coupled-cluster-py

Name	coupled-cluster-py JSON
Version	0.0.3 JSON
	download
home_page	None
Summary	Coupled-cluster package written in Python.
upload_time	2024-10-26 04:51:48
maintainer	None
docs_url	None
author	None
requires_python	>=3.10
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# CCpy: A coupled-cluster package written in Python.

## Overview
<p align="justify">
CCpy is a research-level Python package for performing non-relativistic electronic structure calculations for molecular systems 
using methods based on the ground-state coupled-cluster (CC) theory and its equation-of-motion (EOM) extension
to electronic excited, attached, and ionized states. As a design philosophy, CCpy favors simplicity over efficiency, and this is reflected in the
usage of computational routines that are transparent enough so that they can be easily used, modified, and extended, while 
still maintaining reasonable efficiency. To this end, CCpy employs a hybrid Python-Fortran programming approach made possible
with the f2py package, which allows one to compile Fortran code into shared object libraries containing subroutines
that are callable from Python and interoperable with Numpy arrays. 

*Important Note: The compliation of Fortran modules with ```f2py``` is not currently compatible with Python 3.12 due to
the migration away from ```numpy.distutils```. In order to fix this, we are moving over to compilation using
```meson```. In the meantime, please use Python 3.11 when building CCpy.*
</p>

## Available Computational Options
<p align="justify">
CCpy specializes in applying the CC(P;Q) and externally corrected (ec) CC methodologies developed in the Piecuch group at 
Michigan State University. In CC(P;Q), the energetics obtained by solving the ground- or excited-state CC/EOMCC equations in
one subspace of the many-electron Hilbert space, called the P space, are corrected for the missing many-electron correlation
effects captured with the help of a complementary subspace called the Q space using the state-selective, non-iterative,
and non-perturbative energy corrections based on the CC moment expansion formalism. Currently, CCpy offers implementations
of several CC(P;Q) methods, the majority of which are aimed at converging the high-level CCSDT and EOMCCSDT energetics. 
These include the completely-renormalized (CR) methods such as the CR-CC(2,3) and CR-CC(2,4) triples and quadruples 
corrections to CCSD, the active-space CCSDt and CC(t;3) approaches, which are based on a user-defined selection of active orbitals, 
and the black-box selected configuration interaction (CI) driven and adaptive CC(P;Q) methodologies, which construct the P and Q spaces 
entering the CC(P;Q) computations using information extracted from selected CI wave functions or the adaptive CC(P;Q) moment 
expansions themselves, respectively. The ec-CC approaches on the other hand seek to converge the exact, full CI energetics
directly by solving for the T<sub>1</sub> and T<sub>2</sub> clusters in the presence of the leading T<sub>3</sub> and T<sub>4</sub> clusters extracted from an
external non-CC wave function. Current implementations of the ec-CC approaches in CCpy are designed to iterate T<sub>1</sub> and T<sub>2</sub> clusters 
in the presence of T<sub>3</sub> and T<sub>4</sub> obtained from CI wave functions of the selected CI or multireference CI types, and correct the resulting
energetics for the missing many-electron correlations using the generalized moment expansions of the ec-CC equations.
</p>

### Møller-Plesset (MP) perturbation theory
  - MP2 
  - MP3 

### Ground-state CC methodologies
<details>
<summary>CCD</summary>

### Summary

<p align="justify">
The CC with doubles (CCD) method truncates the cluster operator as T = T<sub>2</sub>.
It has iterative computational costs that scale as 
n<sub>o</sub><sup>2</sup>n<sub>u</sub><sup>4</sup>, where n<sub>o</sub> is 
the number of correlated occupied orbitals and n<sub>u</sub> is the number of 
correlated unoccupied orbitals. 
Due to the importance of pair correlations in the many-electron problem, the
CCD approximation was first introduced in Prof. Čížek's landmark 1966 paper
under the name coupled-pair many-electron theory, or CPMET. Although CCD is
often superceeded by the more accurate CC with singles and doubles (CCSD) method,
which has the same computational scaling, CCD is still relevant to modern CC
calculations within the context of correlating orbital-optimized reference
functions, as in Brückner CCD.
</p>

### Example Code

```python3
    from pyscf import gto, scf
    from ccpy.drivers.driver import Driver

    # build molecule using PySCF and run SCF calculation
    mol = gto.M(
        atom=[["O", (0.0, 0.0, -0.0180)],
              ["H", (0.0, 3.030526, -2.117796)],
              ["H", (0.0, -3.030526, -2.117796)]],
        basis="cc-pvdz",
        charge=0,
        spin=0,
        symmetry="C2V",
        cart=False,
        unit="Bohr",
    )
    mf = scf.RHF(mol)
    mf.kernel()
    
    # get the CCpy driver object using PySCF meanfield
    driver = Driver.from_pyscf(mf, nfrozen=1)

    # set calculation parameters
    driver.options["energy_convergence"] = 1.0e-07 # (in hartree)
    driver.options["amp_convergence"] = 1.0e-07
    driver.options["maximum_iterations"] = 80

    # run CCD calculation
    driver.run_cc(method="ccd")
```
### Reference
1. J. Čížek, *J. Chem. Phys.* **45**, 4256 (1966).
</details>

<details>
<summary>CCSD</summary>

### Summary

<p align="justify">
The CC with singles and doubles (CCSD) method approximates the cluster
operator as T = T<sub>1</sub> + T<sub>2</sub>. It is the most commonly used truncation level
in the CC hierarchy and often forms the starting point for more sophisticated 
treatments of many-electron correlation effects. CCSD has iterative computational costs that 
scale as n<sub>o</sub><sup>2</sup>n<sub>u</sub><sup>4</sup>, where n<sub>o</sub> is 
the number of correlated occupied orbitals and n<sub>u</sub> is the number of 
correlated unoccupied orbitals.
</p>

### Sample Code

```python3
    from pyscf import gto, scf
    from ccpy.drivers.driver import Driver

    # build molecule using PySCF and run SCF calculation
    mol = gto.M(
        atom=[["O", (0.0, 0.0, -0.0180)],
              ["H", (0.0, 3.030526, -2.117796)],
              ["H", (0.0, -3.030526, -2.117796)]],
        basis="cc-pvdz",
        charge=0,
        spin=0,
        symmetry="C2V",
        cart=False,
        unit="Bohr",
    )
    mf = scf.RHF(mol)
    mf.kernel()
    
    # get the CCpy driver object using PySCF meanfield
    driver = Driver.from_pyscf(mf, nfrozen=1)

    # set calculation parameters
    driver.options["energy_convergence"] = 1.0e-07 # (in hartree)
    driver.options["amp_convergence"] = 1.0e-07
    driver.options["maximum_iterations"] = 80

    # run CCSD calculation
    driver.run_cc(method="ccsd")
```
### References

1. G. D. Purvis and R. J. Bartlett, *J. Chem. Phys.* **76**, 1910 (1982).
2. J. M. Cullen and M. C. Zerner, *J. Chem. Phys.* **77**, 4088 (1982).
3. G. E. Scuseria, A. C. Scheiner, T. J. Lee, J. E. Rice, and H. F. Schaefer, *J. Chem. Phys.* **86**, 2881 (1987).
4. P. Piecuch and J. Paldus, *Int. J. Quantum Chem.* **36**, 429 (1989).
</details>

<details>
<summary>CCSDT</summary>

### Summary
<p align="justify">
The CC with singles, doubles, and triples (CCSDT) method approximates the cluster
operator as T = T<sub>1</sub> + T<sub>2</sub> + T<sub>3</sub>. CCSDT is a high-level
method capable of providing nearly exact results for closed-shell molecules
as well as chemically accurate energetics for single bond breaking and a variety
of open-shell systems. CCSDT has iterative computational costs that scale as 
n<sub>o</sub><sup>3</sup>n<sub>u</sub><sup>5</sup>, where n<sub>o</sub> is 
the number of correlated occupied orbitals and n<sub>u</sub> is the number of 
correlated unoccupied orbitals. 
</p>

### Sample Code

```python3
    from pyscf import gto, scf
    from ccpy.drivers.driver import Driver

    # build molecule using PySCF and run SCF calculation
    mol = gto.M(
        atom=[["O", (0.0, 0.0, -0.0180)],
              ["H", (0.0, 3.030526, -2.117796)],
              ["H", (0.0, -3.030526, -2.117796)]],
        basis="cc-pvdz",
        charge=0,
        spin=0,
        symmetry="C2V",
        cart=False,
        unit="Bohr",
    )
    mf = scf.RHF(mol)
    mf.kernel()
    
    # get the CCpy driver object using PySCF meanfield
    driver = Driver.from_pyscf(mf, nfrozen=1)

    # set calculation parameters
    driver.options["energy_convergence"] = 1.0e-07 # (in hartree)
    driver.options["amp_convergence"] = 1.0e-07
    driver.options["maximum_iterations"] = 80

