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Implement particle-particle random phase approximation (ppRPA)
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ppRPA can be used to calculate excitation energies
and correlation energies of molecules and gamma points.

Refs:
[1] https://doi.org/10.1103/PhysRevA.88.030501
[2] https://doi.org/10.1063/1.4895792
[3] https://doi.org/10.1021/acs.jpca.3c02834
[4] https://doi.org/10.1021/acs.jpclett.4c00184

Co-authored-by: Jiachen Li <[email protected]>
@pi246 @lijiachen417
pi246 and lijiachen417 committed Nov 19, 2024
1 parent 9564956 commit 84d7fbd
Showing 9 changed files with 2,728 additions and 0 deletions.
42 changes: 42 additions & 0 deletions examples/pprpa/01-pprpa_total_energy.py
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from pyscf import gto, dft

# For ppRPA total energy of N-electron system
# mean field is also N-electron

mol = gto.Mole()
mol.verbose = 5
mol.atom = [
["O", (0.0, 0.0, 0.0)],
["H", (0.0, -0.7571, 0.5861)],
["H", (0.0, 0.7571, 0.5861)]]
mol.basis = 'def2-svp'
mol.build()

# =====> Part I. Restricted ppRPA <=====
mf = dft.RKS(mol)
mf.xc = "b3lyp"
mf.kernel()

from pyscf.pprpa.rpprpa_direct import RppRPADirect
pp = RppRPADirect(mf)
ec = pp.get_correlation()
etot, ehf, ec = pp.energy_tot()
print("H2O Hartree-Fock energy = %.8f" % ehf)
print("H2O ppRPA correlation energy = %.8f" % ec)
print("H2O ppRPA total energy = %.8f" % etot)

# =====> Part II. Unrestricted ppRPA <=====
# unrestricted KS-DFT calculation as starting point of UppRPA
umf = dft.UKS(mol)
umf.xc = "b3lyp"
umf.kernel()

# direct diagonalization, N6 scaling
from pyscf.pprpa.upprpa_direct import UppRPADirect
pp = UppRPADirect(umf)
ec = pp.get_correlation()
etot, ehf, ec = pp.energy_tot()
print("H2O Hartree-Fock energy = %.8f" % ehf)
print("H2O ppRPA correlation energy = %.8f" % ec)
print("H2O ppRPA total energy = %.8f" % etot)

64 changes: 64 additions & 0 deletions examples/pprpa/02-pprpa_excitation_energy.py
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from pyscf import gto, dft

# For ppRPA excitation energy of N-electron system in particle-particle channel
# mean field is (N-2)-electron

mol = gto.Mole()
mol.verbose = 5
mol.atom = [
["O", (0.0, 0.0, 0.0)],
["H", (0.0, -0.7571, 0.5861)],
["H", (0.0, 0.7571, 0.5861)]]
mol.basis = 'def2-svp'
# create a (N-2)-electron system for charged-neutral H2O
mol.charge = 2
mol.build()

# =====> Part I. Restricted ppRPA <=====
# restricted KS-DFT calculation as starting point of RppRPA
rmf = dft.RKS(mol)
rmf.xc = "b3lyp"
rmf.kernel()

# direct diagonalization, N6 scaling
from pyscf.pprpa.rpprpa_direct import RppRPADirect
# ppRPA can be solved in an active space
pp = RppRPADirect(rmf, nocc_act=None, nvir_act=10)
# number of two-electron addition states to print
pp.pp_state = 10
# solve for singlet states
pp.kernel("s")
# solve for triplet states
pp.kernel("t")
pp.analyze()

# Davidson algorithm, N4 scaling
from pyscf.pprpa.rpprpa_davidson import RppRPADavidson
# ppRPA can be solved in an active space
pp = RppRPADavidson(rmf, nocc_act=3, nvir_act=None, nroot=10)
# solve for singlet states
pp.kernel("s")
# solve for triplet states
pp.kernel("t")
pp.analyze()

