DFT Calculations for Beginners: ORCA and Gaussian Input Files, Functionals and Basis Sets, Optimization and Frequency Checks

Software

Choosing software: ORCA, Gaussian, xtb/CREST and periodic codes

For DFT on molecules, academic users usually choose ORCA or Gaussian; xtb/CREST handles conformer search and pre-optimization; crystals and surfaces need plane-wave or mixed-basis codes.

In Bing, only about one in ten results for the bare query “orca” points to the quantum chemistry program; the rest are about killer whales and other software named Orca. Download ORCA from orcaforum.kofo.mpg.de or the FACCTs website.

CentOS and similar systems ship a screen reader also called orca, so typing orca may start that program. Calling ORCA by its full path or an alias avoids this.

Functional and basis set

Functional and basis set: decide the task first, then the level

The common practice is to optimize and compute frequencies at a cheap level and compute single-point energies at a higher level. Geometries and frequencies are insensitive to the basis set; energies are sensitive to both basis set and functional.

Always add a dispersion correction. Standard functionals such as B3LYP and PBE0 cannot describe van der Waals attraction; the 2022 best-practice guide by Grimme and co-workers calls dispersion correction “indispensable in any DFT treatment”. Adding D3(BJ) costs almost nothing.

B3LYP/6-31G* is outdated for two reasons: missing dispersion makes it “over-repulsive”, and the small basis set causes a large basis set superposition error (BSSE). Kruse, Goerigk and Grimme analysed the error compensation of this combination for thermochemistry in J. Org. Chem. 2012; the Angew. Chem. guide by Bursch et al. (2022) states that improved methods have made B3LYP/6-31G* computations “obsolete”. Sobereva places 6-31G* in the “minimum acceptable” double-zeta tier and adds that “minimum acceptable” does not mean publishable as is.

BSSE is the artificial stabilization of a dimer when each monomer borrows the other's basis functions; it grows as the basis set shrinks. Use counterpoise correction for binding energies with double-zeta basis sets; for chemical bond energies Sobereva considers counterpoise unnecessary or even harmful.

In ORCA, ωB97M-V has analytic gradients but no analytic Hessian, so frequency calculations are expensive; use it for single points only. M06-2X is sensitive to the integration grid, and optimizations with it often show small imaginary frequencies and convergence trouble.

Flexible molecules (more than two or three rotatable single bonds) need a conformer search first; otherwise the optimization only finds the local minimum nearest the starting structure. The 2022 guide by Grimme and co-workers recommends an automated search with CREST, followed by DFT re-optimization and re-ranking of the conformers within the energy window; relative energies from xtb are only for screening.

For excited states, note that ORCA's TD-DFT uses the Tamm–Dancoff approximation (TDA) by default, whereas Gaussian's TD keyword runs full TDDFT by default. Excitation energies and oscillator strengths differ between the two; to compare with Gaussian results or the literature, write TDA false in the ORCA %tddft block. The number of states is set with %tddft NRoots 10 end in ORCA and TD(NStates=10) in Gaussian.

Level                   water dimer noCP / CP   benzene dimer (parallel-displaced) noCP / CP
B3LYP/6-31G*            -7.32 / -5.70           +2.39 / +4.58
B3LYP/def2-SVP          -8.11 / -4.81           +2.52 / +4.03
B3LYP-D3(BJ)/def2-SVP   -8.75 / -5.45           -4.18 / -2.67
B3LYP/def2-TZVP         -5.53 / -4.91           +3.43 / +3.76
B3LYP-D3(BJ)/def2-TZVP  -6.17 / -5.55           -3.27 / -2.94
Reference               -4.99                   -2.65
noCP: no counterpoise correction; CP: counterpoise-corrected. Negative values mean binding.

ORCA input

The ORCA input file line by line, and the Gaussian equivalent

Below is an optimization + frequency input for ethanol. ORCA input is case-insensitive (except file names), and text after # is a comment.