    # run CCSDT calculation
    driver.run_cc(method="ccsdt")
```

### References
1. M. R. Hoffmann and H. F. Schaefer, *Adv. Quantum Chem.* **18**, 207 (1986).
2. J. Noga and R. J. Bartlett, *J. Chem. Phys.* **86**, 7041 (1987).
3. G. E. Scuseria and H. F. Schaefer, *Chem. Phys. Lett.* **152**, 382 (1988).
4. J. D. Watts and R. J. Bartlett, *J. Chem. Phys.* **93**, 6104 (1990).

</details>

<details>
<summary>CCSDTQ</summary>

### Summary
<p align="justify">
The CC with singles, doubles, triples, and quadruples (CCSDTQ) method 
approximates the cluster operator as 
T = T<sub>1</sub> + T<sub>2</sub> + T<sub>3</sub> + T<sub>4</sub>. 
CCSDTQ is a very high-level method and is often capable of providing 
near-exact energetics for most problems of chemical interest, as long
as the number of strongly correlated electrons is not too large (for
methods designed to treat genuine strong correlations, see the
approximate coupled-pair, or ACP approaches).
CCSDTQ has iterative computational costs that scale as 
n<sub>o</sub><sup>4</sup>n<sub>u</sub><sup>6</sup>, where n<sub>o</sub> is 
the number of correlated occupied orbitals and n<sub>u</sub> is the number of 
correlated unoccupied orbitals. 
</p>

### Sample Code

```python3
    from pyscf import gto, scf
    from ccpy.drivers.driver import Driver

    # build molecule using PySCF and run SCF calculation
    mol = gto.M(
        atom=[["O", (0.0, 0.0, -0.0180)],
              ["H", (0.0, 3.030526, -2.117796)],
              ["H", (0.0, -3.030526, -2.117796)]],
        basis="cc-pvdz",
        charge=0,
        spin=0,
        symmetry="C2V",
        cart=False,
        unit="Bohr",
    )
    mf = scf.RHF(mol)
    mf.kernel()
    
    # get the CCpy driver object using PySCF meanfield
    driver = Driver.from_pyscf(mf, nfrozen=1)

    # set calculation parameters
    driver.options["energy_convergence"] = 1.0e-07 # (in hartree)
    driver.options["amp_convergence"] = 1.0e-07
    driver.options["maximum_iterations"] = 80

    # run CCSDTQ calculation
    driver.run_cc(method="ccsdtq")
```

### References
1. N. Oliphant and L. Adamowicz, *J. Chem. Phys.* **95**, 6645 (1991).
2. S. A. Kucharski and R. J. Bartlett, *Theor. Chem. Acc.* **80**, 387 (1991).
3. S. A. Kucharski and R. J. Bartlett, *J. Chem. Phys.* **97**, 4282 (1992).
4. P. Piecuch and L. Adamowicz, *J. Chem. Phys.* **100**, 5792 (1994).

</details>

<details>
<summary>CCSD(T)</summary>

### Summary

<p align="justify">
The CCSD(T) method corrects the CCSD energy for the correlation effects
due to T<sub>3</sub> clusters using formulas derived using many-body perturbation
theory (MBPT). In particular, the CCSD(T) correction includes the leading 
4th-order energy correction for T<sub>3</sub> along with 5th-order contribution
due to disconnected triples. The inclusion
of the latter term distinguishes CCSD(T) from its CCSD[T] precedessor.
CCSD(T) has noniterative computational costs that 
scale as n<sub>o</sub><sup>3</sup>n<sub>4</sub><sup>4</sup>, where n<sub>o</sub> is 
the number of correlated occupied orbitals and n<sub>u</sub> is the number of 
correlated unoccupied orbitals.
</p>

### Sample Code

```python3
    from pyscf import gto, scf
    from ccpy.drivers.driver import Driver

    # build molecule using PySCF and run SCF calculation
    mol = gto.M(
        atom=[["O", (0.0, 0.0, -0.0180)],
              ["H", (0.0, 3.030526, -2.117796)],
              ["H", (0.0, -3.030526, -2.117796)]],
        basis="cc-pvdz",
        charge=0,
        spin=0,
        symmetry="C2V",
        cart=False,
        unit="Bohr",
    )
    mf = scf.RHF(mol)
    mf.kernel()
    
    # get the CCpy driver object using PySCF meanfield
    driver = Driver.from_pyscf(mf, nfrozen=1)

    # set calculation parameters
    driver.options["energy_convergence"] = 1.0e-07 # (in hartree)
    driver.options["amp_convergence"] = 1.0e-07
    driver.options["maximum_iterations"] = 80

    # run CCSD calculation
    driver.run_cc(method="ccsd")
    # perform CCSD(T) correction
    driver.run_ccp3(method="ccsd(t)")
```
### References

1. K. Raghavachari, G. W. Trucks, J. A. Pople, and M. Head-Gordon, *Chem. Phys. Lett.* **157**, 479 (1989).
2. J. F. Stanton, *Chem. Phys. Lett.* **281**, 130 (1997).
3. S. A. Kucharski and R. J. Bartlett, *J. Chem. Phys.* **108**, 5243 (1998).
4. T. D. Crawford and J. F. Stanton, *Int. J. Quantum Chem.* **70**, 601 (1998).
</details>

<details>
<summary>CR-CC(2,3)</summary>

### Summary

<p align="justify">
The CR-CC(2,3) approach is a nonperturbative and noniterative correction to the
CCSD energetics that accounts for the correlation effects due to T<sub>3</sub>
clusters using formulas derived from the biorthogonal moment energy expansions of CC
theory. In particular, CR-CC(2,3) represents the most robust scheme to noniteratively
include the effects of connected triples on top of CCSD, and it is capable of providing an 
accurate description of closed-shell molecules in addition to commonly encountered
multireference problems, such as single bond breaking and open-shell radical 
and diradical species, which are generally beyond the scope of perturbative 
methods like CCSD(T). The CR-CC(2,3) triples correction uses noniterative steps
that scale as n<sub>o</sub><sup>3</sup>n<sub>4</sub><sup>4</sup>, where n<sub>o</sub> is 
the number of correlated occupied orbitals and n<sub>u</sub> is the number of 
correlated unoccupied orbitals, however, due to the precise form of the 
expressions defining the CR-CC(2,3) triples correction, it is approximately
twice as expensive as its CCSD(T) counterpart. One must also solve the companion 
left-CCSD system of linear equations (roughly as expensive as CCSD) prior
to computing the CR-CC(2,3) correction.

The CR-CC(2,3) calculation returns four distinct energetics, labelled as 
CR-CC(2,3)<sub>X</sub>, for X = A, B, C, and D, where each variant A-D corresponds to 
a different treatment of the energy denominators entering the formula for 
the CR-CC(2,3) triples correction. The variant CR-CC(2,3)<sub>A</sub> uses the simplest 
Møller-Plesset form of the energy denominator and is equivalent to the method 
called CCSD(2)<sub>T</sub>. Meanwhile, the CR-CC(2,3)<sub>D</sub> result, which employs 
the full Epstein-Nesbet energy denominator, is generally most accurate and often 
reported as the CR-CC(2,3) energy (or by its former name, CR-CCSD(T)<sub>L</sub>).
</p>

### Sample Code

```python3
    from pyscf import gto, scf
    from ccpy.drivers.driver import Driver

    # build molecule using PySCF and run SCF calculation
    mol = gto.M(
        atom=[["O", (0.0, 0.0, -0.0180)],
              ["H", (0.0, 3.030526, -2.117796)],
              ["H", (0.0, -3.030526, -2.117796)]],
        basis="cc-pvdz",
        charge=0,
        spin=0,
        symmetry="C2V",
        cart=False,
        unit="Bohr",
    )
    mf = scf.RHF(mol)
    mf.kernel()
    
    # get the CCpy driver object using PySCF meanfield
    driver = Driver.from_pyscf(mf, nfrozen=1)

    # set calculation parameters
    driver.options["energy_convergence"] = 1.0e-07 # (in hartree)
    driver.options["amp_convergence"] = 1.0e-07
    driver.options["maximum_iterations"] = 80

    # run CCSD calculation
    driver.run_cc(method="ccsd")
    # build CCSD similarity-transformed Hamiltonian (this overwrites original MO integrals)
    driver.run_hbar(method="ccsd")
    # run companion left-CCSD calculation
    driver.run_leftcc(method="left_ccsd")
    # run CR-CC(2,3) triples correction
    driver.run_ccp3(method="crcc23")
```
### References

1. P. Piecuch and M. Włoch, *J. Chem. Phys.* **123**, 224105 (2005).
2. P. Piecuch, M. Włoch, J. R. Gour, and A. Kinal, *Chem. Phys. Lett* **418**, 467 (2006).
3. M. Włoch, M. D. Lodriguito, P. Piecuch, and J. R. Gour, *Mol. Phys.* **104**, 2149 (2006), **104**, 2991 (2006) [Erratum].
4. M. Włoch, J. R. Gour, and P. Piecuch, *J. Phys. Chem. A.* **111**, 11359 (2007).
5. P. Piecuch, J. R. Gour, and M. Włoch, *Int. J. Quantum Chem.* **108**, 2128 (2008).
</details>

<details>
<summary>CR-CC(2,4)</summary>

### Summary

### Sample Code

### References

</details>

<details>
<summary>CC3</summary>

### Summary

### Sample Code

```python3
    from pyscf import gto, scf
    from ccpy.drivers.driver import Driver

    # build molecule using PySCF and run SCF calculation
    mol = gto.M(
        atom=[["O", (0.0, 0.0, -0.0180)],
              ["H", (0.0, 3.030526, -2.117796)],
              ["H", (0.0, -3.030526, -2.117796)]],
        basis="cc-pvdz",
        charge=0,
        spin=0,
        symmetry="C2V",
        cart=False,
        unit="Bohr",
    )
    mf = scf.RHF(mol)
    mf.kernel()
    
