Psithon: Structuring an Input File

To allow arbitrarily complex computations to be performed, PSI4 was built upon the Python interpreter. However, to make the input syntax simpler, some pre-processing of the input file is performed before it is interpreted, resulting in Python syntax that is customized for PSI, termed Psithon. In this section we will describe the essential features of the Psithon language. PSI4 is distributed with an extensive test suite, described in section Test Suite and Sample Inputs; the input files for these test cases can be found in the samples subdirectory of the top-level PSI4 source directory and should serve as useful examples.

Physical Constants

For convenience, the Python interpreter will execute the contents of the ~/.psi4rc file in the current user’s home area (if present) before performing any tasks in the input file. This allows frequently used python variables to be automatically defined in all input files. For example, if we repeatedly make use of the universal gravitational constant, the following line could be placed in the ~/.psi4rc file

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UGC = 6.67384E-11  # m^3 / kg^-1 s^-2

which would make the variable UGC available in all PSI4 input files. For convenience, the physical constants used within the PSI4 code (which are obtained from the 3rd edition of the IUPAC Green book [Cohen:GreenBook:2008]) are also automatically loaded as Psithon variables (before ~/.psi4rc is loaded, so that the user’s ~/.psi4rc values can override the builtins (in the input file, not in the C++ code).

The physical constants used within PSI4, which are automatically made available within all PSI4 input files.

# Do not modify this file! It is auto-generated by the document_options_and_tests
# script, from psi4topdir/psi4/include/psi4/physconst.h
h                         = 6.62606896E-34       # The Planck constant (Js)               
c                         = 2.99792458E8         # Speed of light (ms$^{-1}$)             
kb                        = 1.3806504E-23        # The Boltzmann constant (JK$^{-1}$)     
R                         = 8.314472             # Universal gas constant (JK$^{-1}$mol$^{-1}$) 
bohr2angstroms            = 0.52917720859        # Bohr to Angstroms conversion factor    
bohr2m                    = 0.52917720859E-10    # Bohr to meters conversion factor       
bohr2cm                   = 0.52917720859E-8     # Bohr to centimeters conversion factor  
amu2g                     = 1.660538782E-24      # Atomic mass units to grams conversion factor 
amu2kg                    = 1.660538782E-27      # Atomic mass units to kg conversion factor 
au2amu                    = 5.485799097E-4       # Atomic units (m$@@e$) to atomic mass units conversion factor 
hartree2J                 = 4.359744E-18         # Hartree to joule conversion factor     
hartree2aJ                = 4.359744             # Hartree to attojoule (10$^{-18}$J) conversion factor 
cal2J                     = 4.184                # Calorie to joule conversion factor     
dipmom_au2si              = 8.47835281E-30       # Atomic units to SI units (Cm) conversion factor for dipoles 
dipmom_au2debye           = 2.54174623           # Atomic units to Debye conversion factor for dipoles 
dipmom_debye2si           = 3.335640952E-30      # Debye to SI units (Cm) conversion factor for dipoles 
c_au                      = 137.035999679        # Speed of light in atomic units         
hartree2ev                = 27.21138             # Hartree to eV conversion factor        
hartree2wavenumbers       = 219474.6             # Hartree to cm$^{-1}$ conversion factor 
hartree2kcalmol           = 627.5095             # Hartree to kcal mol$^{-1}$ conversion factor 
hartree2kJmol             = 2625.500             # Hartree to kilojoule mol$^{-1}$ conversion factor 
hartree2MHz               = 6.579684E9           # Hartree to MHz conversion factor       
kcalmol2wavenumbers       = 349.7551             # kcal mol$^{-1}$ to cm$^{-1}$ conversion factor 
e0                        = 8.854187817E-12      # Vacuum permittivity (Fm$^{-1}$)        
na                        = 6.02214179E23        # Avagadro's number                      
me                        = 9.10938215E-31       # Electron rest mass (in kg)             

In Psithon input files, prepend physical constants with psi_ to prevent clashes with user-defined variables (e.g., psi_h). In PsiAPI mode, access as, e.g., psi4.constants.h.

Memory Specification

By default, PSI4 assumes that 256 Mb of memory are available. While this is enough for many computations, many of the algorithms will perform better if more is available. To specify memory, the memory keyword should be used. The following lines are all equivalent methods for specifying that 2 Gb of RAM is available to PSI4:

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# all equivalent

memory 2 Gb

memory 2000 Mb

memory 2000000 Kb

One convenient way to override the PSI4 default memory is to place a memory command in the ~/.psi4rc file (Sec. ~/.psi4rc File). For example, the following makes the default memory 2 Gb.

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set_memory(2000000000)

However, unless you’re assured of having only one job running on a node at a time (and all nodes on the filesystem with ~/.psi4rc have similar memory capacities), it is advised to set memory in the input file on a per-calculation basis.

That same command can be used for PsiAPI mode:

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psi4.set_memory(int(5e8))

Note

For parallel jobs, the memory keyword represents the total memory available to the job, not the memory per thread.

