APMOLPRO

APMOLPRO is an interface between the APMO (Any Particle Molecular Orbital) code and the electronic structure package MOLPRO [https://www.molpro.net/]. The any particle molecular orbital APMO code [González et al., Int. J. Quantum Chem. 108, 1742 (2008)] implements the model where electrons and light nuclei are treated simultaneously at Hartree-Fock or second-order Möller-Plesset levels of theory. The APMO -MOLPRO interface allows to include high- level electronic correlation as implemented in the MOLPRO package and to describe nuclear quantum effects at Hartree-Fock level of theory with the APMO code.

The examples given in the paper [Aguirre et al. J. Chem. Phys. 138, 184113 (2013)] illustrate the use of this implementation on different model systems: ⁴ He₂ dimer as a protype of a weakly bound van der Waals system; isotopomers of [He–H–He]⁺ molecule as an example of a hydrogen bonded system; and molecular hydrogen to compare with very accurate non-Born-Oppenheimer calculations.

Authors

• Nestor F. Aguirre ( nfaguirrec@gmail.com )
• Edwin F. Posada ( efposadac@unal.edu.co )
• Andres Reyes ( areyesv@unal.edu.co )
• Alexander O. Mitrushchenkov ( Alexander.Mitrushchenkov@univ-paris-est.fr )
• Maria P. de Lara-Castells ( pilar.delara.castells@csic.es )

Citing

To cite the code, please proceed as follows:

Flow diagram of the APMO-MOLPRO interface.

Specifying the electron and nuclear basis set:

In this example, a basis aug-cc-pVQZ is chosen for the electrons of the hydrogen atoms and a 5sp even-tempered for the hydrogen nuclei.

basis={
  set ORBITAL
  H=aug-cc-pVQZ
  
  set NUCBASIS
  s,H,even,nprim=2,ratio=2.5,centre=33.7,dratio=0.8
  p,H,even,nprim=2,ratio=2.5,centre=33.7,dratio=0.8
  
  default ORBITAL
}
cartesian

Example of Molpro input file:

This example corresponds to the calculation of the molecule [HeHHe]⁺ where helium nuclei and the hydrogen nucleus are represented as quantum particles with an even-tempered basis set and a single 1s function respectively. CCSD(T)/aug-cc-pVQZ level of theory is used for the electronic part.

include apmolpro.com

APMOLPRO_maxit = 30
APMOLPRO_tol = 1e-6
APMOLPRO_hforb = 2100.2
APMOLPRO_dm = 21400.2

! First call to APMO to build the nuclear wave function
APMOLPRO_begin={
  {apmo
    species H_1,He_4,He_4
    nucbasis nucbasis,dirac,dirac
    save I,ICOUP
    save J,JCOUP
    save K,KIN
  }
}

! Updating the nuclear energy including the kinetic energy from the nuclei
APMOLPRO_enuc={
  {apmo
    update enuc H_1
  }
}

! Lets to relax the nuclei keeping frozen the electrons
APMOLPRO_nrelax={
  {apmo
    load den EDEN
    frozen e-
    species H_1,He_4,He_4
    nucbasis nucbasis,dirac,dirac
  }
}

! Electronic method to use
APMOLPRO_eMethod={
  ccsd(t)
}

! Nuclear-electron interaction method through the
! first-order reduced density matrix (record=21400.2)
APMOLPRO_cMethod={
  {ccsd
    core 0
    expec relax,dm
    expec dm
    dm $APMOLPRO_dm
    natorb $APMOLPRO_dm
  }
}

basis={
  set ORBITAL

  H=aug-cc-pVQZ
  He=aug-cc-pVQZ

  set NUCBASIS
  s,H,even,nprim=5,ratio=2.5,centre=33.7,dratio=0.8
  p,H,even,nprim=5,ratio=2.5,centre=33.7,dratio=0.8
  d,H,even,nprim=5,ratio=2.5,centre=33.7,dratio=0.8

  s, He, 30.0
  c, 1.1, 1.000000

  default ORBITAL
}
cartesian

r = 0.92491089

set charge=1
symmetry nosym
angstrom
geometry={
  H
  He  1  r
  He  1  r   2  180.0
}

{optg procedure=apmolpro
}

{property
  density $APMOLPRO_dm-10.0
  orbital $APMOLPRO_dm-10.0
  dm
  qm
}

{put molden HeTHeorb.molden
  orb $APMOLPRO_dm-10.0
}

Contour plots of the nuclear density for the different isotopic substitutions of the central hydrogen atom in the system [HeHHe]⁺.

Optimizing a nuclear basis set:

This example shows how to optimize variationally the exponent 1s of the Helium atoms in the He₂ diatomic molecule by using the simplex method (geometry optimization included).

c1s = 200.0

basis={
  set ORBITAL
  He=aug-cc-pVTZ
  
  set NUCBASIS
  s He c1s
    c 1.1 1.00000
    
  default ORBITAL
}
cartesian

r = 2.99773304

symmetry nosym
angstrom
geometry={
  He
  He 1 r
}

optBasis={
  {optg procedure=apmolpro gradient=1e-5
  }
}

{minimize energy c1s
  method energy simplex,varscale=2,thresh=1e-6,proc=optBasis
}

Results of the nuclear basis set optimization (even-tempered) at CCSD(T){CCSD}:HF level of theory for the [HeHHe]⁺ molecule.