    # get the CCpy driver object using PySCF meanfield
    driver = Driver.from_pyscf(mf, nfrozen=1)

    # set calculation parameters
    driver.options["energy_convergence"] = 1.0e-07 # (in hartree)
    driver.options["amp_convergence"] = 1.0e-07
    driver.options["maximum_iterations"] = 80

    # run CC3 calculation
    driver.run_cc(method="cc3")
```
### References

</details>

<details>
<summary>CCSDt</summary>

### Summary 
The active-orbital-based CCSDt calculation

### Sample Code

```python3
    from pyscf import gto, scf
    from ccpy.drivers.driver import Driver

    # build molecule using PySCF and run SCF calculation
    mol = gto.M(
        atom=[["F", (0.0, 0.0, -2.66816)],
              ["F", (0.0, 0.0, 2.66816)]],
        basis="cc-pvdz",
        charge=0,
        spin=0,
        symmetry="D2H",
        cart=True,
        unit="Bohr",
    )
    mf = scf.RHF(mol)
    mf.kernel()
    
    # get the CCpy driver object using PySCF meanfield
    driver = Driver.from_pyscf(mf, nfrozen=1)

    # set the active space
    driver.set_active_space(nact_occupied=5, nact_unoccupied=8)

    # set calculation parameters
    driver.options["energy_convergence"] = 1.0e-07 # (in hartree)
    driver.options["amp_convergence"] = 1.0e-07
    driver.options["maximum_iterations"] = 80

    # run CCSDt calculation
    driver.run_cc(method="ccsdt1")
```
or
```python3
    from pyscf import gto, scf
    from ccpy.drivers.driver import Driver
    from ccpy.utilities.pspace import get_active_triples_pspace

    # build molecule using PySCF and run SCF calculation
    mol = gto.M(
        atom=[["F", (0.0, 0.0, -2.66816)],
              ["F", (0.0, 0.0, 2.66816)]],
        basis="cc-pvdz",
        charge=0,
        spin=0,
        symmetry="D2H",
        cart=True,
        unit="Bohr",
    )
    mf = scf.RHF(mol)
    mf.kernel()
    
    # get the CCpy driver object using PySCF meanfield
    driver = Driver.from_pyscf(mf, nfrozen=1)

    # set the active space
    driver.set_active_space(nact_occupied=5, nact_unoccupied=8)
    # get triples entering P space corresponding to the CCSDt truncation scheme
    t3_excitations = get_active_triples_pspace(driver.system,
                                              driver.system.reference_symmetry,
                                              num_active=1)
    # set calculation parameters
    driver.options["energy_convergence"] = 1.0e-07 # (in hartree)
    driver.options["amp_convergence"] = 1.0e-07
    driver.options["maximum_iterations"] = 80

    # Run CC(P) calculation equivalent to CCSDt
    driver.run_ccp(method="ccsdt_p", t3_excitations=t3_excitations)
```
The latter CC(*P*)-based approach offers two advantages: (i) it can take advantage of
the Abelian point group symmetry of a molecule by restricting the CC calculation to
include only those triply excited cluster amplitudes belonging to a particular irrep,
as specified by the keyword `target_irrep` and (ii) it can be used to perform other
types of active-orbital-based CCSDt calculations based on restricting `num_active` 
occupied/unoccupied indices to the active set. The standard choice of 
`num_active=1` results in the usual CCSDt method, however `num_active=2` and 
`num_active=3` result in the CCSDt(II) and CCSDt(III) approaches introduced in Ref. [X].

### References

</details>

<details>
<summary>CC(t;3)</summary>

### Summary

### Sample Code

```python3
    from pyscf import gto, scf
    from ccpy.drivers.driver import Driver

    # build molecule using PySCF and run SCF calculation
    mol = gto.M(
        atom=[["F", (0.0, 0.0, -2.66816)],
              ["F", (0.0, 0.0, 2.66816)]],
        basis="cc-pvdz",
        charge=0,
        spin=0,
        symmetry="D2H",
        cart=True,
        unit="Bohr",
    )
    mf = scf.RHF(mol)
    mf.kernel()
    
    # get the CCpy driver object using PySCF meanfield
    driver = Driver.from_pyscf(mf, nfrozen=1)

    # set the active space
    driver.set_active_space(nact_occupied=5, nact_unoccupied=8)

    # set calculation parameters
    driver.options["energy_convergence"] = 1.0e-07 # (in hartree)
    driver.options["amp_convergence"] = 1.0e-07
    driver.options["maximum_iterations"] = 80

    # run CCSDt calculation
    driver.run_cc(method="ccsdt1")
    # build CCSD-like similarity-transformed Hamiltonian (this overwrites original MO integrals)
    driver.run_hbar(method="ccsd")
    # run companion left-CCSD-like calculation
    driver.run_leftcc(method="left_ccsd")
    # run CC(t;3) triples correction
    driver.run_ccp3(method="cct3")
```
or
```python3
    from pyscf import gto, scf
    from ccpy.drivers.driver import Driver
    from ccpy.utilities.pspace import get_active_triples_pspace

    # build molecule using PySCF and run SCF calculation
    mol = gto.M(
        atom=[["F", (0.0, 0.0, -2.66816)],
              ["F", (0.0, 0.0, 2.66816)]],
        basis="cc-pvdz",
        charge=0,
        spin=0,
        symmetry="D2H",
        cart=True,
        unit="Bohr",
    )
    mf = scf.RHF(mol)
    mf.kernel()
    
    # get the CCpy driver object using PySCF meanfield
    driver = Driver.from_pyscf(mf, nfrozen=1)

    # set the active space
    driver.set_active_space(nact_occupied=5, nact_unoccupied=8)
    # get triples entering P space corresponding to the CCSDt truncation scheme
    t3_excitations = get_active_triples_pspace(driver.system,
                                              driver.system.reference_symmetry)
    # set calculation parameters
    driver.options["energy_convergence"] = 1.0e-07 # (in hartree)
    driver.options["amp_convergence"] = 1.0e-07    
    driver.options["maximum_iterations"] = 80

    # Run CC(P) calculation equivalent to CCSDt
    driver.run_ccp(method="ccsdt_p", t3_excitations=t3_excitations)
    # build CCSD-like similarity-transformed Hamiltonian (this overwrites original MO integrals)
    driver.run_hbar(method="ccsd")
    # run companion left-CCSD-like calculation
    driver.run_leftcc(method="left_ccsd")
    # run CC(t;3) triples correction
    driver.run_ccp3(method="ccp3", t3_excitations=t3_excitations)
```
As in the case of the CCSDt calculations, the general CC(*P*) approach allows one
to perform alternative active-orbital-based truncation schemes of the CCSDt(II) 
and CCSDt(III) types in addition to the standard CCSDt method. The corresponding
CC(*P*;*Q*) corrections result in the CC(t;3)(II), CC(t;3)(III), and CC(t;3) 
approaches, respectively.

### References

</details>

<details>
<summary>CIPSI-driven CC(P;Q) aimed at converging CCSDT</summary>

### Summary

### Sample Code

```python3
from pathlib import Path
import numpy as np
from ccpy.drivers.driver import Driver
from ccpy.utilities.pspace import get_pspace_from_cipsi

TEST_DATA_DIR = str(Path(__file__).parents[1].absolute() / "data")

def test_cipsi_ccpq_h2o():

    driver = Driver.from_gamess(
        logfile=TEST_DATA_DIR + "/h2o/h2o-Re.log",
        onebody=TEST_DATA_DIR + "/h2o/onebody.inp",
        twobody=TEST_DATA_DIR + "/h2o/twobody.inp",
        nfrozen=0,
    )

    civecs = TEST_DATA_DIR + "/h2o/civecs-10k.dat"
    _, t3_excitations, _ = get_pspace_from_cipsi(civecs, driver.system, nexcit=3)

    driver.run_ccp(method="ccsdt_p", t3_excitations=t3_excitations)
    driver.run_hbar(method="ccsdt_p", t3_excitations=t3_excitations)
    driver.run_leftccp(method="left_ccsdt_p", t3_excitations=t3_excitations)
    driver.run_ccp3(method="ccp3", state_index=0, t3_excitations=t3_excitations)
```    
    
### References
1. K. Gururangan, J. E. Deustua, J. Shen, and P. Piecuch, J. Chem. Phys. **155**, 174114 (2021) <br />
(see https://doi.org/10.1063/5.0064400; cf. also https://doi.org/10.48550/arXiv.2107.10994) <br />
</details>

<details>
<summary>Adaptive CC(P;Q) aimed at converging CCSDT</summary>

### Summary

### Sample Code