# =====> Part II. Unrestricted ppRPA <=====
# unrestricted KS-DFT calculation as starting point of UppRPA
umf = dft.UKS(mol)
umf.xc = "b3lyp"
umf.kernel()

# direct diagonalization, N6 scaling
from pyscf.pprpa.upprpa_direct import UppRPADirect
# ppRPA can be solved in an active space
pp = UppRPADirect(umf, nocc_act=None, nvir_act=10)
# number of two-electron addition states to print
pp.pp_state = 10
# solve ppRPA in the (alpha alpha, alpha alpha) subspace
pp.kernel(subspace=['aa'])
# solve ppRPA in the (alpha beta, alpha beta) subspace
pp.kernel(subspace=['ab'])
# solve ppRPA in the (beta beta, beta beta) subspace
pp.kernel(subspace=['bb'])
pp.analyze()

63 changes: 63 additions & 0 deletions examples/pprpa/03-hhrpa_excitation_energy.py
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from pyscf import gto, dft

# For ppRPA excitation energy of N-electron system in hole-hole channel
# mean field is (N+2)-electron

mol = gto.Mole()
mol.verbose = 5
mol.atom = [
["O", (0.0, 0.0, 0.0)],
["H", (0.0, -0.7571, 0.5861)],
["H", (0.0, 0.7571, 0.5861)]]
mol.basis = 'def2-svp'
# create a (N+2)-electron system for charged-neutral H2O
mol.charge = -2
mol.build()

# =====> Part I. Restricted ppRPA <=====
mf = dft.RKS(mol)
mf.xc = "b3lyp"
mf.kernel()

# direct diagonalization, N6 scaling
# ppRPA can be solved in an active space
from pyscf.pprpa.rpprpa_direct import RppRPADirect
pp = RppRPADirect(mf, nvir_act=10, nelec="n+2")
# number of two-electron removal states to print
pp.hh_state = 10
# solve for singlet states
pp.kernel("s")
# solve for triplet states
pp.kernel("t")
pp.analyze()

# Davidson algorithm, N4 scaling
# ppRPA can be solved in an active space
from pyscf.pprpa.rpprpa_davidson import RppRPADavidson
pp = RppRPADavidson(mf, nvir_act=10, channel="hh")
# solve for singlet states
pp.kernel("s")
# solve for triplet states
pp.kernel("t")
pp.analyze()

# =====> Part II. Unrestricted ppRPA <=====
# unrestricted KS-DFT calculation as starting point of UppRPA
umf = dft.UKS(mol)
umf.xc = "b3lyp"
umf.kernel()

# direct diagonalization, N6 scaling
from pyscf.pprpa.upprpa_direct import UppRPADirect
# ppRPA can be solved in an active space
pp = UppRPADirect(umf, nvir_act=10, nelec='n+2')
# number of two-electron addition states to print
pp.pp_state = 10
# solve ppRPA in the (alpha alpha, alpha alpha) subspace
pp.kernel(subspace=['aa'])
# solve ppRPA in the (alpha beta, alpha beta) subspace
pp.kernel(subspace=['ab'])
# solve ppRPA in the (beta beta, beta beta) subspace
pp.kernel(subspace=['bb'])
pp.analyze()

166 changes: 166 additions & 0 deletions examples/pprpa/04-gamma_pprpa_excitation_energy.py
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import os