! B3LYP D3BJ def2-SVP Opt Freq      # method, dispersion, basis, task; case-insensitive
%pal nprocs 8 end                    # 8 MPI processes
%maxcore 3000                        # 3000 MB per process, about 24 GB in total
* xyz 0 1                            # coordinate format, charge, spin multiplicity
  C   -1.1855   -0.2259    0.0000
  C    0.1586    0.4880    0.0000
  O    1.2075   -0.4708    0.0000
  H   -1.2848   -0.8641    0.8823
  H   -1.2848   -0.8641   -0.8823
  H   -2.0068    0.4987    0.0000
  H    0.2384    1.1393    0.8822
  H    0.2384    1.1393   -0.8822
  H    2.0491    0.0005    0.0000
*

%nprocshared=8
%mem=24GB
%chk=ethanol.chk
# opt freq B3LYP/def2SVP EmpiricalDispersion=GD3BJ

ethanol opt freq

0 1
C   -1.1855   -0.2259    0.0000
C    0.1586    0.4880    0.0000
O    1.2075   -0.4708    0.0000
H   -1.2848   -0.8641    0.8823
H   -1.2848   -0.8641   -0.8823
H   -2.0068    0.4987    0.0000
H    0.2384    1.1393    0.8822
H    0.2384    1.1393   -0.8822
H    2.0491    0.0005    0.0000

1. 01

   ! keyword line

   Method, dispersion, basis set and task; several ! lines are allowed. Common tasks: Opt, Freq (analytic frequencies), NumFreq (numerical frequencies), OptTS, IRC, TightOpt, TightSCF. Since ORCA 5.0, RIJCOSX is on by default for hybrid functionals and the def2/J auxiliary basis is chosen automatically. Optimizations use TightSCF automatically.

2. 02

   %pal nprocs N end

   Number of parallel processes; equivalently write PAL8 on the keyword line. Parallel runs must call orca by its full path and must not be wrapped in mpirun; otherwise the output is interleaved or the job fails.

3. 03

   %maxcore M

   Memory per process in MB, default 4096. Total memory is about M × nprocs, and ORCA often uses more than M, so the manual advises keeping the total at no more than 75–80% of physical memory. Example: a 32 GB, 8-core machine has about 30 GB left after the operating system; 30000/8 = 3750, and Sobereva recommends 3000. When memory is too low, the SCF stops with Not enough memory available! Please increase MaxCore to more than: … MB.

4. 04

   * xyz charge multiplicity

   The first line gives the coordinate format, total charge and spin multiplicity 2S+1, and the block ends with a line containing *. You can also write * xyzfile 0 1 file.xyz to read a file. A closed-shell neutral molecule is 0 1; a radical is 0 2. An even number of electrons requires an odd multiplicity, and an odd number requires an even one.

5. 05

   Gaussian equivalents

   %nprocshared corresponds to %pal; %mem is the total memory of the job (default 800 MB), unlike ORCA's per-core maxcore; the route line starting with # corresponds to the ! line; basis set names have no hyphen (def2SVP); dispersion is EmpiricalDispersion=GD3BJ; blank lines are required after the title and after the coordinates.

Optimization and frequencies

Geometry optimization and frequencies: convergence criteria and the output lines to check

Frequencies must be computed at exactly the same level as the optimization (functional, basis set, dispersion, solvent model, integration grid); otherwise they are meaningless and spurious imaginary frequencies appear. The simplest way is to put Opt Freq in the same job.

Measured on this page (Psi4 1.11, B3LYP-D3(BJ)/def2-SVP, 8 threads): ethanol optimization 8.2 s, frequencies 104.8 s, lowest frequency 259.8 cm⁻¹, no imaginary frequency; the three harmonic frequencies of water are 1639, 3792 and 3887 cm⁻¹ with a zero-point energy of 13.32 kcal/mol. Harmonic frequencies are generally higher than experimental fundamentals; multiply by a frequency scaling factor for the functional and basis set before comparing with experimental IR spectra (see Sobereva 221).