```python3
import numpy as np
from pyscf import scf, gto
from ccpy.drivers.driver import Driver
from ccpy.drivers.adaptive import AdaptDriver

def test_adaptive_f2():
    geometry = [["F", (0.0, 0.0, -2.66816)], ["F", (0.0, 0.0, 2.66816)]]
    mol = gto.M(
        atom=geometry,
        basis="cc-pvdz",
        charge=0,
        spin=0,
        symmetry="D2H",
        cart=True,
        unit="Bohr",
    )
    mf = scf.RHF(mol)
    mf.kernel()

    percentages = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]
    driver = Driver.from_pyscf(mf, nfrozen=2)
    driver.system.print_info()
    driver.options["RHF_symmetry"] = False
    adaptdriver = AdaptDriver(driver, percentage=percentages)
    adaptdriver.options["energy_tolerance"] = 1.0e-08
    adaptdriver.options["two_body_approx"] = True
    adaptdriver.run()
```
### References

1. K. Gururangan and P. Piecuch, J. Chem. Phys. **159**, 084108 (2023) <br />
(see https://doi.org/10.1063/5.0162873; cf. also https://doi.org/10.48550/arXiv.2306.09638) <br />
</details>

<details>
<summary>CC4</summary>

### Summary
<p align="justify">
</p>

### Sample Code

```python3
    from pyscf import gto, scf
    from ccpy.drivers.driver import Driver

    # build molecule using PySCF and run SCF calculation
    mol = gto.M(
        atom=[["O", (0.0, 0.0, -0.0180)],
              ["H", (0.0, 3.030526, -2.117796)],
              ["H", (0.0, -3.030526, -2.117796)]],
        basis="cc-pvdz",
        charge=0,
        spin=0,
        symmetry="C2V",
        cart=False,
        unit="Bohr",
    )
    mf = scf.RHF(mol)
    mf.kernel()
    
    # get the CCpy driver object using PySCF meanfield
    driver = Driver.from_pyscf(mf, nfrozen=1)

    # set calculation parameters
    driver.options["energy_convergence"] = 1.0e-07 # (in hartree)
    driver.options["amp_convergence"] = 1.0e-07
    driver.options["maximum_iterations"] = 80

    # run CC4 calculation
    driver.run_cc(method="cc4")
```
### References
</details>

#### Externally Corrected (ec) CC Approaches

<details>
<summary>CIPSI-driven ec-CC-II and ec-CC-II<sub>3</sub> </summary>

### Summary

### Sample Code

```python3
from pathlib import Path
import numpy as np
from ccpy.drivers.driver import Driver
from ccpy.utilities.pspace import get_pspace_from_cipsi

TEST_DATA_DIR = str(Path(__file__).parents[1].absolute() / "data")

def test_eccc23_h2o():

    driver = Driver.from_gamess(
        logfile=TEST_DATA_DIR + "/h2o/h2o-Re.log",
        onebody=TEST_DATA_DIR + "/h2o/onebody.inp",
        twobody=TEST_DATA_DIR + "/h2o/twobody.inp",
        nfrozen=0,
    )

    civecs = TEST_DATA_DIR + "/h2o/civecs-10k.dat"
    _, t3_excitations, _ = get_pspace_from_cipsi(civecs, driver.system, nexcit=3)