from pyscf.pbc import df, dft, gto, lib

# For ppRPA excitation energy of N-electron system in particle-particle channel
# mean field is (N-2)-electron

# carbon vacancy in diamond
# see Table.1 in https://doi.org/10.1021/acs.jctc.4c00829
cell = gto.Cell()
cell.build(unit='angstrom',
a=[[7.136000, 0.000000, 0.000000],
[0.000000, 7.136000, 0.000000],
[0.000000, 0.000000, 7.136000]],
atom=[
["C", (0.001233209267, 0.001233209267, 1.777383281725)],
["C", (0.012225089066, 1.794731051862, 3.561871956432)],
["C", (1.782392880032, 1.782392880032, 5.362763822515)],
["C", (1.780552680464, -0.013167298675, -0.008776569968)],
["C", (3.557268948138, 0.012225089066, 1.790128043568)],
["C", (5.339774910934, 1.794731051862, 1.790128043568)],
["C", (-0.013167298675, 1.780552680464, -0.008776569968)],
["C", (1.782392880032, 3.569607119968, -0.010763822515)],
["C", (1.794731051862, 5.339774910934, 1.790128043568)],
["C", (2.671194343578, 0.900046784093, 0.881569117555)],
["C", (0.887735886768, 0.887735886768, 6.244403380954)],
["C", (0.900046784093, 2.680805656422, 4.470430882445)],
["C", (2.680805656422, 4.451953215907, 0.881569117555)],
["C", (0.895786995277, 6.238213500378, 0.896853305635)],
["C", (0.930821705350, 0.930821705350, 2.673641624787)],
["C", (4.421178294650, 0.930821705350, 2.678358375213)],
["C", (0.900046784093, 2.671194343578, 0.881569117555)],
["C", (6.238213500378, 0.895786995277, 0.896853305635)],
["C", (2.680805656422, 0.900046784093, 4.470430882445)],
["C", (4.451953215907, 2.680805656422, 0.881569117555)],
["C", (0.930821705350, 4.421178294650, 2.678358375213)],
["C", (1.794731051862, 0.012225089066, 3.561871956432)],
["C", (0.012225089066, 3.557268948138, 1.790128043568)],
["C", (3.569607119968, 1.782392880032, -0.010763822515)],
["C", (1.736746319267, 1.736746319267, 1.671367479693)],
["C", (5.351404126874, 0.000595873126, 0.004129648157)],
["C", (0.000595873126, 5.351404126874, 0.004129648157)],
["C", (2.676000000000, 2.676000000000, 6.244000000000)],
["C", (6.244000000000, 2.676000000000, 2.676000000000)],
["C", (2.676000000000, 6.244000000000, 2.676000000000)],
["C", (0.000595873126, 0.000595873126, 5.347870351843)],
["C", (0.001233209267, 5.350766790733, 3.574616718275)],
["C", (1.780552680464, 5.365167298675, 5.360776569968)],
["C", (3.571447319536, -0.013167298675, 5.360776569968)],
["C", (5.365167298675, 1.780552680464, 5.360776569968)],
["C", (5.365167298675, 3.571447319536, -0.008776569968)],
["C", (5.350766790733, 5.350766790733, 1.777383281725)],
["C", (4.464264113232, 0.887735886768, 6.243596619046)],
["C", (4.451953215907, 2.671194343578, 4.470430882445)],
["C", (2.671194343578, 4.451953215907, 4.470430882445)],
["C", (0.895786995277, 6.249786499622, 4.455146694365)],
["C", (4.421178294650, 4.421178294650, 2.673641624787)],
["C", (6.249786499622, 4.456213004723, 0.896853305635)],
["C", (0.887735886768, 4.464264113232, 6.243596619046)],
["C", (6.249786499622, 0.895786995277, 4.455146694365)],
["C", (4.456213004723, 6.249786499622, 0.896853305635)],
["C", (5.350766790733, 0.001233209267, 3.574616718275)],
["C", (-0.013167298675, 3.571447319536, 5.360776569968)],
["C", (3.571447319536, 5.365167298675, -0.008776569968)],
["C", (3.615253680733, 1.736746319267, 3.680632520307)],
["C", (3.615253680733, 3.615253680733, 1.671367479693)],
["C", (6.244000000000, 2.676000000000, 6.244000000000)],
["C", (6.244000000000, 6.244000000000, 2.676000000000)],
["C", (1.736746319267, 3.615253680733, 3.680632520307)],
["C", (2.676000000000, 6.244000000000, 6.244000000000)],
["C", (3.557268948138, 5.339774910934, 3.561871956432)],
["C", (5.351404126874, 5.351404126874, 5.347870351843)],
["C", (3.569607119968, 3.569607119968, 5.362763822515)],
["C", (5.339774910934, 3.557268948138, 3.561871956432)],
["C", (4.464264113232, 4.464264113232, 6.244403380954)],
["C", (4.456213004723, 6.238213500378, 4.455146694365)],
["C", (6.238213500378, 4.456213004723, 4.455146694365)],
["C", (6.244000000000, 6.244000000000, 6.244000000000)],
],
dimension=3,
max_memory=90000,
verbose=5,
basis='cc-pvdz',
# create a (N-2)-electron system
charge=2,
precision=1e-12)