• ORCA: the output must contain THE OPTIMIZATION HAS CONVERGED. When the optimization hits the maximum number of cycles, ORCA can still end with ORCA TERMINATED NORMALLY, so checking only the last line is misleading.
• Gaussian: four YES in the optimization summary and Stationary point found; the file ends with Normal termination.
• Frequencies: ORCA marks imaginary modes with ***imaginary mode***; Gaussian prints negative numbers on the Frequencies lines. The six zero frequencies of translation and rotation (five for linear molecules) are projected out and say nothing about Hessian quality.
• Gaussian re-checks convergence at the end of freq: four YES after the optimization but NO for displacement after freq happens because the optimization uses an approximate Hessian and freq uses the exact one. Values less than twice the threshold without imaginary frequencies are generally acceptable (Sobereva 278).
• ORCA analytic Hessians are available for SCF methods only; double hybrids and RI-JK need NumFreq, and numerical frequencies can be off by up to 50 cm⁻¹.

Optimization not converging

When the optimization does not converge: work through this order

Most non-converging optimizations oscillate around the minimum. First play the optimization trajectory in GaussView or Chemcraft and look at the energy and force curves to see whether it oscillates or is still going down.

1. 01

   Energy and forces still decreasing overall

   There were simply not enough steps. Use opt=maxcycles=N in Gaussian or MaxIter N in the ORCA %geom block, and restart from the last structure. If it already oscillates, more steps will not help.

2. 02

   Rule out SCF problems first

   An SCF failure at one step also stops the optimization. In Gaussian this is an L502 error; from G16 B.01 an unconverged SCF only prints Convergence criterion not met and does not stop, so check for it yourself.

3. 03

   Use a finer integration grid

   Most effective for Minnesota functionals such as M06-2X. G16 already defaults to int=ultrafine; ORCA 6 defaults to DefGrid2, which you can raise to DefGrid3.

4. 04

   Use an exact Hessian

   Gaussian: opt=calcfc (first step only), opt=recalc=3~5 (G16, every 3–5 steps), opt=calcall (every step, small systems only). ORCA: %geom Calc_Hess true, Recalc_Hess 5 end.

5. 05

   Change the optimizer or reduce the step

   In Gaussian, try opt=gdiis first for noncovalent complexes and flexible large molecules; when the structure keeps oscillating slightly, use opt(gdiis,maxstep=3~5,notrust). In ORCA, adjust Trust in %geom (default -0.3; a negative value means a fixed trust radius).

6. 06

   Check symmetry and the solvent model

   If the starting structure has higher symmetry than the true minimum, the optimization stops at a saddle point; break the symmetry. Opt freq with SMD tends to converge poorly and give spurious imaginary frequencies; Sobereva recommends IEFPCM for optimization and frequencies, and SMD for the energies.

7. 07

   Loosen the criteria only as a last resort

   opt=loose or LooseOpt only gives a rough structure, and frequencies afterwards often show imaginary modes.

Imaginary frequencies

Imaginary frequencies: how many are right, how large matters, how to remove them

A minimum (reactant, product, intermediate) must have no imaginary frequency; a transition state must have exactly one, and its vibration must correspond to the reaction coordinate under study.

Displacing along the imaginary mode is the first choice only when symmetry causes the imaginary frequency. Sobereva points out that the common online advice to push the structure along every imaginary mode is wrong; small imaginary frequencies should first be addressed through convergence criteria, integration grid and Hessian quality.

A small imaginary frequency that cannot be removed has little effect on the electronic energy and zero-point energy: a 30 cm⁻¹ mode contributes only 0.18 kJ/mol to the ZPE. Its effect on entropy and free energy is larger: ignoring a mode of about 20 cm⁻¹ as imaginary can shift the free energy by about 5 kJ/mol (Sobereva 699). Grimme and co-workers (2022) suggest treating small imaginary frequencies below 50–100 cm⁻¹ as real and computing the entropy with mRRHO; Sobereva considers this approach insufficiently tested and does not recommend it lightly. Either way, state the treatment in the paper.