    driver.run_eccc(method="eccc2", ci_vectors_file=civecs)
    driver.run_hbar(method="ccsd")
    driver.run_leftcc(method="left_ccsd")
    driver.run_ccp3(method="ccp3", state_index=0, t3_excitations=t3_excitations)
```    
    
### References
1. I. Magoulas, K. Gururangan, P. Piecuch, J. E. Deustua, and J. Shen, J. Chem. Theory Comput. **17**, 4006 (2021) <br />
(see https://doi.org/10.1021/acs.jctc.1c00181; cf. also https://doi.org/10.48550/arXiv.2102.10143)
</details>

#### Approximate Coupled-Pair (ACP) Approaches
  - ACCD
  - ACCSD
  - ACCSDt
  - ACC(2,3)
  - ACC(t;3)
  
### EOMCC approaches for ground, excited, attached, and ionized states
  - EOMCCSD
  - CR-EOMCC(2,3) and its size-intensive *δ*-CR-EOMCC(2,3) extension
  - EOMCCSD(T)(a)*
  - EOM-CC3
  - EOMCCSDt
  - Excited-state CC(t;3)
  - Adaptive CC(*P*;*Q*) aimed at converging EOMCCSDT
  - EOMCCSDT
  - SF-EOMCCSD
  - SF-EOMCC(2,3)
  - IP-EOMCCSD(2h-1p)
  - IP-EOMCCSD(T)(a)*
  - Active-space IP-EOMCCSD(3h-2p){N<sub>o</sub>} (also known as IP-EOMCCSDt)
  - IP-EOMCCSD(3h-2p)
  - IP-EOMCCSDT
  - EA-EOMCCSD(2p-1h)
  - EA-EOMCCSD(T)(a)*
  - Active-space EA-EOMCCSD(3p-2h){N<sub>u</sub>} (also known as EA-EOMCCSDt)
  - EA-EOMCCSD(3p-2h)
  - EA-EOMCCSDT
  - DEA-EOMCCSD(3p-1h)
  - DEA-EOMCCSD(4p-2h)
  - DIP-EOMCCSD(3h-1p)
  - DIP-EOMCCSD(4h-2p)

<p align="justify">
Because CCpy is primarily used for CC method development work, we use interfaces to GAMESS and PySCF to obtain the mean-field (typically Hartree-Fock)
reference state and associated one- and two-electron integrals in the molecular orbital basis prior to performing the correlated CC calculations. All implementations
in CCpy are based on the spin-integrated spinorbital formulation and are compatible with RHF and ROHF references. 
</p>

## Installation and Support
<p align="justify">
  
Installation instructions are provided in the CCpy documentation page (https://piecuch-group.github.io/ccpy/). If you have any questions about CCpy or need additional information about its functionality,
please e-mail gururang@msu.edu.
</p>

## CCpy Development Team

Karthik Gururangan\
Doctoral student, Department of Chemistry, Michigan State University  
e-mail: gururang@msu.edu\
(lead developer)

Dr. J. Emiliano Deustua\
COO and Co-founder, Examol\
(co-developer)

Professor Piotr Piecuch\
University Distinguished Professor and MSU Research Foundation Professor, Department of Chemistry, Michigan State University\
Adjunct Professor, Department of Physics and Astronomy, Michigan State University\
e-mail: piecuch@chemistry.msu.edu\
(co-developer and principal investigator)

Additional contributors: Tiange Deng (doctoral student, Department of Chemistry, Michigan State University; ACCD and ACCSD options).

## Acknowledgements

We acknowledge support from the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy 
(Grant No. DE-FG02-01ER15228 to Piotr Piecuch).

<p align="justify">
  
CCpy is an open-source code under the [GPLv3](https://www.gnu.org/licenses/gpl-3.0.html) license
developed and maintained by the [Piecuch Group](https://www2.chemistry.msu.edu/faculty/piecuch/) 
at Michigan State University. 

</p>

            

Raw data

            {
    "_id": null,
    "home_page": null,
    "name": "coupled-cluster-py",
    "maintainer": null,
    "docs_url": null,
    "requires_python": ">=3.10",
    "maintainer_email": "Karthik Gururangan <gururang@msu.edu>, Emiliano Deustua <edeustua@gmail.com>, Piotr Piecuch <piecuch@chemistry.msu.edu>",
    "keywords": null,
    "author": null,
    "author_email": "Karthik Gururangan <gururang@msu.edu>",
    "download_url": null,
    "platform": null,
    "description": "\n# CCpy: A coupled-cluster package written in Python.\n\n## Overview\n<p align=\"justify\">\nCCpy is a research-level Python package for performing non-relativistic electronic structure calculations for molecular systems \nusing methods based on the ground-state coupled-cluster (CC) theory and its equation-of-motion (EOM) extension\nto electronic excited, attached, and ionized states. As a design philosophy, CCpy favors simplicity over efficiency, and this is reflected in the\nusage of computational routines that are transparent enough so that they can be easily used, modified, and extended, while \nstill maintaining reasonable efficiency. To this end, CCpy employs a hybrid Python-Fortran programming approach made possible\nwith the f2py package, which allows one to compile Fortran code into shared object libraries containing subroutines\nthat are callable from Python and interoperable with Numpy arrays. \n\n*Important Note: The compliation of Fortran modules with ```f2py``` is not currently compatible with Python 3.12 due to\nthe migration away from ```numpy.distutils```. In order to fix this, we are moving over to compilation using\n```meson```. In the meantime, please use Python 3.11 when building CCpy.*\n</p>\n\n## Available Computational Options\n<p align=\"justify\">\nCCpy specializes in applying the CC(P;Q) and externally corrected (ec) CC methodologies developed in the Piecuch group at \nMichigan State University. In CC(P;Q), the energetics obtained by solving the ground- or excited-state CC/EOMCC equations in\none subspace of the many-electron Hilbert space, called the P space, are corrected for the missing many-electron correlation\neffects captured with the help of a complementary subspace called the Q space using the state-selective, non-iterative,\nand non-perturbative energy corrections based on the CC moment expansion formalism. Currently, CCpy offers implementations\nof several CC(P;Q) methods, the majority of which are aimed at converging the high-level CCSDT and EOMCCSDT energetics. \nThese include the completely-renormalized (CR) methods such as the CR-CC(2,3) and CR-CC(2,4) triples and quadruples \ncorrections to CCSD, the active-space CCSDt and CC(t;3) approaches, which are based on a user-defined selection of active orbitals, \nand the black-box selected configuration interaction (CI) driven and adaptive CC(P;Q) methodologies, which construct the P and Q spaces \nentering the CC(P;Q) computations using information extracted from selected CI wave functions or the adaptive CC(P;Q) moment \nexpansions themselves, respectively. The ec-CC approaches on the other hand seek to converge the exact, full CI energetics\ndirectly by solving for the T<sub>1</sub> and T<sub>2</sub> clusters in the presence of the leading T<sub>3</sub> and T<sub>4</sub> clusters extracted from an\nexternal non-CC wave function. Current implementations of the ec-CC approaches in CCpy are designed to iterate T<sub>1</sub> and T<sub>2</sub> clusters \nin the presence of T<sub>3</sub> and T<sub>4</sub> obtained from CI wave functions of the selected CI or multireference CI types, and correct the resulting\nenergetics for the missing many-electron correlations using the generalized moment expansions of the ec-CC equations.\n</p>\n\n### M\u00f8ller-Plesset (MP) perturbation theory\n  - MP2 \n  - MP3 \n\n### Ground-state CC methodologies\n<details>\n<summary>CCD</summary>\n\n### Summary\n\n<p align=\"justify\">\nThe CC with doubles (CCD) method truncates the cluster operator as T = T<sub>2</sub>.\nIt has iterative computational costs that scale as \nn<sub>o</sub><sup>2</sup>n<sub>u</sub><sup>4</sup>, where n<sub>o</sub> is \nthe number of correlated occupied orbitals and n<sub>u</sub> is the number of \ncorrelated unoccupied orbitals. \nDue to the importance of pair correlations in the many-electron problem, the\nCCD approximation was first introduced in Prof. \u010c\u00ed\u017eek's landmark 1966 paper\nunder the name coupled-pair many-electron theory, or CPMET. Although CCD is\noften superceeded by the more accurate CC with singles and doubles (CCSD) method,\nwhich has the same computational scaling, CCD is still relevant to modern CC\ncalculations within the context of correlating orbital-optimized reference\nfunctions, as in Br\u00fcckner CCD.\n</p>\n\n### Example Code\n\n```python3\n    from pyscf import gto, scf\n    from ccpy.drivers.driver import Driver\n\n    # build molecule using PySCF and run SCF calculation\n    mol = gto.M(\n        atom=[[\"O\", (0.0, 0.0, -0.0180)],\n              [\"H\", (0.0, 3.030526, -2.117796)],\n              [\"H\", (0.0, -3.030526, -2.117796)]],\n        basis=\"cc-pvdz\",\n        charge=0,\n        spin=0,\n        symmetry=\"C2V\",\n        cart=False,\n        unit=\"Bohr\",\n    )\n    mf = scf.RHF(mol)\n    mf.kernel()\n    \n    # get the CCpy driver object using PySCF meanfield\n    driver = Driver.from_pyscf(mf, nfrozen=1)\n\n    # set calculation parameters\n    driver.options[\"energy_convergence\"] = 1.0e-07 # (in hartree)\n    driver.options[\"amp_convergence\"] = 1.0e-07\n    driver.options[\"maximum_iterations\"] = 80\n\n    # run CCD calculation\n    driver.run_cc(method=\"ccd\")\n```\n### Reference\n1. J. \u010c\u00ed\u017eek, *J. Chem. Phys.* **45**, 4256 (1966).\n</details>\n\n<details>\n<summary>CCSD</summary>\n\n### Summary\n\n<p align=\"justify\">\nThe CC with singles and doubles (CCSD) method approximates the cluster\noperator as T = T<sub>1</sub> + T<sub>2</sub>. It is the most commonly used truncation level\nin the CC hierarchy and often forms the starting point for more sophisticated \ntreatments of many-electron correlation effects. CCSD has iterative computational costs that \nscale as n<sub>o</sub><sup>2</sup>n<sub>u</sub><sup>4</sup>, where n<sub>o</sub> is \nthe number of correlated occupied orbitals and n<sub>u</sub> is the number of \ncorrelated unoccupied orbitals.