gdf = df.RSDF(cell)
gdf.auxbasis = "cc-pvdz-ri"
gdf_fname = 'gdf_ints.h5'
gdf._cderi_to_save = gdf_fname
if not os.path.isfile(gdf_fname):
gdf.build()

# =====> Part I. Restricted ppRPA <=====
# After SCF, PySCF might fail in Makov-Payne correction
# save chkfile to restart
chkfname = 'scf.chk'
if os.path.isfile(chkfname):
kmf = dft.RKS(cell).rs_density_fit()
kmf.xc = "b3lyp"
kmf.exxdiv = None
kmf.with_df = gdf
kmf.with_df._cderi = gdf_fname
data = lib.chkfile.load(chkfname, 'scf')
kmf.__dict__.update(data)
else:
kmf = dft.RKS(cell).rs_density_fit()
kmf.xc = "b3lyp"
kmf.exxdiv = None
kmf.with_df = gdf
kmf.with_df._cderi = gdf_fname
kmf.chkfile = chkfname
kmf.kernel()

# direct diagonalization, N6 scaling
# ppRPA can be solved in an active space
from pyscf.pprpa.rpprpa_direct import RppRPADirect
pp = RppRPADirect(kmf, nocc_act=50, nvir_act=50)
# number of two-electron addition states to print
pp.pp_state = 50
# solve for singlet states
pp.kernel("s")
# solve for triplet states
pp.kernel("t")
pp.analyze()

# Davidson algorithm, N4 scaling
# ppRPA can be solved in an active space
from pyscf.pprpa.rpprpa_davidson import RppRPADavidson
pp = RppRPADavidson(kmf, nocc_act=50, nvir_act=50, nroot=50)
# solve for singlet states
pp.kernel("s")
# solve for triplet states
pp.kernel("t")
pp.analyze()

# =====> Part II. Unrestricted ppRPA <=====
chkfname = 'uscf.chk'
if os.path.isfile(chkfname):
kmf = dft.UKS(cell).rs_density_fit()
kmf.xc = "b3lyp"
kmf.exxdiv = None
kmf.with_df = gdf
kmf.with_df._cderi = gdf_fname
data = lib.chkfile.load(chkfname, 'scf')
kmf.__dict__.update(data)
else:
kmf = dft.UKS(cell).rs_density_fit()
kmf.xc = "b3lyp"
kmf.exxdiv = None
kmf.with_df = gdf
kmf.with_df._cderi = gdf_fname
kmf.chkfile = chkfname
kmf.kernel()

# direct diagonalization, N6 scaling
# ppRPA can be solved in an active space
from pyscf.pprpa.upprpa_direct import UppRPADirect
pp = UppRPADirect(kmf, nocc_act=50, nvir_act=50)
# number of two-electron addition states to print
pp.pp_state = 50
# solve ppRPA
pp.kernel()
pp.analyze()