Measured on this page: ethane built in the eclipsed form and optimized with its symmetry kept “converged” in 3.9 seconds, and the frequency calculation gave one imaginary frequency of 308.3i cm⁻¹, the relative twist of the two methyl groups. Changing one H–C–C–H dihedral to 20° to break the symmetry and re-optimizing gave the staggered form with no imaginary frequency (lowest 317.9 cm⁻¹) and an energy 2.93 kcal/mol lower, the torsional barrier of ethane. This is the typical symmetry-induced imaginary frequency, removed by adjusting the structure along the mode.

Thermal corrections

Zero-point energy, enthalpy and free energy: which output line to read

Thermal corrections come from the frequency calculation and are added to the electronic energy to give enthalpy and free energy. With a higher-level single point, add the correction from the lower-level frequencies to the higher-level electronic energy.

ORCA computes the entropy with Grimme's quasi-RRHO by default (reference frequency QRRHORefFreq 100 cm⁻¹), while Gaussian uses the harmonic RRHO. The same structure can therefore give G values that differ by a few tenths to more than 1 kcal/mol between the two programs, more for flexible molecules. To match Gaussian, set QuasiRRHO false in the ORCA %freq block, or recompute both with Shermo.

Free energies of reactions in solution need a standard-state correction: gas-phase calculations refer to 1 atm, the solution standard state is 1 mol/L, and at 298.15 K each species gets 1.89 kcal/mol (Sobereva 327). For a reaction A + B → C, omitting it shifts ΔG by 1.89 kcal/mol.

Absolute energies from different functionals cannot be compared. Measured on this page: for the same ethanol structure, B3LYP-D3(BJ)/def2-TZVP gives −155.11617 Eh and M06-2X/def2-TZVP gives −155.02666 Eh, a difference of 56 kcal/mol; only energy differences at the same level are meaningful.

1 Eh (Hartree) = 627.5095 kcal/mol = 2625.4996 kJ/mol = 27.2114 eV = 219474.63 cm⁻¹
1 kcal/mol = 4.184 kJ/mol
1 bohr = 0.529177 Å
Example: ΔE = −0.0046731 Eh → −0.0046731 × 627.5095 = −2.93 kcal/mol

Transition states

Transition state search: scan for a guess, OptTS, frequencies, IRC

TS optimization is far more sensitive to the starting structure and Hessian quality than minimization. The standard workflow has four steps: scan for a guess, optimize the TS with an exact Hessian, confirm one imaginary frequency, and run an IRC to confirm the reactant and product it connects.

# Step 1: relaxed scan for a TS guess (ORCA counts atoms from 0)
! B3LYP D3BJ def2-SVP Opt
%pal nprocs 8 end
%maxcore 3000
%geom
  Scan B 0 5 = 3.00, 1.50, 16 end   # distance between atoms 0 and 5 from 3.00 to 1.50 Angstrom, 16 points
end
* xyzfile 0 1 reactant.xyz

# Step 2: take the highest-energy scan point, compute an exact Hessian, optimize the TS, then frequencies
! B3LYP D3BJ def2-SVP OptTS Freq
%pal nprocs 8 end
%maxcore 3000
%geom
  Calc_Hess true      # exact Hessian at the first step
  Recalc_Hess 5       # recompute every 5 steps for difficult cases
end
* xyzfile 0 1 tsguess.xyz

# Step 3: IRC to check which reactant and product the TS connects
! B3LYP D3BJ def2-SVP IRC
%pal nprocs 8 end
%maxcore 3000
%irc
  MaxIter 60                     # default is 20, often too few to reach the minima
  InitHess read
  Hess_Filename "ts.hess"        # reuse the Hessian from step 2
end
* xyzfile 0 1 ts.xyz

1. 01

   Scan for a guess

   Run a relaxed scan along the forming or breaking bond and take the highest-energy point. ORCA can also do the scan and TS optimization in one job with ScanTS. ORCA numbers atoms from 0, so copying Gaussian atom numbers scans the wrong atoms.

2. 02

   OptTS needs an exact Hessian

   In ORCA write Calc_Hess true or read an existing .hess; in Gaussian write opt(ts,calcfc,noeigentest). With the default approximate Hessian TS optimizations often drift away. Gaussian's QST2 interpolated guess is usually worse than a structure you build by hand.

