Single point calculations are performed when you do not request geometry optimization. It is perfectly fine to carry out single point calculations on molecules, a typical example being a calculation of MP4(SDTQ) energy of 1,2-dichloroethane with cc-pVTZ basis set based on the geometry that was obtained in HF/6-31+G(d,p) optimization. Such a calculation would be commonly noted as MP4/cc-pVTZ//HF/6-31+G(d,p). Single point calculations are valuable because it allows us rapidly esimate the effect of electron correlation and larger basis sets without a need for time-consuming optimization of geometry using expensive methods such as MP4/cc-pVTZ. The results of such single point calculations with Gaussian appear near the middle of the file in a block like this
E2= -0.4368350986D+00 EUMP2= -0.11552896351550D+03 Would need an additional 317305303 words for in-memory AO integral storage. DD1Dir will call FoFDir 1 times, MxPair= 56 NAB= 28 NAA= 0 NBB= 0 NumPrc= 2. Petite list used in FoFDir. MinBra= 0 MaxBra= 3 Meth= 1. IRaf= 0 NMat= 56 IRICut= 56 DoRegI=T DoRafI=T ISym2E=-1 JSym2E=1. MP4(D)= -0.89430527D-02 MP4(S)= -0.32709493D-02 MP4(R+Q)= 0.82939466D-02 Time for triples= 381.47 seconds. MP4(T)= -0.16615675D-01 E3= -0.14219127D-01 EUMP3= -0.11554318264D+03 E4(DQ)= -0.64910604D-03 UMP4(DQ)= -0.11554383175D+03 E4(SDQ)= -0.39200554D-02 UMP4(SDQ)= -0.11554710270D+03 E4(SDTQ)= -0.20535731D-01 UMP4(SDTQ)= -0.11556371837D+03
Here, E2 is the correlation energy in the second order Moller-Plesset theory, and EUMP2 is the total (HF + E2) energy in MP2 approximation. Similarly, EUMP3 is the total (HF + E2 + E3) in MP3 approximation, and UMP4(SDTQ) is the total MP4 energy. A report about molecular orbitals follows showingh the energies of occupied and unoccupied orbitals. Notice that in stable molecules, occupied orbitals have negative energies, meaning that the electrons are stably bound in the molecule:
Alpha occ. eigenvalues -- -20.55978 -11.27039 -1.35923 -0.92635 -0.69229 Alpha occ. eigenvalues -- -0.62102 -0.59378 -0.50516 -0.45212 Alpha virt. eigenvalues -- 0.02847 0.04298 0.04659 0.05303 0.09912 Alpha virt. eigenvalues -- 0.11650 0.12919 0.13997 0.16541 0.17327
At the end, the program reports CPU time that was needed for this calculation ("Job cpu time: 0 days 0 hours 9 minutes 52.2 seconds."). An actual wall clock time might be longer than the CPU time (e.g. if using a shared slow disk), or shorter (if using multiple CPUs). An annotated example explaining other aspects of Gaussian output is available.
Even with nprint=-5 directive, PC GAMESS prints out a large amount of information about the geometry, basis set, and calculation methodology before solving the SCF equations. The results of PC GAMESS / Firefly calculation are organized near the end of the file. Notice a slightly different labeling but the results are essentially the same
RESULTS OF MOLLER-PLESSET 4TH ORDER CORRECTION ARE
E(RHF) = -115.0921284169
E(D,2) = -0.4368351038
E(MP2) = -115.5289635207
E(D,3) = -0.0142191251
E(D,2+3) = -0.4510542289
E(MP3) = -115.5431826458
E(S,4) = -0.0032709496
E(D,4) = -0.0089430532
E(D,2+3+4) = -0.4599972821
E(T,4) = -0.0166156761
E(R+Q,4) = 0.0082939469
E(SDTQ,4) = -0.0205357319
E(SDTQ,2+3+4)= -0.4715899608
E(MP4-SDTQ) = -115.5637183777
..... DONE WITH MP4 ENERGY .....
CPU TIME: STEP = 57.30 , TOTAL = 117.8 SECONDS ( 2.0 MIN)
WALL CLOCK TIME: STEP = 57.34 , TOTAL = 117.9 SECONDS ( 2.0 MIN)
Notice that the energy in programs such as Gaussian and PC GAMESS / Firefly is in atomic (Hartree) units. In most situations we are interested in energy differences between two structures (product - reactant) because these energy differences are closely related to observable properties, such a reaction enthalpy. For example, if the HF calculation for reactant (S)-3,4,4-trimethyl-1-(methylthio)-1-(2-propenylthio-(Z)-1-pentene gave SCF Done: E(RHF) = -1262.32177116 and the HF calculation for the product methyl ester of 2-[(1S)-1,2,2-trimethylpropyl]-4-pentene(dithioic) acid with the same basis set gave SCF Done: E(RHF) = -1262.32878468 then the energy difference between reactant and product in kcal/mol units can be calculated with Python as
[kalju@sulev Gaussian]$ python Python 2.4.3 (#1, May 24 2008, 13:57:05) [GCC 4.1.2 20070626 (Red Hat 4.1.2-14)] on linux2 Type "help", "copyright", "credits" or "license" for more information. >>> 627.51*(-1262.32878468+1262.32177116) -4.401053935120367
Here, 627.51 is a conversion factor from Hartrees to kcal/mol. Notice that the negative sign suggests that the thio-Claisen reaction is predicted to be enthalpically favorable by the HF method.