# Introduction to Molpro

Molpro is a complete system of ab initio programs for molecular electronic structure calculations, designed and maintained by H.-J. Werner and P. J. Knowles, and containing contributions from a number of other authors. As distinct from other commonly used quantum chemistry packages, the emphasis is on highly accurate computations, with extensive treatment of the electron correlation problem through the multiconfiguration-reference CI, coupled cluster and associated methods. The recently developed explicitly correlated coupled-cluster methods yield CCSD(T) results with near basis set limit accuracy already with double$-\zeta$ or triple$-\zeta$ basis sets, thus reducing the computational effort for calculations of this quality by two orders of magnitude. Using local electron correlation methods, which significantly reduce the increase of the computational cost with molecular size, accurate ab initio calculations can be performed for much larger molecules than with most other programs. These methods have recently been augmented by explicitly correlated terms, which strongly reduce both the basis set truncation errors and the errors of the local approximations.

The heart of the program consists of the multiconfiguration SCF, multireference CI, and coupled-cluster routines, and these are accompanied by a full set of supporting features. The package comprises

• Integral generation for generally contracted symmetry adapted gaussian basis functions ($spdfghi$). There are two programs with identical functionality: the preferred code is Seward (R. Lindh) which is the best on most machines; Argos (R. M. Pitzer) is available as an alternative, and in some cases is optimum for small memory scalar machines. Also two different gradient integral codes, namely Cadpac (R. Amos) and Alaska (R. Lindh) are available. Only the latter allows the use of generally contracted symmetry adapted gaussian basis functions.
• Effective Core Potentials (contributions from H. Stoll).
• Many one-electron properties.
• Some two-electron properties, e.g. $L_x^2$, $L_y^2$, $L_z^2$, $L_xL_y$ etc..
• Closed-shell and open-shell (spin restricted and unrestricted) self consistent field.
• Density-functional theory in the Kohn-Sham framework with various gradient corrected exchange and correlation potentials.
• Multiconfiguration self consistent field. This is the quadratically convergent MCSCF procedure described in J. Chem. Phys. 82, 5053 (1985). The program can optimize a weighted energy average of several states, and is capable of treating both completely general configuration expansions and also long CASSCF expansions as described in Chem. Phys. Lett. 115, 259 (1985).
• Multireference perturbation theory (MRPT2, CASPT2, CASPT3), including (extended) multi-state methods MS-CASPT2 and XMS-CASPT2 as described in Mol. Phys. 89, 645 (1996), J. Chem. Phys. 112, 5546 (2000), J. Chem. Phys. 135, 081106 (2011).
• Multireference CI. As well as the usual single reference function approaches (MP2, SDCI, CEPA), this module implements the internally contracted multireference CI method as described in J. Chem. Phys. 89, 5803 (1988) and Chem. Phys. Lett. 145, 514 (1988). Non variational variants (e.g. MR-ACPF), as described in Theor. Chim. Acta 78 (1990) 175, are also available. Electronically excited states can be computed as described in Theor. Chim. Acta, 84 95 (1992). A new more efficient MRCI implementation is described in J. Chem. Phys. 135, 054101 (2011).
• Møller-Plesset perturbation theory (MPPT), Coupled-Cluster (CCSD), Quadratic configuration interaction (QCISD), and Brueckner Coupled-Cluster (BCCD) for closed shell systems, as described in Chem. Phys. Lett. 190, 1 (1992). Perturbative corrections for triple excitations can also be calculated (Chem. Phys. Lett. 227, 321 (1994)).
• Open-shell coupled cluster theories as described in J. Chem. Phys. 99, 5219 (1993), Chem. Phys. Lett. 227, 321 (1994).
• An interface to the MRCC program of M. Kallay, allowing coupled-cluster calculations with arbitrary excitation level.
• Full Configuration Interaction. This is the determinant based benchmarking program described in Comp. Phys. Commun. 54 (1989) 75.
• Analytical energy gradients for SCF, DFT, state-averaged MCSCF/CASSCF, MRPT2/CASPT2, MP2, QCISD(T), and CCSD(T) methods.
• Analytical non-adiabatic coupling matrix elements for MCSCF.
• Valence-Bond analysis of CASSCF wavefunction, and energy-optimized valence bond wavefunctions as described in Int. J. Quant. Chem. 65, 439 (1997).