Job Control Keywords

PSI4 comprises a number of C++ modules that each perform specific tasks and are callable directly from the Python front end. Each module recognizes specific keywords in the input file which control its function. These keywords are detailed in Appendix Keywords by Module. The keywords can be made global, or scoped to apply to certain specific modules. The following examples demonstrate some of the ways that global keywords can be specified:

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# all equivalent

set globals basis cc-pVDZ

set basis cc-pVDZ

set globals basis = cc-pVDZ

set basis = cc-pVDZ

set globals{
  basis cc-pVDZ
}

set {
  basis cc-pVDZ
}

set {
  basis = cc-pVDZ
}

Note the lack of quotes around cc-pVDZ, even though it is a string. The Psithon preprocessor automatically wraps any string values in set commands in strings. The last three examples provide a more convenient way for specifying multiple keywords:

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set {
  basis = cc-pVDZ
  print = 1
  reference = rhf
}

For arguments that require an array input, standard Python list syntax should be used, viz.:

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set {
  docc = [3, 0, 1, 1]
}

List/matrix inputs may span multiple lines, as long as the opening [ is on the same line as the name of the keyword.

Any of the above keyword specifications can be scoped to individual modules, by adding the name of the module after the set keyword. Omitting the module name, or using the name global or globals will result in the keyword being applied to all modules. For example, in the following input

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molecule{
  o
  h 1 roh
  h 1 roh 2 ahoh

  roh = 0.957
  ahoh = 104.5
}

set basis cc-pVDZ
set ccenergy print 3
set scf print 1
energy('ccsd')

the basis set is set to cc-pVDZ throughout, the SCF code will have a print level of 1 and the ccenergy code, which performs coupled cluster computations, will use a print level of 3. In this example a full CCSD computation is performed by running the SCF code first, then the coupled cluster modules; the energy() Python helper function ensures that this is performed correctly. Note that the Python interpreter executes commands in the order they appear in the input file, so if the last four commands in the above example were to read

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set basis cc-pVDZ
energy('ccsd')
set ccenergy print 3
set scf print 1

the commands that set the print level would be ineffective, as they would be processed after the CCSD computation completes.

In PsiAPI mode, one can use commands set_options() and set_module_options() like below. Note that these values should be of correct type, strings for strings, floats for floats like convergences. The function ~psi4.core.clean_options that reinitializes all options may also be useful to separate calculations in a PsiAPI session.

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psi4.set_options({
    'scf_type': 'pk',
    'e_convergence': 1.e-5,
    'soscf': True
})

psi4.set_module_options({
    'geom_maxiter': 50
})

PSI Variables

To harness the power of Python, PSI4 makes the most pertinent results of each computation available to the Python interpreter for post-processing. To demonstrate, we can embellish the previous example of H2 and H atom:

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molecule h2 {
  H
  H 1 0.9
}

set basis cc-pvdz
set reference rhf
h2_energy = energy('scf')

molecule h {
  H
}

set basis cc-pvdz
set reference uhf
h_energy = energy('scf')

D_e = psi_hartree2kcalmol * (2*h_energy - h2_energy)
print "De=%f" % D_e

The energy() function returns the final result of the computation, the requested total energy in Hartrees, which we assign to a Python variable. The two energies are then converted to a dissociation energy and printed to the output file using standard Python notation.

Generally, there are multiple quantities of interest. Appendix PSI Variables by Module lists PSI variables variables set by each module, and PSI Variables by Alpha defines them. These can be accessed through the get_variable() function. For example, after performing a density fitted MP2 computation, both the spin component scaled energy and the unscaled MP2 energy are made available:

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e_mp2 = get_variable('MP2 TOTAL ENERGY')
e_scs_mp2 = get_variable('SCS-MP2 TOTAL ENERGY')

Each module and the Python driver set PSI variables over the course of a calculation. The values for all can be printed in the output file with the input file command print_variables(). Note that PSI variables are cleared at the start of each energy(), etc. in an input file by clean_variables(). So if you run in a single input file a STO-3G FCI followed by a aug-cc-pVQZ SCF followed by a print_variables() command, the last will include SCF TOTAL ENERGY but not FCI TOTAL ENERGY. The entire dictionary of PSI variables can be obtained through get_variables().

Return Values

Most of the usual user computation functions (i.e., energy(), optimize(), and frequency()) return simply the current total energy. Consult the descriptions of other functions in Psithon Functions: Invoking a Calculation for what quantities they return and for what data structures they make available for post-processing. Many users need only deal with the simple return form for the computation functions.

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# E is total energy float
# G is gradient array
# H is hessian array
# wfn is class instance with many computational details

# simple returns
E = energy(...)
E = optimize(...)
E = frequency(...)
G = gradient(...)  # used by optimize()
H = hessian(...)  # used by frequency()

For more elaborate post-processing of computations, adding return_wfn=True keyword argument additionally returns Wavefunction.