3. 03

   Confirm with frequencies

   Exactly one imaginary frequency; animate it in GaussView, Chemcraft or orca_pltvib to confirm that the atoms move along the intended reaction. TS, IRC and minimum optimizations should use the same level.

4. 04

   Verify with IRC

   ORCA runs both directions by default (Direction both) and writes _IRC_F.xyz, _IRC_B.xyz and _IRC_Full_trj.xyz. The default MaxIter is 20, which often does not reach the end; IRC end points are not strict minima, so optimize them before comparing with the reactant and product.

Analysis

Reading energies, frequencies and orbitals, and the main entry points of Multiwfn

Multiwfn analyses wavefunction files. Gaussian's formchk converts .chk to .fchk; ORCA's orca_2mkl name -molden writes .molden.input; Psi4 can write .fchk directly.

On Windows, do not redirect ORCA output in PowerShell 5: the resulting .out file is Unicode-encoded and Multiwfn and OfakeG cannot read it. Use cmd or cmder (Sobereva 451).

Basis sets with diffuse functions make basis-function-based analyses (Mulliken, Mayer bond order, orbital composition) meaningless; real-space analyses such as electron density, ELF and electrostatic potential need only 6-31G* to def2-TZVP (Sobereva 336).

# Parallel runs must call orca by its full path; do not start it with mpirun
/opt/orca_6_1_1/orca ethanol.inp > ethanol.out

# Check real convergence (ORCA TERMINATED NORMALLY at the end is not enough)
grep "THE OPTIMIZATION HAS CONVERGED" ethanol.out
grep "FINAL SINGLE POINT ENERGY" ethanol.out | tail -1
grep "imaginary mode" ethanol.out          # no output means no imaginary frequency

# Write a molden file that Multiwfn can read
/opt/orca_6_1_1/orca_2mkl ethanol -molden

Errors

Common errors: message, cause and fix

Raising the SCF iteration limit (scf=maxcyc=500 or MaxIter 500) almost never fixes non-convergence. Gaussian's default limit is 128 cycles; if the SCF does not converge within that, more cycles rarely help (Sobereva 61).

When the SCF is very hard to converge, check the structure itself first: atoms too close, missing hydrogens, unsaturated cuts in cluster models, or a transition-metal multiplicity that is not the ground state all make SCF convergence hard.

Measured on this page

Running the same workflow with Psi4 and xtb when ORCA is not available

ORCA requires registration on its forum before download, so this page used Psi4 1.11 from conda-forge for the same optimization, frequency, TS and IRC steps, and xtb for semi-empirical optimization and frequencies. Test conditions on this page: Psi4 1.11 and xtb 6.7.1 (both from conda-forge) on an 8-core, 16 GB Apple Silicon laptop, 8 threads.

In Psi4 1.11, functionals with -d3bj need the dftd3-python package; otherwise the run fails with Program s-dftd3 is registered with QCEngine, but cannot be found.

Psi4 computes B3LYP-D3(BJ) frequencies by finite differences of gradients, so the ethanol frequencies took 13 times as long as the optimization. ORCA and Gaussian have analytic Hessians for B3LYP, so their frequency-to-optimization time ratio is much smaller.

The conda-forge macOS arm64 build of CREST 3.0.2 did not complete on this machine: the default mode hit ERROR STOP at Setting up backup calculator; with --legacy --quick the metadynamics for ibuprofen (33 atoms) finished in 347 seconds, but the CREGEN sorting step hit ERROR STOP again. In full mode CREST estimated 1 hour 38 minutes on 8 threads for ibuprofen. Run conformer searches on Linux.

