CHAPTER 04 · COMMON CALCULATIONS

Single point energy

Energy and wavefunction at a fixed geometry — the most basic ORCA job, and the starting point for every other calculation.

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Basic examples — HF, DFT

A single-point calculation is the simplest thing you can do in ORCA. You need a method, a basis set, and the coordinates. If no run-type keyword is given, ORCA defaults to a single-point job.

HF single point

# HF single point on CO
! HF def2-SVP

* xyz 0 1
  C   0.0   0.0   0.0
  O   0.0   0.0   1.13
*

DFT (B3LYP) single point

# B3LYP/def2-TZVP single point on cyclohexane
! B3LYP D4 def2-TZVP RIJCOSX def2/J TightSCF

* xyzfile 0 1 cyclohexane.xyz

Combining RIJCOSX with def2/J is the de-facto standard acceleration scheme for hybrid DFT. Enabling both treats the Coulomb term with RI and the exchange term with COSX (Chain-of-Spheres exchange); for medium-sized molecules you typically see an order-of-magnitude speed-up.

RIJCOSX is essentially free

According to the benchmarks cited in the manual, the energy error introduced by RIJCOSX is at the level of microhartrees (μEh) relative to exact integrals — completely negligible for chemical applications. If you are running hybrid DFT, leave RIJCOSX on by default.

Element-specific basis sets

For transition-metal complexes a common strategy is to use a large basis on the metal and a smaller one on the ligands. ORCA supports this with a concise syntax. 

# CuCl4 anion — TZVPP on Cu, DUNNING-DZP on Cl
! HF

%basis
   basis "SV"                          # default SV for all atoms
   newGTO Cl "DUNNING-DZP" end      # replace just Cl
end

* xyz -2 2
  Cu   0.00   0.00   0.00   newGTO "TZVPP" end  # replace just Cu
  Cl   2.25   0.00   0.00
  Cl  -2.25   0.00   0.00
  Cl   0.00   2.25   0.00
  Cl   0.00  -2.25   0.00
*

You can mix and match bases at the per-atom or per-element level this freely. Effective core potentials (ECPs) are specified in the same way.

Open-shell calculations

For odd-electron molecules or multiplet systems with unpaired electrons, it is best to specify unrestricted spin (UHF / UKS) explicitly. 

# OH radical (doublet)
! UKS B3LYP D4 def2-TZVP TightSCF UNO

* xyz 0 2
  O   0.0   0.0   0.000
  H   0.0   0.0   0.969
*

The UNO keyword prints Unrestricted Natural Orbitals (UNOs) and Unrestricted Corresponding Orbitals (UCOs). These are extremely useful for diagnosing spin contamination and bond multiplicity. The output contains a table such as: 

----------------------
Orbital    Overlap(*)
----------------------
...
101:      0.99563
102:      0.74329   <-- well below 1 → spin-coupled pair
103:      0.00000

An overlap close to 1 indicates a doubly occupied orbital, 0 indicates a singly occupied one, and values in between (typically below ~0.85) suggest a spin-coupled pair — e.g. a singlet diradical. That single column of numbers is a very fast electronic-structure diagnostic.

Reading the output — the essentials

ORCA's output file is long, but the most important lines fit into a handful of sections. For a DFT single point, look at these in order:

① Input echo

-----------
INPUT FILE
-----------
NAME = water.inp
...
> ! B3LYP D4 def2-TZVP RIJCOSX def2/J TightSCF
> * xyz 0 1
>   O   0.000000   0.000000   0.119262
...

Confirm that the input was recognised the way you intended.

② SCF iterations

               SCF ITERATIONS
ITER       Energy         Delta-E        Max-DP      RMS-DP
  0    -76.3987452578   0.000000000000  0.04123455  0.00234567
  1    -76.4128931256  -0.014147867    0.01234567  0.00112345
  ...
  8    -76.4259743074  -0.000000012    0.00000012  0.00000003

         *****************************************************
         *                     SUCCESS                       *
         *           SCF CONVERGED AFTER  8 CYCLES           *
         *****************************************************

Check that the SCF converged, how many iterations it took, and the final energy change. You want to see the "SUCCESS" message.

③ Final single-point energy

----------------
TOTAL SCF ENERGY
----------------
Total Energy       :       -76.42597431 Eh        -2079.65649 eV

Components:
Nuclear Repulsion  :         9.08829372 Eh           247.30504 eV
Electronic Energy  :       -85.51429074 Eh         -2326.96215 eV
One Electron Energy:      -122.91588773 Eh         -3344.71135 eV
Two Electron Energy:        37.40159699 Eh          1017.74920 eV
...

FINAL SINGLE POINT ENERGY       -76.426286364763

The number on the FINAL SINGLE POINT ENERGY line is the final energy in Hartree. Useful conversions: 1 Hartree ≈ 627.5095 kcal/mol ≈ 27.2114 eV.

④ Orbital energies and HOMO–LUMO gap

----------------
ORBITAL ENERGIES
----------------
  NO   OCC          E(Eh)           E(eV)
   0   2.0000     -19.125255      -520.4246
   1   2.0000      -1.009023       -27.4569
   2   2.0000      -0.527546       -14.3553
   3   2.0000      -0.388987       -10.5849
   4   2.0000      -0.312749        -8.5103    <- HOMO
   5   0.0000       0.015311         0.4166    <- LUMO
   6   0.0000       0.090386         2.4595
   ...

The HOMO and LUMO give first-pass estimates for redox propensity and optical properties.