156 changes: 156 additions & 0 deletions examples/pprpa/05-gamma_hhrpa_excitation_energy.py
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import os

from pyscf.pbc import df, dft, gto, lib

# For ppRPA excitation energy of N-electron system in hole-hole channel
# mean field is (N+2)-electron

# nitrogen vacancy in diamond (NV-)
# see in Table.1 https://doi.org/10.1021/acs.jpclett.4c00184
cell = gto.Cell()
cell.build(unit='angstrom',
a=[[7.136000, 0.000000, 0.000000],
[0.000000, 7.136000, 0.000000],
[0.000000, 0.000000, 7.136000]],
atom=[
["C", (0.906073512160, 2.664323563008, 2.694339584224)],
["C", (0.894090626784, 2.684866651264, 6.241909316128)],
["C", (0.899084378176, 6.235829736704, 2.679298965664)],
["C", (0.892434989152, 6.244294788160, 6.243564953760)],
["C", (4.459048614208, 2.719457426496, 2.676951150304)],
["C", (4.441660180288, 2.664323563008, 6.229926430752)],
["C", (4.460040375488, 6.254734827520, 2.675959389024)],
["C", (4.456700798848, 6.235829736704, 6.236915564736)],
["C", (0.000121369088, 0.000121369088, -0.000121369088)],
["C", (-0.010102670688, -0.010102670688, 3.575517319296)],
["C", (-0.010102670688, 3.560482680704, 0.010102670688)],
["C", (0.008425625056, 3.562468772224, 3.573531227776)],
["C", (3.560482680704, -0.010102670688, 0.010102670688)],
["C", (3.562468772224, 0.008425625056, 3.573531227776)],
["C", (3.562468772224, 3.562468772224, -0.008425625056)],
["C", (0.892434989152, 0.892434989152, 0.891705154752)],
["C", (0.894090626784, 0.894090626784, 4.451133113248)],
["C", (0.899084378176, 4.456700798848, 0.900170206208)],
["C", (0.906073512160, 4.441660180288, 4.471676201504)],
["C", (4.456700798848, 0.899084378176, 0.900170206208)],
["C", (4.441660180288, 0.906073512160, 4.471676201504)],
["C", (4.460040375488, 4.460040375488, 0.881265115392)],
["C", (4.459048614208, 4.459048614208, 4.416542338016)],
["C", (-0.006901660896, 1.786905622208, 1.780569760480)],
["C", (0.002512956672, 1.784927308928, 5.351072569760)],
["C", (0.006719393184, 5.349206041920, 1.786793836768)],
["C", (-0.006901660896, 5.355430118208, 5.349094256480)],
["C", (3.557699819104, 1.801090513056, 1.799927287968)],
["C", (3.623443694336, 1.707240281568, 5.428759597120)],
["C", (3.570268719936, 5.363769868640, 1.772230010048)],
["C", (3.557699819104, 5.336072590720, 5.334909365632)],
["C", (2.675027363200, 2.675027363200, 0.892428602432)],
["C", (2.675779925760, 6.243436648480, 0.892563294432)],
["C", (2.675027363200, 6.243571340480, 4.460972401312)],
["C", (6.243436648480, 2.675779925760, 0.892563294432)],
["C", (6.243571340480, 2.675027363200, 4.460972401312)],
["C", (6.244306769504, 6.244306769504, 0.891693173408)],
["C", (6.243436648480, 6.243436648480, 4.460219838752)],
["C", (1.786905622208, -0.006901660896, 1.780569760480)],
["C", (1.784927308928, 0.002512956672, 5.351072569760)],
["C", (1.801090513056, 3.557699819104, 1.799927287968)],
["C", (1.707240281568, 3.623443694336, 5.428759597120)],
["C", (5.349206041920, 0.006719393184, 1.786793836768)],
["C", (5.355430118208, -0.006901660896, 5.349094256480)],
["C", (5.363769868640, 3.570268719936, 1.772230010048)],
["C", (5.336072590720, 3.557699819104, 5.334909365632)],
["C", (2.664323563008, 0.906073512160, 2.694339584224)],
["C", (2.684866651264, 0.894090626784, 6.241909316128)],
["C", (2.719457426496, 4.459048614208, 2.676951150304)],
["C", (2.664323563008, 4.441660180288, 6.229926430752)],
["C", (6.235829736704, 0.899084378176, 2.679298965664)],
["C", (6.244294788160, 0.892434989152, 6.243564953760)],
["C", (6.254734827520, 4.460040375488, 2.675959389024)],
["C", (6.235829736704, 4.456700798848, 6.236915564736)],
["C", (1.784927308928, 1.784927308928, -0.002512956672)],
["C", (1.707240281568, 1.707240281568, 3.512556305664)],
["C", (1.786905622208, 5.355430118208, 0.006901660896)],
["C", (1.801090513056, 5.336072590720, 3.578300180896)],
["C", (5.355430118208, 1.786905622208, 0.006901660896)],
["C", (5.336072590720, 1.801090513056, 3.578300180896)],
["C", (5.349206041920, 5.349206041920, -0.006719393184)],
["C", (5.363769868640, 5.363769868640, 3.565731280064)],
["N", (3.661895773440, 3.661895773440, 3.474104226560)],
],
dimension=3,
max_memory=90000,
verbose=5,
basis='cc-pvdz',
# create a (N+2)-electron system
charge=-3,
precision=1e-12)