# conda env: micromamba create -n qc -c conda-forge python=3.11 psi4 dftd3-python dftd4-python
import psi4
psi4.set_num_threads(8)
psi4.set_memory('10 GB')                       # Psi4 memory is the total for the job
psi4.core.set_output_file('ethanol.out', False)
mol = psi4.geometry("""
0 1
C   -1.1855   -0.2259    0.0000
C    0.1586    0.4880    0.0000
O    1.2075   -0.4708    0.0000
H   -1.2848   -0.8641    0.8823
H   -1.2848   -0.8641   -0.8823
H   -2.0068    0.4987    0.0000
H    0.2384    1.1393    0.8822
H    0.2384    1.1393   -0.8822
H    2.0491    0.0005    0.0000
""")
e_opt = psi4.optimize('b3lyp-d3bj/def2-svp')            # geometry optimization
e, wfn = psi4.frequency('b3lyp-d3bj/def2-svp', return_wfn=True)  # frequencies and thermochemistry
print('freqs (cm-1):', wfn.frequencies().to_array())    # negative values are imaginary
print('G correction (Eh):', psi4.variable('GIBBS FREE ENERGY CORRECTION'))
e_sp = psi4.energy('wb97x-d/def2-tzvp')                 # higher-level single point

# Install: micromamba create -n xtb -c conda-forge xtb crest
export OMP_NUM_THREADS=8 OMP_STACKSIZE=1G
xtb ethanol.xyz --ohess --gfn 2 > xtb.out      # optimization + frequencies, writes xtbopt.xyz
crest ibuprofen.xyz --gfn2 -T 8 > crest.out    # conformer search, writes crest_conformers.xyz and crest_best.xyz

Chinese community

Experience verified in the Chinese community

The items below come from the Computational Chemistry Commune (keinsci), Sobereva's blog and CSDN. Only items with concrete parameters or error messages that agree with the official manuals or the runs on this page are included.

Hand it to an agent

Hand this workflow to an agent

You can describe the calculation in one sentence and let Scientify's science agent run it in a cloud computer.

Example instruction: “Here are xyz files of the reactant and product. Run a CREST conformer search first, optimize the lowest conformer at B3LYP-D3(BJ)/def2-SVP with frequencies; scan the C1–O5 distance for a TS guess, optimize the TS with OptTS and an exact Hessian, confirm a single imaginary frequency and run an IRC; finally compute ωB97M-V/def2-TZVP single points and report ΔG‡ and ΔG including thermal corrections and the 1 M standard-state correction.”

What the agent does: installs the needed programs in the workspace (xtb, CREST, open-source quantum chemistry codes; ORCA can run from an installer you provide or on your own server over SSH), writes the inputs, checks the convergence lines and imaginary frequencies at every step, works through non-convergence in the order on this page and logs each change; compiles the energy table, converts units, and reviews the results adversarially, for example checking the direction of the imaginary mode and whether the IRC end points match the reactant and product. The task keeps running after you shut down your computer.

Outputs: all inputs, outputs and logs, xyz files of the optimized structures, a summary table of energies and thermal corrections, scan curves and IRC energy profiles. The workspace keeps code and parameters so the work can be reproduced.

You still need to check: the chemical plausibility of the mechanism and guess structures, charge and multiplicity, whether the functional and basis set suit your system, the choice of solvent model, and whether the TS imaginary mode corresponds to the reaction you study.

Writing the paper

Settings to report in the methods section

Reviewers and readers need the following to reproduce the calculations; missing any of them may prompt a request for more information.

• Programs and versions: ORCA 6.1.1, Gaussian 16 Rev. C.02, xtb 6.7.1, CREST 3.0.2, Multiwfn version date
• Optimization and frequency level: functional, dispersion correction (D3(BJ) or D4), basis set, and whether RIJCOSX was used
• Single-point level and how the final energy was combined (E single point + G correction)
• Solvent model and solvent, and whether optimization and single point used different models
• Thermochemistry settings: temperature, pressure, RRHO or quasi-RRHO, standard-state correction, frequency scaling factor
• Conformer search method (CREST, energy window)
• How transition states were confirmed: imaginary frequency value, IRC
• Treatment of imaginary frequencies: whether small imaginary modes remain and how they were handled
• Citations: functional, dispersion correction, basis set, program papers; Multiwfn requires both papers