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# power user returns
E, wfn = energy(..., return_wfn=True)
E, wfn = optimize(..., return_wfn=True)
E, wfn = frequency(..., return_wfn=True)
G, wfn = gradient(..., return_wfn=True)  # used by optimize()
H, wfn = hessian(..., return_wfn=True)  # used by frequency()

# print gradient array and its rms
wfn.gradient.print_out()
print wfn.gradient().rms()

# format output for other programs
molden(wfn, 'mycalc.molden')

# access array in another format
np.array(wfn.hessian())

Loops

Python provides many control structures, any of which can be used within PSI4 input files. For example, to loop over three basis sets, the following code can be used:

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basis_sets = ["cc-pVDZ", "cc-pVTZ", "cc-pVQZ"]
for basis_set in basis_sets:
    set basis = $basis_set
    energy('scf')

The declaration of basis_sets is completely standard Python, as is the next line, which iterates over the list. However, because the Psithon preprocessor wraps strings in quotes by default, we have to tell it that basis_set is a Python variable, not a string, by prefixing it with a dollar sign.

The geometry specification supports delayed initialization of variable, which permits potential energy scans. As an example, we can scan both the angle and bond length in water:

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molecule h2o{
  O
  H 1 R
  H 1 R 2 A
}

Rvals = [0.9, 1.0, 1.1]
Avals = range(102, 106, 2)

set basis cc-pvdz
set scf e_convergence=11
for R in Rvals:
    h2o.R = R
    for A in Avals:
        h2o.A = A
        energy('scf')

The declarations of Rvals and Avals are both completely standard Python syntax. Having named our molecule h2o we can then set the values of R and A within the loops. Note that we do not need the dollar sign to access the Python variable in this example; that is required only when using Python variables with the set keyword.

Cartesian geometries, because of details of the geometry update process, need to be specified within the loop(s) along with their basis set when geometry scans are performed. See scf4 for analogous Z-matrix and Cartiesian scans.

Tables of Results

The results of computations can be compactly tabulated with the Table() Psithon function. For example, in the following potential energy surface scan for water

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molecule h2o {
  O
  H 1 R
  H 1 R 2 A
}

Rvals=[0.9,1.0,1.1]
Avals=range(100,102,2)

table=Table(rows=["R","A"], cols=["E(SCF)","E(SCS)","E(DFMP2)"])

set basis cc-pvdz

for R in Rvals:
    h2o.R = R
    for A in Avals:
        h2o.A = A
        energy('mp2')
        escf = get_variable('SCF TOTAL ENERGY')
        edfmp2 = get_variable('MP2 TOTAL ENERGY')
        escsmp2 = get_variable('SCS-MP2 TOTAL ENERGY')
        table[R][A] = [escf, escsmp2, edfmp2]

print table
relative=table.copy()
relative.absolute_to_relative()
print relative

we first define a table (on line 10) with two row indices and three column indices. As the potential energy scan is performed, the results are stored (line 22) and the final table is printed to the output file (line 24). The table is converted from absolute energies to relative energies (in kcal mol-1) on line 26, before being printed again. The relative energies are reported with respect to the lowest value in each column. More examples of how to control the formatting of the tables can be found in the sample input files provided; see Appendix Test Suite and Sample Inputs for a complete listing.

Python Wrappers

The Python foundations of the PSI4 driver and Psithon syntax permit many commonly performed post-processing procedures to be integrated into the PSI4 suite.

As seen in the neon dimer example from the tutorial section, the nbody_gufunc() wrapper provides automatic computation of counterpoise-corrected interaction energies between two molecules. For example,

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energy('mp2', bsse_type='cp')

will compute the counterpoise-corrected density-fitted MP2 interaction energy between two molecules.

PSI4 also provides the cbs() wrapper, which automatically computes a complete-basis-set extrapolation (and automatically sets up the computations with different basis sets required to do the extrapolation). For example,:

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# all equivalent

cbs('mp2', corl_basis='cc-pv[dt]z', corl_scheme=corl_xtpl_helgaker_2)

energy('mp2/cc-pv[dt]z')

will compute a 2-point Helgaker extrapolation of the correlation energy using the cc-pVDZ and cc-pVTZ basis sets (with method MP2) and add this extrapolated correlation energy to the Hartree–Fock energy in the largest basis (cc-pVTZ). cbs() can either be called directly, as in the first example, or the convenience syntax of the equivalent second example can be used.

Another very useful and powerful feature of PSI4 is the ability to compute results on entire databases of molecules at a time, as provided by the database() wrapper. For example,:

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database('mp2', 'S22', cp=1, benchmark='S22B')

will perform DF-MP2 counterpoise-corrected interaction energies (cp=1) on all members of Hobza’s S22 database set of van der Waals dimers, and then compare the results against the S22B benchmark energies. Built-in databases include S22, A24, HTBH, HBC6, HSG, S22by5, S66, JSCH, NCB31, S66by8, and NBC10, among others.

These wrapper functions are discussed separately in Psithon Functions: Invoking a Calculation. Note that the options documented for Python functions are placed as arguments in the command that calls the function, not in the set {...} block or with any other set command.