⑤ Dipole and higher multipole moments

-------------
DIPOLE MOMENT
-------------
                                X          Y          Z
Electronic contribution:   0.00000    0.00000    0.17251
Nuclear contribution   :   0.00000    0.00000   -0.99269
                          -----------------------------------------
Total Dipole Moment    :   0.00000    0.00000   -0.82018
                          -----------------------------------------
Magnitude (a.u.)       :   0.82018
Magnitude (Debye)      :   2.08473

What to do after the SCF converges

Common follow-up tasks after a single point are population analysis and orbital visualisation. Both are turned on with a couple of keywords.

Population analysis

The manual's recommended combination is:

! HF def2-SVP Mulliken Loewdin Mayer ReducedPOP

The population-analysis section of the output then looks like this:

-----------------------
MULLIKEN ATOMIC CHARGES
-----------------------
   0 O :   -0.612345
   1 H :    0.306173
   2 H :    0.306173
Sum of atomic charges:   -0.0000000

-----------------------------------------
LOEWDIN ATOMIC CHARGES
-----------------------------------------
   0 O :   -0.487654
   1 H :    0.243827
   2 H :    0.243827

-----------------
MAYER POPULATION ANALYSIS
-----------------
   0 O :  Total valence: 2.012  Mean: 1.006  ...
...
   ATOM    ATOM     BOND ORDER
   0 O     1 H        0.987
   0 O     2 H        0.987
Which analysis to trust

Mulliken charges are very sensitive to the basis set and tend to diverge with large bases. Löwdin is more stable, and Mayer bond orders generally agree well with chemical intuition. For serious quantitative work prefer NPA (Natural Population Analysis) or CHELPG.

Visualising molecular orbitals

To inspect orbitals in 3D, either generate cube files inside the input via a %plots block, or use the standalone orca_plot utility.

Option ①: generate cubes inside the input

! B3LYP def2-SVP TightSCF

%plots
   dim1  45
   dim2  45
   dim3  45
   Format Gaussian_Cube
   MO("homo.cube", 4, 0)    # alpha MO index 4
   MO("lumo.cube", 5, 0)
end

* xyzfile 0 1 water.xyz

Option ②: use orca_plot after the calculation

# interactive mode - follow the menu
orca_plot water.gbw -i

The resulting .cube files can be visualised in VMD, Avogadro, ChimeraX, PyMOL, and similar tools.

Spectroscopic applications — NMR shielding and EPR g-tensor

One of the most common follow-ups to a single point is the calculation of spectroscopic parameters. ORCA's %eprnmr block lets you handle NMR chemical shifts, EPR g-tensors, hyperfine splittings (A-tensor), and quadrupole couplings (Q-tensor) in a single input.

① NMR shielding and chemical shifts

An NMR calculation prints absolute shielding constants σ (ppm). Chemical shifts δ are obtained by subtracting the σ of a reference molecule (TMS for ¹H / ¹³C and so on). For the basis, Jensen's pcSseg-1 / pcSseg-2 bases are specifically optimised for NMR and are the standard choice. 

# 1H · 13C NMR shielding constants of ethanol
! PBE0 D4 pcSseg-2 RIJK def2/JK TightSCF NMR

%eprnmr
   Nuclei = all H { shift }    # every H
   Nuclei = all C { shift }    # every C
end

* xyzfile 0 1 ethanol.xyz

The key output section looks like:

-------------------------------
CHEMICAL SHIELDING SUMMARY (ppm)
-------------------------------
Nucleus            Element   Isotropic Value         Anisotropy
   0                  C         170.123                  39.412
   1                  C         157.876                  28.501
   2                  H          31.245                   8.103
   3                  H          31.122                   7.984
   ...

Subtracting the shielding constant of the reference compound (TMS at PBE0/pcSseg-2 ≈ 31.5 ppm for ¹H, 188.1 ppm for ¹³C) gives the chemical shifts δ that can be compared directly to experiment. NIST CCCBDB (cccbdb.nist.gov) collects functional- and basis-specific reference values.

② EPR g-tensor and A-tensor (radicals / magnetic systems)

The EPR parameters of open-shell radicals and transition-metal complexes are expressed through the g-tensor (electronic Zeeman splitting) and the A-tensor (hyperfine coupling). ORCA handles both in a single input. Spin-orbit coupling is enabled with the SOMF(1X) operator. 

# g-tensor + A-tensor of the vanadyl(IV) cation (51V, 16O)
! UKS PBE0 D4 def2-TZVP DKH2 SARC-DKH-TZVP RIJCOSX SARC/J TightSCF SOMF(1X)

%eprnmr
   GTensor     1
   DTensor     true           # zero-field splitting
   Nuclei = all V { aiso, adip, fc, sd }
   Nuclei = all O { aiso, adip }
end

* xyz 2 2             # V(IV)=O doublet
   V    0.000   0.000   0.000
   O    0.000   0.000   1.580
*

The output contains tables like:

-------------------
g-TENSOR (origin = center of electronic charge)
-------------------
g(1) =  1.9698     g_iso = (g1 + g2 + g3) / 3
g(2) =  1.9701
g(3) =  1.9925
delta-g_iso (vs g_e) =  -0.0156 ppt

-------------------
HYPERFINE COUPLING (A) MATRIX, Nucleus  0V
-------------------
A(iso) = -156.42 MHz
A(dip) =  -28.13,  +14.21,  +13.92  MHz
Magnetic properties almost always need ZORA or DKH

For pure 3d radicals a non-relativistic calculation can still be useful as a first approximation. For 4d and heavier transition metals or lanthanides, however, scalar relativity (ZORA or DKH2) and a relativistically recontracted basis (ZORA-def2-TZVP / SARC-DKH-TZVP) are essentially mandatory. Functionals whose EPR-specific performance has been benchmarked (PBE0, B3LYP) generally fit g-tensors better.

The way of reading the output covered here carries over unchanged to almost every other calculation. The single point held the geometry fixed and only read off the energy; next comes letting the geometry itself relax — geometry optimisation.