\n</p>\n\n### Sample Code\n\n```python3\n    from pyscf import gto, scf\n    from ccpy.drivers.driver import Driver\n\n    # build molecule using PySCF and run SCF calculation\n    mol = gto.M(\n        atom=[[\"O\", (0.0, 0.0, -0.0180)],\n              [\"H\", (0.0, 3.030526, -2.117796)],\n              [\"H\", (0.0, -3.030526, -2.117796)]],\n        basis=\"cc-pvdz\",\n        charge=0,\n        spin=0,\n        symmetry=\"C2V\",\n        cart=False,\n        unit=\"Bohr\",\n    )\n    mf = scf.RHF(mol)\n    mf.kernel()\n    \n    # get the CCpy driver object using PySCF meanfield\n    driver = Driver.from_pyscf(mf, nfrozen=1)\n\n    # set calculation parameters\n    driver.options[\"energy_convergence\"] = 1.0e-07 # (in hartree)\n    driver.options[\"amp_convergence\"] = 1.0e-07\n    driver.options[\"maximum_iterations\"] = 80\n\n    # run CCSD calculation\n    driver.run_cc(method=\"ccsd\")\n```\n### References\n\n1. G. D. Purvis and R. J. Bartlett, *J. Chem. Phys.* **76**, 1910 (1982).\n2. J. M. Cullen and M. C. Zerner, *J. Chem. Phys.* **77**, 4088 (1982).\n3. G. E. Scuseria, A. C. Scheiner, T. J. Lee, J. E. Rice, and H. F. Schaefer, *J. Chem. Phys.* **86**, 2881 (1987).\n4. P. Piecuch and J. Paldus, *Int. J. Quantum Chem.* **36**, 429 (1989).\n</details>\n\n<details>\n<summary>CCSDT</summary>\n\n### Summary\n<p align=\"justify\">\nThe CC with singles, doubles, and triples (CCSDT) method approximates the cluster\noperator as T = T<sub>1</sub> + T<sub>2</sub> + T<sub>3</sub>. CCSDT is a high-level\nmethod capable of providing nearly exact results for closed-shell molecules\nas well as chemically accurate energetics for single bond breaking and a variety\nof open-shell systems. CCSDT has iterative computational costs that scale as \nn<sub>o</sub><sup>3</sup>n<sub>u</sub><sup>5</sup>, where n<sub>o</sub> is \nthe number of correlated occupied orbitals and n<sub>u</sub> is the number of \ncorrelated unoccupied orbitals. \n</p>\n\n### Sample Code\n\n```python3\n    from pyscf import gto, scf\n    from ccpy.drivers.driver import Driver\n\n    # build molecule using PySCF and run SCF calculation\n    mol = gto.M(\n        atom=[[\"O\", (0.0, 0.0, -0.0180)],\n              [\"H\", (0.0, 3.030526, -2.117796)],\n              [\"H\", (0.0, -3.030526, -2.117796)]],\n        basis=\"cc-pvdz\",\n        charge=0,\n        spin=0,\n        symmetry=\"C2V\",\n        cart=False,\n        unit=\"Bohr\",\n    )\n    mf = scf.RHF(mol)\n    mf.kernel()\n    \n    # get the CCpy driver object using PySCF meanfield\n    driver = Driver.from_pyscf(mf, nfrozen=1)\n\n    # set calculation parameters\n    driver.options[\"energy_convergence\"] = 1.0e-07 # (in hartree)\n    driver.options[\"amp_convergence\"] = 1.0e-07\n    driver.options[\"maximum_iterations\"] = 80\n\n    # run CCSDT calculation\n    driver.run_cc(method=\"ccsdt\")\n```\n\n### References\n1. M. R. Hoffmann and H. F. Schaefer, *Adv. Quantum Chem.* **18**, 207 (1986).\n2. J. Noga and R. J. Bartlett, *J. Chem. Phys.* **86**, 7041 (1987).\n3. G. E. Scuseria and H. F. Schaefer, *Chem. Phys. Lett.* **152**, 382 (1988).\n4. J. D. Watts and R. J. Bartlett, *J. Chem. Phys.* **93**, 6104 (1990).\n\n</details>\n\n<details>\n<summary>CCSDTQ</summary>\n\n### Summary\n<p align=\"justify\">\nThe CC with singles, doubles, triples, and quadruples (CCSDTQ) method \napproximates the cluster operator as \nT = T<sub>1</sub> + T<sub>2</sub> + T<sub>3</sub> + T<sub>4</sub>. \nCCSDTQ is a very high-level method and is often capable of providing \nnear-exact energetics for most problems of chemical interest, as long\nas the number of strongly correlated electrons is not too large (for\nmethods designed to treat genuine strong correlations, see the\napproximate coupled-pair, or ACP approaches).\nCCSDTQ has iterative computational costs that scale as \nn<sub>o</sub><sup>4</sup>n<sub>u</sub><sup>6</sup>, where n<sub>o</sub> is \nthe number of correlated occupied orbitals and n<sub>u</sub> is the number of \ncorrelated unoccupied orbitals. \n</p>\n\n### Sample Code\n\n```python3\n    from pyscf import gto, scf\n    from ccpy.drivers.driver import Driver\n\n    # build molecule using PySCF and run SCF calculation\n    mol = gto.M(\n        atom=[[\"O\", (0.0, 0.0, -0.0180)],\n              [\"H\", (0.0, 3.030526, -2.117796)],\n              [\"H\", (0.0, -3.030526, -2.117796)]],\n        basis=\"cc-pvdz\",\n        charge=0,\n        spin=0,\n        symmetry=\"C2V\",\n        cart=False,\n        unit=\"Bohr\",\n    )\n    mf = scf.RHF(mol)\n    mf.kernel()\n    \n    # get the CCpy driver object using PySCF meanfield\n    driver = Driver.from_pyscf(mf, nfrozen=1)\n\n    # set calculation parameters\n    driver.options[\"energy_convergence\"] = 1.0e-07 # (in hartree)\n    driver.options[\"amp_convergence\"] = 1.0e-07\n    driver.options[\"maximum_iterations\"] = 80\n\n    # run CCSDTQ calculation\n    driver.run_cc(method=\"ccsdtq\")\n```\n\n### References\n1. N. Oliphant and L. Adamowicz, *J. Chem. Phys.* **95**, 6645 (1991).\n2. S. A. Kucharski and R. J. Bartlett, *Theor. Chem. Acc.* **80**, 387 (1991).\n3. S. A. Kucharski and R. J. Bartlett, *J. Chem. Phys.* **97**, 4282 (1992).\n4. P. Piecuch and L. Adamowicz, *J. Chem. Phys.* **100**, 5792 (1994).\n\n</details>\n\n<details>\n<summary>CCSD(T)</summary>\n\n### Summary\n\n<p align=\"justify\">\nThe CCSD(T) method corrects the CCSD energy for the correlation effects\ndue to T<sub>3</sub> clusters using formulas derived using many-body perturbation\ntheory (MBPT). In particular, the CCSD(T) correction includes the leading \n4th-order energy correction for T<sub>3</sub> along with 5th-order contribution\ndue to disconnected triples. The inclusion\nof the latter term distinguishes CCSD(T) from its CCSD[T] precedessor.\nCCSD(T) has noniterative computational costs that \nscale as n<sub>o</sub><sup>3</sup>n<sub>4</sub><sup>4</sup>, where n<sub>o</sub> is \nthe number of correlated occupied orbitals and n<sub>u</sub> is the number of \ncorrelated unoccupied orbitals.\n</p>\n\n### Sample Code\n\n```python3\n    from pyscf import gto, scf\n    from ccpy.drivers.driver import Driver\n\n    # build molecule using PySCF and run SCF calculation\n    mol = gto.M(\n        atom=[[\"O\", (0.0, 0.0, -0.0180)],\n              [\"H\", (0.0, 3.030526, -2.117796)],\n              [\"H\", (0.0, -3.030526, -2.117796)]],\n        basis=\"cc-pvdz\",\n        charge=0,\n        spin=0,\n        symmetry=\"C2V\",\n        cart=False,\n        unit=\"Bohr\",\n    )\n    mf = scf.RHF(mol)\n    mf.kernel()\n    \n    # get the CCpy driver object using PySCF meanfield\n    driver = Driver.from_pyscf(mf, nfrozen=1)\n\n    # set calculation parameters\n    driver.options[\"energy_convergence\"] = 1.0e-07 # (in hartree)\n    driver.options[\"amp_convergence\"] = 1.0e-07\n    driver.options[\"maximum_iterations\"] = 80\n\n    # run CCSD calculation\n    driver.run_cc(method=\"ccsd\")\n    # perform CCSD(T) correction\n    driver.run_ccp3(method=\"ccsd(t)\")\n```\n### References\n\n1. K. Raghavachari, G. W. Trucks, J. A. Pople, and M. Head-Gordon, *Chem. Phys. Lett.* **157**, 479 (1989).\n2. J. F. Stanton, *Chem. Phys. Lett.* **281**, 130 (1997).\n3. S. A. Kucharski and R. J. Bartlett, *J. Chem. Phys.* **108**, 5243 (1998).\n4. T. D. Crawford and J. F. Stanton, *Int. J. Quantum Chem.* **70**, 601 (1998).\n</details>\n\n<details>\n<summary>CR-CC(2,3)</summary>\n\n### Summary\n\n<p align=\"justify\">\nThe CR-CC(2,3) approach is a nonperturbative and noniterative correction to the\nCCSD energetics that accounts for the correlation effects due to T<sub>3</sub>\nclusters using formulas derived from the biorthogonal moment energy expansions of CC\ntheory. In particular, CR-CC(2,3) represents the most robust scheme to noniteratively\ninclude the effects of connected triples on top of CCSD, and it is capable of providing an \naccurate description of closed-shell molecules in addition to commonly encountered\nmultireference problems, such as single bond breaking and open-shell radical \nand diradical species, which are generally beyond the scope of perturbative \nmethods like CCSD(T). The CR-CC(2,3) triples correction uses noniterative steps\nthat scale as n<sub>o</sub><sup>3</sup>n<sub>4</sub><sup>4</sup>, where n<sub>o</sub> is \nthe number of correlated occupied orbitals and n<sub>u</sub> is the number of \ncorrelated unoccupied orbitals, however, due to the precise form of the \nexpressions defining the CR-CC(2,3) triples correction, it is approximately\ntwice as expensive as its CCSD(T) counterpart. One must also solve the companion \nleft-CCSD system of linear equations (roughly as expensive as CCSD) prior\nto computing the CR-CC(2,3) correction.\n\nThe CR-CC(2,3) calculation returns four distinct energetics, labelled as \nCR-CC(2,3)<sub>X</sub>, for X = A, B, C, and D, where each variant A-D corresponds to \na different treatment of the energy denominators entering the formula for \nthe CR-CC(2,3) triples correction. The variant CR-CC(2,3)<sub>A</sub> uses the simplest \nM\u00f8ller-Plesset form of the energy denominator and is equivalent to the method \ncalled CCSD(2)<sub>T</sub>. Meanwhile, the CR-CC(2,3)<sub>D</sub> result, which employs \nthe full Epstein-Nesbet energy denominator, is generally most accurate and often \nreported as the CR-CC(2,3) energy (or by its former name, CR-CCSD(T)<sub>L</sub>).