gdf = df.RSDF(cell)
gdf.auxbasis = "cc-pvdz-ri"
gdf_fname = 'gdf_ints.h5'
gdf._cderi_to_save = gdf_fname
if not os.path.isfile(gdf_fname):
gdf.build()

# =====> Part I. Restricted ppRPA <=====
# After SCF, PySCF might fail in Makov-Payne correction
# save chkfile to restart
chkfname = 'scf.chk'
if os.path.isfile(chkfname):
kmf = dft.RKS(cell).rs_density_fit()
kmf.xc = "b3lyp"
kmf.exxdiv = None
kmf.with_df = gdf
kmf.with_df._cderi = gdf_fname
data = lib.chkfile.load(chkfname, 'scf')
kmf.__dict__.update(data)
else:
kmf = dft.RKS(cell).rs_density_fit()
kmf.xc = "b3lyp"
kmf.exxdiv = None
kmf.with_df = gdf
kmf.with_df._cderi = gdf_fname
kmf.chkfile = chkfname
kmf.kernel()

# direct diagonalization, N6 scaling
# ppRPA can be solved in an active space
from pyscf.pprpa.rpprpa_direct import RppRPADirect
pp = RppRPADirect(kmf, nocc_act=50, nvir_act=50, nelec="n+2")
# number of two-electron removal states to print
pp.hh_state = 50
# solve for singlet states
pp.kernel("s")
# solve for triplet states
pp.kernel("t")
pp.analyze()

# =====> Part II. Unrestricted ppRPA <=====
chkfname = 'uscf.chk'
if os.path.isfile(chkfname):
kmf = dft.UKS(cell).rs_density_fit()
kmf.xc = "b3lyp"
kmf.exxdiv = None
kmf.with_df = gdf
kmf.with_df._cderi = gdf_fname
data = lib.chkfile.load(chkfname, 'scf')
kmf.__dict__.update(data)
else:
kmf = dft.UKS(cell).rs_density_fit()
kmf.xc = "b3lyp"
kmf.exxdiv = None
kmf.with_df = gdf
kmf.with_df._cderi = gdf_fname
kmf.chkfile = chkfname
kmf.kernel()

# direct diagonalization, N6 scaling
# ppRPA can be solved in an active space
from pyscf.pprpa.upprpa_direct import UppRPADirect
pp = UppRPADirect(kmf, nocc_act=50, nvir_act=50, nelec="n+2")
# number of two-electron addition states to print
pp.pp_state = 50
# solve ppRPA
pp.kernel()
pp.analyze()

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751 changes: 751 additions & 0 deletions pyscf/pprpa/upprpa_direct.py
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