• One-electron transition properties for MCSCF, MRCI, and EOM-CCSD wavefunctions, CASSCF and MRCI transition properties also between wavefunctions with different orbitals, as described in Mol. Phys. 105, 1239, (2007).
• Spin-orbit coupling, as described in Mol. Phys. 98, 1823 (2000). More recently, a new spin-orbit integral program for generally contracted basis sets has been implemented.
• Douglas-Kroll-Hess Hamiltonian up to arbitrary order and the eXact-2-Component (X2C) Hamiltonian.
• Density-functional theory symmetry-adapted intermolecular perturbation theory (with density fitting), DFT-SAPT , as described in J. Chem. Phys. 122, 014103 (2005).
• Some two-electron transition properties for MCSCF wavefunctions (e.g., $L_x^2$ etc.).
• Mulliken population analysis and Natural Population Analysis (NPA)
• Orbital localization.
• Natural bond orbitals (NBOs).
• Distributed Multipole Analysis (A. J. Stone).
• Automatic geometry optimization as described in J. Comp. Chem. 18, (1997), 1473. Constrained optimization is also possible.
• Automatic calculation of vibrational frequencies, intensities, and thermodynamic properties.
• Reaction path following, as described in Theor. Chem. Acc. 100, (1998), 21.
• Efficient facilities to treat large lattices of point charges for QM/MM calculations, including lattice gradients.
• Various utilities allowing other more general optimizations, looping and branching (e.g., for automatic generation of complete potential energy surfaces), general housekeeping operations.
• Geometry output in XYZ, MOLDEN and Gaussian formats; molecular orbital and frequency output in MOLDEN format.
• Integral-direct implementation of all Hartree-Fock, DFT and pair-correlated methods (MP, CCSD, MRCI etc.), as described in Mol. Phys., 96, (1999), 719. At present, perturbative triple excitation methods are not implemented.
• Local second-order Møller-Plesset perturbation theory (LMP2) and local coupled cluster methods, as described in in J. Chem. Phys. 104, 6286 (1996), Chem. Phys. Lett. 290, 143 (1998), J. Chem. Phys. 111, 5691 (1999), J. Chem. Phys. 113, 9443 (2000), J. Chem. Phys. 113, 9986 (2000), Chem. Phys. Lett. 318, 370 (2000), J. Chem. Phys. 114, 661 (2001), Phys. Chem. Chem. Phys. 4, 3941 (2002), J. Chem. Phys. 116, 8772 (2002).
• Local density fitting methods, as described in J. Chem. Phys. 118, 8149 (2003), Phys. Chem. Chem. Phys. 5, 3349 (2003), Mol. Phys. 102, 2311 (2004).
• Analytical energy gradients for LMP2, DF-LMP2, and LQCISD as described in J. Chem. Phys. 108, 5185, (1998), Phys. Chem. Chem. Phys. 3, 4853 (2001), J. Chem. Phys. 121, 737 (2004).
• Analytical energy gradients for CASSCF, CASPT2, MS-CASPT2, and XMS-CASPT2 as described in J. Chem. Phys. 119, 5044 (2003), J. Chem. Phys. 135, 081106 (2011), J. Chem. Phys. 138, 104104 (2013).
• Explicitly correlated MP2-F12 and CCSD(T)-F12 methods, as described in J. Chem. Phys. 119, 4607 (2003), J. Chem. Phys. 121, 4479 (2004), J. Chem. Phys. 124, 054114 (2006), J. Chem. Phys. 124, 094103 (2006), J. Chem. Phys. 127, 221106 (2007), J. Chem. Phys. 130, 054104 (2009).
• Explicitly correlated local LMP2-F12 and LCCSD(T)-F12 methods, as described in J. Chem. Phys. 129, 101103 (2009), J. Chem. Phys. 130, 054106 (2009), J. Chem. Phys. 130, 241101 (2009), J. Chem. Phys. 135, 144117 (2011), Phys. Chem. Chem. Phys. 14, 7591 (2012).
• Explicitly correlated multireference methods (CASPT2-F12, MRCI-F12), as described in J. Chem. Phys. 133, 141103 (2010), J. Chem. Phys. 134, 034113 (2011), J. Chem. Phys. 134, 184104 (2011), Mol. Phys. 111, 607 (2013).
• Analytical energy gradients for explicitly correlated methods (DF-MP2-F12, DF-CCSD(T)-F12), as described in J. Chem. Phys. 147, 214101 (2017), J. Chem. Phys. 148, xxxxxx (2018).
• Parallel execution on distributed memory machines, as described in J. Comp. Chem. 19, (1998), 1215. At present, SCF, DFT, MRCI, MP2, LMP2, CCSD(T), LCCSD(T) energies and SCF, DFT gradients are parallelized. Most density fitted codes such as DF-HF, DF-KS, DF-LMP2, DF-LMP2 gradients, DF-LCCSD(T), DF-MP2-F12, DF-DFT-SAPT, and GIAO-DF-HF NMR shieldings are also parallelized.
• Automatic embarrassingly parallel computation of numerical gradients and Hessians (mppx Version).

The program is written mostly in standard Fortran–90. Those parts which are machine dependent are maintained through the use of a supplied preprocessor, which allows easy interconversion between versions for different machines. Each release of the program is ported and tested on a number of systems. A large library of commonly used orbital basis sets is available, which can be extended as required. There is a comprehensive online users’ manual, which includes installation instructions.