\n</p>\n\n### Sample Code\n\n```python3\n    from pyscf import gto, scf\n    from ccpy.drivers.driver import Driver\n\n    # build molecule using PySCF and run SCF calculation\n    mol = gto.M(\n        atom=[[\"O\", (0.0, 0.0, -0.0180)],\n              [\"H\", (0.0, 3.030526, -2.117796)],\n              [\"H\", (0.0, -3.030526, -2.117796)]],\n        basis=\"cc-pvdz\",\n        charge=0,\n        spin=0,\n        symmetry=\"C2V\",\n        cart=False,\n        unit=\"Bohr\",\n    )\n    mf = scf.RHF(mol)\n    mf.kernel()\n    \n    # get the CCpy driver object using PySCF meanfield\n    driver = Driver.from_pyscf(mf, nfrozen=1)\n\n    # set calculation parameters\n    driver.options[\"energy_convergence\"] = 1.0e-07 # (in hartree)\n    driver.options[\"amp_convergence\"] = 1.0e-07\n    driver.options[\"maximum_iterations\"] = 80\n\n    # run CCSD calculation\n    driver.run_cc(method=\"ccsd\")\n    # build CCSD similarity-transformed Hamiltonian (this overwrites original MO integrals)\n    driver.run_hbar(method=\"ccsd\")\n    # run companion left-CCSD calculation\n    driver.run_leftcc(method=\"left_ccsd\")\n    # run CR-CC(2,3) triples correction\n    driver.run_ccp3(method=\"crcc23\")\n```\n### References\n\n1. P. Piecuch and M. W\u0142och, *J. Chem. Phys.* **123**, 224105 (2005).\n2. P. Piecuch, M. W\u0142och, J. R. Gour, and A. Kinal, *Chem. Phys. Lett* **418**, 467 (2006).\n3. M. W\u0142och, M. D. Lodriguito, P. Piecuch, and J. R. Gour, *Mol. Phys.* **104**, 2149 (2006), **104**, 2991 (2006) [Erratum].\n4. M. W\u0142och, J. R. Gour, and P. Piecuch, *J. Phys. Chem. A.* **111**, 11359 (2007).\n5. P. Piecuch, J. R. Gour, and M. W\u0142och, *Int. J. Quantum Chem.* **108**, 2128 (2008).\n</details>\n\n<details>\n<summary>CR-CC(2,4)</summary>\n\n### Summary\n\n### Sample Code\n\n### References\n\n</details>\n\n<details>\n<summary>CC3</summary>\n\n### Summary\n\n### Sample Code\n\n```python3\n    from pyscf import gto, scf\n    from ccpy.drivers.driver import Driver\n\n    # build molecule using PySCF and run SCF calculation\n    mol = gto.M(\n        atom=[[\"O\", (0.0, 0.0, -0.0180)],\n              [\"H\", (0.0, 3.030526, -2.117796)],\n              [\"H\", (0.0, -3.030526, -2.117796)]],\n        basis=\"cc-pvdz\",\n        charge=0,\n        spin=0,\n        symmetry=\"C2V\",\n        cart=False,\n        unit=\"Bohr\",\n    )\n    mf = scf.RHF(mol)\n    mf.kernel()\n    \n    # get the CCpy driver object using PySCF meanfield\n    driver = Driver.from_pyscf(mf, nfrozen=1)\n\n    # set calculation parameters\n    driver.options[\"energy_convergence\"] = 1.0e-07 # (in hartree)\n    driver.options[\"amp_convergence\"] = 1.0e-07\n    driver.options[\"maximum_iterations\"] = 80\n\n    # run CC3 calculation\n    driver.run_cc(method=\"cc3\")\n```\n### References\n\n</details>\n\n<details>\n<summary>CCSDt</summary>\n\n### Summary \nThe active-orbital-based CCSDt calculation\n\n### Sample Code\n\n```python3\n    from pyscf import gto, scf\n    from ccpy.drivers.driver import Driver\n\n    # build molecule using PySCF and run SCF calculation\n    mol = gto.M(\n        atom=[[\"F\", (0.0, 0.0, -2.66816)],\n              [\"F\", (0.0, 0.0, 2.66816)]],\n        basis=\"cc-pvdz\",\n        charge=0,\n        spin=0,\n        symmetry=\"D2H\",\n        cart=True,\n        unit=\"Bohr\",\n    )\n    mf = scf.RHF(mol)\n    mf.kernel()\n    \n    # get the CCpy driver object using PySCF meanfield\n    driver = Driver.from_pyscf(mf, nfrozen=1)\n\n    # set the active space\n    driver.set_active_space(nact_occupied=5, nact_unoccupied=8)\n\n    # set calculation parameters\n    driver.options[\"energy_convergence\"] = 1.0e-07 # (in hartree)\n    driver.options[\"amp_convergence\"] = 1.0e-07\n    driver.options[\"maximum_iterations\"] = 80\n\n    # run CCSDt calculation\n    driver.run_cc(method=\"ccsdt1\")\n```\nor\n```python3\n    from pyscf import gto, scf\n    from ccpy.drivers.driver import Driver\n    from ccpy.utilities.pspace import get_active_triples_pspace\n\n    # build molecule using PySCF and run SCF calculation\n    mol = gto.M(\n        atom=[[\"F\", (0.0, 0.0, -2.66816)],\n              [\"F\", (0.0, 0.0, 2.66816)]],\n        basis=\"cc-pvdz\",\n        charge=0,\n        spin=0,\n        symmetry=\"D2H\",\n        cart=True,\n        unit=\"Bohr\",\n    )\n    mf = scf.RHF(mol)\n    mf.kernel()\n    \n    # get the CCpy driver object using PySCF meanfield\n    driver = Driver.from_pyscf(mf, nfrozen=1)\n\n    # set the active space\n    driver.set_active_space(nact_occupied=5, nact_unoccupied=8)\n    # get triples entering P space corresponding to the CCSDt truncation scheme\n    t3_excitations = get_active_triples_pspace(driver.system,\n                                              driver.system.reference_symmetry,\n                                              num_active=1)\n    # set calculation parameters\n    driver.options[\"energy_convergence\"] = 1.0e-07 # (in hartree)\n    driver.options[\"amp_convergence\"] = 1.0e-07\n    driver.options[\"maximum_iterations\"] = 80\n\n    # Run CC(P) calculation equivalent to CCSDt\n    driver.run_ccp(method=\"ccsdt_p\", t3_excitations=t3_excitations)\n```\nThe latter CC(*P*)-based approach offers two advantages: (i) it can take advantage of\nthe Abelian point group symmetry of a molecule by restricting the CC calculation to\ninclude only those triply excited cluster amplitudes belonging to a particular irrep,\nas specified by the keyword `target_irrep` and (ii) it can be used to perform other\ntypes of active-orbital-based CCSDt calculations based on restricting `num_active` \noccupied/unoccupied indices to the active set. The standard choice of \n`num_active=1` results in the usual CCSDt method, however `num_active=2` and \n`num_active=3` result in the CCSDt(II) and CCSDt(III) approaches introduced in Ref. [X].\n\n### References\n\n</details>\n\n<details>\n<summary>CC(t;3)</summary>\n\n### Summary\n\n### Sample Code\n\n```python3\n    from pyscf import gto, scf\n    from ccpy.drivers.driver import Driver\n\n    # build molecule using PySCF and run SCF calculation\n    mol = gto.M(\n        atom=[[\"F\", (0.0, 0.0, -2.66816)],\n              [\"F\", (0.0, 0.0, 2.66816)]],\n        basis=\"cc-pvdz\",\n        charge=0,\n        spin=0,\n        symmetry=\"D2H\",\n        cart=True,\n        unit=\"Bohr\",\n    )\n    mf = scf.RHF(mol)\n    mf.kernel()\n    \n    # get the CCpy driver object using PySCF meanfield\n    driver = Driver.from_pyscf(mf, nfrozen=1)\n\n    # set the active space\n    driver.set_active_space(nact_occupied=5, nact_unoccupied=8)\n\n    # set calculation parameters\n    driver.options[\"energy_convergence\"] = 1.0e-07 # (in hartree)\n    driver.options[\"amp_convergence\"] = 1.0e-07\n    driver.options[\"maximum_iterations\"] = 80\n\n    # run CCSDt calculation\n    driver.run_cc(method=\"ccsdt1\")\n    # build CCSD-like similarity-transformed Hamiltonian (this overwrites original MO integrals)\n    driver.run_hbar(method=\"ccsd\")\n    # run companion left-CCSD-like calculation\n    driver.run_leftcc(method=\"left_ccsd\")\n    # run CC(t;3) triples correction\n    driver.run_ccp3(method=\"cct3\")\n```\nor\n```python3\n    from pyscf import gto, scf\n    from ccpy.drivers.driver import Driver\n    from ccpy.utilities.pspace import get_active_triples_pspace\n\n    # build molecule using PySCF and run SCF calculation\n    mol = gto.M(\n        atom=[[\"F\", (0.0, 0.0, -2.66816)],\n              [\"F\", (0.0, 0.0, 2.66816)]],\n        basis=\"cc-pvdz\",\n        charge=0,\n        spin=0,\n        symmetry=\"D2H\",\n        cart=True,\n        unit=\"Bohr\",\n    )\n    mf = scf.RHF(mol)\n    mf.kernel()\n    \n    # get the CCpy driver object using PySCF meanfield\n    driver = Driver.from_pyscf(mf, nfrozen=1)\n\n    # set the active space\n    driver.set_active_space(nact_occupied=5, nact_unoccupied=8)\n    # get triples entering P space corresponding to the CCSDt truncation scheme\n    t3_excitations = get_active_triples_pspace(driver.system,\n                                              driver.system.reference_symmetry)\n    # set calculation parameters\n    driver.options[\"energy_convergence\"] = 1.0e-07 # (in hartree)\n    driver.options[\"amp_convergence\"] = 1.0e-07    \n    driver.options[\"maximum_iterations\"] = 80\n\n    # Run CC(P) calculation equivalent to CCSDt\n    driver.run_ccp(method=\"ccsdt_p\", t3_excitations=t3_excitations)\n    # build CCSD-like similarity-transformed Hamiltonian (this overwrites original MO integrals)\n    driver.run_hbar(method=\"ccsd\")\n    # run companion left-CCSD-like calculation\n    driver.run_leftcc(method=\"left_ccsd\")\n    # run CC(t;3) triples correction\n    driver.run_ccp3(method=\"ccp3\", t3_excitations=t3_excitations)\n```\nAs in the case of the CCSDt calculations, the general CC(*P*) approach allows one\nto perform alternative active-orbital-based truncation schemes of the CCSDt(II) \nand CCSDt(III) types in addition to the standard CCSDt method. The corresponding\nCC(*P*;*Q*) corrections result in the CC(t;3)(II), CC(t;3)(III), and CC(t;3) \napproaches, respectively.\n\n### References\n\n</details>\n\n<details>\n<summary>CIPSI-driven CC(P;Q) aimed at converging CCSDT</summary>\n\n### Summary\n\n### Sample Code\n\n```python3\nfrom pathlib import Path\nimport numpy as np\nfrom ccpy.drivers.driver import Driver\nfrom ccpy.utilities.pspace import get_pspace_from_cipsi\n\nTEST_DATA_DIR = str(Path(__file__).parents[1].absolute() / \"data\")\n\ndef test_cipsi_ccpq_h2o():\n\n    driver = Driver.from_gamess(\n        logfile=TEST_DATA_DIR + \"/h2o/h2o-Re.log\",\n        onebody=TEST_DATA_DIR + \"/h2o/onebody.inp\",\n        twobody=TEST_DATA_DIR + \"/h2o/twobody.inp\",\n        nfrozen=0,\n    )\n\n    civecs = TEST_DATA_DIR + \"/h2o/civecs-10k.dat\"\n    _, t3_excitations, _ = get_pspace_from_cipsi(civecs, driver.system, nexcit=3)\n\n    driver.run_ccp(method=\"ccsdt_p\", t3_excitations=t3_excitations)\n    driver.run_hbar(method=\"ccsdt_p\", t3_excitations=t3_excitations)\n    driver.run_leftccp(method=\"left_ccsdt_p\", t3_excitations=t3_excitations)\n    driver.run_ccp3(method=\"ccp3\", state_index=0, t3_excitations=t3_excitations)\n```    \n    \n### References\n1. K. Gururangan, J. E. Deustua, J. Shen, and P. Piecuch, J. Chem. Phys. **155**, 174114 (2021) <br />\n(see https://doi.org/10.1063/5.0064400; cf. also https://doi.org/10.48550/arXiv.2107.10994) <br />\n</details>\n\n<details>\n<summary>Adaptive CC(P;Q) aimed at converging CCSDT</summary>\n\n### Summary\n\n### Sample Code\n\n```python3\nimport numpy as np\nfrom pyscf import scf, gto\nfrom ccpy.drivers.driver import Driver\nfrom ccpy.drivers.adaptive import AdaptDriver\n\ndef test_adaptive_f2():\n    geometry = [[\"F\", (0.0, 0.0, -2.66816)], [\"F\", (0.0, 0.0, 2.66816)]]\n    mol = gto.M(\n        atom=geometry,\n        basis=\"cc-pvdz\",\n        charge=0,\n        spin=0,\n        symmetry=\"D2H\",\n        cart=True,\n        unit=\"Bohr\",\n    )\n    mf = scf.RHF(mol)\n    mf.kernel()\n\n    percentages = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]\n    driver = Driver.from_pyscf(mf, nfrozen=2)\n    driver.system.print_info()\n    driver.options[\"RHF_symmetry\"] = False\n    adaptdriver = AdaptDriver(driver, percentage=percentages)\n    adaptdriver.options[\"energy_tolerance\"] = 1.0e-08\n    adaptdriver.options[\"two_body_approx\"] = True\n    adaptdriver.run()\n```\n### References\n\n1. K. Gururangan and P. Piecuch, J. Chem. Phys. **159**, 084108 (2023) <br />\n(see https://doi.org/10.1063/5.0162873; cf. also https://doi.org/10.48550/arXiv.2306.09638) <br />\n</details>\n\n<details>\n<summary>CC4</summary>\n\n### Summary\n<p align=\"justify\">\n</p>\n\n### Sample Code\n\n```python3\n    from pyscf import gto, scf\n    from ccpy.drivers.driver import Driver\n\n    # build molecule using PySCF and run SCF calculation\n    mol = gto.M(\n        atom=[[\"O\", (0.0, 0.0, -0.0180)],\n              [\"H\", (0.0, 3.030526, -2.117796)],\n              [\"H\", (0.0, -3.030526, -2.117796)]],\n        basis=\"cc-pvdz\",\n        charge=0,\n        spin=0,\n        symmetry=\"C2V\",\n        cart=False,\n        unit=\"Bohr\",\n    )\n    mf = scf.RHF(mol)\n    mf.kernel()\n    \n    # get the CCpy driver object using PySCF meanfield\n    driver = Driver.from_pyscf(mf, nfrozen=1)\n\n    # set calculation parameters\n    driver.options[\"energy_convergence\"] = 1.0e-07 # (in hartree)\n    driver.options[\"amp_convergence\"] = 1.0e-07\n    driver.options[\"maximum_iterations\"] = 80\n\n    # run CC4 calculation\n    driver.run_cc(method=\"cc4\")\n```\n### References\n</details>\n\n#### Externally Corrected (ec) CC Approaches\n\n<details>\n<summary>CIPSI-driven ec-CC-II and ec-CC-II<sub>3</sub> </summary>\n\n### Summary\n\n### Sample Code\n\n```python3\nfrom pathlib import Path\nimport numpy as np\nfrom ccpy.drivers.driver import Driver\nfrom ccpy.utilities.pspace import get_pspace_from_cipsi\n\nTEST_DATA_DIR = str(Path(__file__).parents[1].absolute() / \"data\")\n\ndef test_eccc23_h2o():\n\n    driver = Driver.from_gamess(\n        logfile=TEST_DATA_DIR + \"/h2o/h2o-Re.log\",\n        onebody=TEST_DATA_DIR + \"/h2o/onebody.inp\",\n        twobody=TEST_DATA_DIR + \"/h2o/twobody.inp\",\n        nfrozen=0,\n    )\n\n    civecs = TEST_DATA_DIR + \"/h2o/civecs-10k.dat\"\n    _, t3_excitations, _ = get_pspace_from_cipsi(civecs, driver.system, nexcit=3)\n\n    driver.run_eccc(method=\"eccc2\", ci_vectors_file=civecs)\n    driver.run_hbar(method=\"ccsd\")\n    driver.run_leftcc(method=\"left_ccsd\")\n    driver.run_ccp3(method=\"ccp3\", state_index=0, t3_excitations=t3_excitations)\n```    \n    \n### References\n1. I. Magoulas, K. Gururangan, P. Piecuch, J. E. Deustua, and J. Shen, J. Chem. Theory Comput. **17**, 4006 (2021) <br />\n(see https://doi.org/10.1021/acs.jctc.1c00181; cf. also https://doi.org/10.48550/arXiv.2102.10143)\n</details>\n\n#### Approximate Coupled-Pair (ACP) Approaches\n  - ACCD\n  - ACCSD\n  - ACCSDt\n  - ACC(2,3)\n  - ACC(t;3)\n  \n### EOMCC approaches for ground, excited, attached, and ionized states\n  - EOMCCSD\n  - CR-EOMCC(2,3) and its size-intensive *\u03b4*-CR-EOMCC(2,3) extension\n  - EOMCCSD(T)(a)*\n  - EOM-CC3\n  - EOMCCSDt\n  - Excited-state CC(t;3)\n  - Adaptive CC(*P*;*Q*) aimed at converging EOMCCSDT\n  - EOMCCSDT\n  - SF-EOMCCSD\n  - SF-EOMCC(2,3)\n  - IP-EOMCCSD(2h-1p)\n  - IP-EOMCCSD(T)(a)*\n  - Active-space IP-EOMCCSD(3h-2p){N<sub>o</sub>} (also known as IP-EOMCCSDt)\n  - IP-EOMCCSD(3h-2p)\n  - IP-EOMCCSDT\n  - EA-EOMCCSD(2p-1h)\n  - EA-EOMCCSD(T)(a)*\n  - Active-space EA-EOMCCSD(3p-2h){N<sub>u</sub>} (also known as EA-EOMCCSDt)\n  - EA-EOMCCSD(3p-2h)\n  - EA-EOMCCSDT\n  - DEA-EOMCCSD(3p-1h)\n  - DEA-EOMCCSD(4p-2h)\n  - DIP-EOMCCSD(3h-1p)\n  - DIP-EOMCCSD(4h-2p)\n\n<p align=\"justify\">\nBecause CCpy is primarily used for CC method development work, we use interfaces to GAMESS and PySCF to obtain the mean-field (typically Hartree-Fock)\nreference state and associated one- and two-electron integrals in the molecular orbital basis prior to performing the correlated CC calculations. All implementations\nin CCpy are based on the spin-integrated spinorbital formulation and are compatible with RHF and ROHF references. \n</p>\n\n## Installation and Support\n<p align=\"justify\">\n  \nInstallation instructions are provided in the CCpy documentation page (https://piecuch-group.github.io/ccpy/). If you have any questions about CCpy or need additional information about its functionality,\nplease e-mail gururang@msu.edu.\n</p>\n\n## CCpy Development Team\n\nKarthik Gururangan\\\nDoctoral student, Department of Chemistry, Michigan State University  \ne-mail: gururang@msu.edu\\\n(lead developer)\n\nDr. J. Emiliano Deustua\\\nCOO and Co-founder, Examol\\\n(co-developer)\n\nProfessor Piotr Piecuch\\\nUniversity Distinguished Professor and MSU Research Foundation Professor, Department of Chemistry, Michigan State University\\\nAdjunct Professor, Department of Physics and Astronomy, Michigan State University\\\ne-mail: piecuch@chemistry.msu.edu\\\n(co-developer and principal investigator)\n\nAdditional contributors: Tiange Deng (doctoral student, Department of Chemistry, Michigan State University; ACCD and ACCSD options).\n\n## Acknowledgements\n\nWe acknowledge support from the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy \n(Grant No. DE-FG02-01ER15228 to Piotr Piecuch).\n\n<p align=\"justify\">\n  \nCCpy is an open-source code under the [GPLv3](https://www.gnu.org/licenses/gpl-3.0.html) license\ndeveloped and maintained by the [Piecuch Group](https://www2.chemistry.msu.edu/faculty/piecuch/) \nat Michigan State University. \n\n</p>\n",
    "bugtrack_url": null,
    "license": "GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007  Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/> Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed.  Preamble  The GNU General Public License is a free, copyleft license for software and other kinds of works.  The licenses for most software and other practical works are designed to take away your freedom to share and change the works.  By contrast, the GNU General Public License is intended to guarantee your freedom to share and change all versions of a program--to make sure it remains free software for all its users.  We, the Free Software Foundation, use the GNU General Public License for most of our software; it applies also to any other work released this way by its authors.  You can apply it to your programs, too.  When we speak of free software, we are referring to freedom, not price.  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Copyright (C) 2024  Karthik Gururangan  This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.  This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more details.  You should have received a copy of the GNU General Public License along with this program.  If not, see <http://www.gnu.org/licenses/>.  Also add information on how to contact you by electronic and paper mail.  If the program does terminal interaction, make it output a short notice like this when it starts in an interactive mode:  ccpy Copyright (C) 2024  Karthik Gururangan This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details.  The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License.  Of course, your program's commands might be different; for a GUI interface, you would use an \"about box\".  You should also get your employer (if you work as a programmer) or school, if any, to sign a \"copyright disclaimer\" for the program, if necessary. For more information on this, and how to apply and follow the GNU GPL, see <http://www.gnu.org/licenses/>.  The GNU General Public License does not permit incorporating your program into proprietary programs.  If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library.  If this is what you want to do, use the GNU Lesser General Public License instead of this License.  But first, please read <http://www.gnu.org/philosophy/why-not-lgpl.html>. ",
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