More recent methods and enhancements include:

1. Explicitly correlated MP2-F12 (closed-shell) and RMP2-F12 (open-shell) methods with many many different ansätze, as described in H.-J. Werner, T. B. Adler, and F. R. Manby, J. Chem. Phys. 126, 164102 (2007) and G. Knizia and H.-J. Werner, J. Chem. Phys. 128, 154103 (2008).
2. Explicitly correlated CCSD(T)-F12 methods as described in T. B. Adler, G. Knizia, and H.-J. Werner, J. Chem. Phys. 127, 221106 (2007) (closed-shell) and G. Knizia, T. B. Adler, and H.-J. Werner, J. Chem. Phys. 130, 054104 (2009) (open-shell).
3. Explicitly correlated LMP2-F12 and LCCSD-F12 methods as described in H.-J. Werner, J. Chem. Phys. 129, 101103 (2009), T. B. Adler, H.-J. Werner, and F. R. Manby, J. Chem. Phys. 130, 054106 (2009), and T. B. Adler and H.-J. Werner, J. Chem. Phys. 130, 241101 (2009).
4. Natural localized orbitals, NPA and NBO analysis and improved methods for domain selection in local correlation calculations as described in R. A. Mata and H.-J. Werner, Mol. Phys. 105, 2753 (2007); see also R. A. Mata and H.-J. Werner, J. Chem. Phys. 125, 184110 (2006).
5. Correlation regions in local correlation calculations as described in R. A. Mata, H.-J. Werner and M. Schütz, J. Chem. Phys. 128, 144106 (2008).
6. Beyond LMP2 treatment of intermolecular pairs in local coupled cluster methods as described in O. Masur, D. Usvyat and M. Schütz, J. Chem. Phys. 139, 164116 (2013), M. Schütz, O. Masur and D. Usvyat, J. Chem. Phys. 140, 244107 (2014).
7. Automated calculation of anharmonic vibrational frequencies and zero-point energies using VCI methods as described in T. Hrenar, H.-J. Werner, and G. Rauhut, J. Chem. Phys. 126, 134108 (2007) and references therein.
8. Dynamical state weighting as described in M. P. Deskevich and D. J. Nesbitt, and H.-J. Werner, J. Chem. Phys. 120, 7281 (2004).
9. Coupling of DFT and coupled cluster methods as described in E. Goll, T. Leininger, F. R. Manby, A. Mitrushchenkov, H.-J. Werner, and H. Stoll, Phys. Chem. Chem. Phys. 10, 3353 (2008) and references therein.
10. NMR chemical shifts, magnetizability, and rotational g-tensor using London atomic orbitals for density-fitted Hartree-Fock, and local MP2, as described in S. Loibl, F.R. Manby, M. Schütz, Mol. Phys. 108, 1362 (2010), S. Loibl, M. Schütz, J. Chem. Phys. 137, 084107 (2012), and S. Loibl and M. Schütz, J. Chem. Phys. 141, 024108 (2014).
11. Local response methods (LCC2) for computing excitation energies and transition properties in large molecule as described in D. Kats, T. Korona, M. Schütz, J. Chem. Phys. 125, 104106 (2006), D. Kats, T. Korona, M. Schütz, J. Chem. Phys. 127, 064107 (2007), D. Kats, M. Schütz, J. Chem. Phys. 131, 124117 (2009), and K. Freundorfer, D. Kats, T. Korona, M. Schütz, J. Chem. Phys. 133, 244110 (2010).
12. LCC2 response and LADC(2) orbital relaxed properties and analytical nuclear gradients as described in K. Ledermüller, D.Kats and M. Schütz, J. Chem. Phys. 139, 084111 (2013), K. Ledermüller and M. Schütz, J. Chem. Phys. 140, 164113 (2014), M. Schütz, J. Chem. Phys. 142, 214103 (2015).
13. Automatic basis set extrapolation.
14. Enhanced connections to other programs, including graphical display of output and 3-dimensional structures.
15. Support for Mac OS X
16. Ring-polymer instanton methods for rate and tunnelling-splitting calculations, as described in J. O. Richardson and S. C. Althorpe, J. Chem. Phys. 131, 214106 (2009), and ibid. 134, 054109 (2011).
17. Full Configuration Interation Quantum Monte Carlo (FCIQMC) as described in G. H. Booth, A. J. W. Thom, and A. Alavi, J. Chem. Phys. 131, 054106 (2009), D. M. Cleland, G. H. Booth, and A. Alavi, J. Chem. Phys. 134, 024112 (2011), and G. H. Booth, D. M. Cleland, A. J. W. Thom, and A. Alavi, J. Chem. Phys. 135, 084104 (2011).

Future enhancements presently under development include

• Analytic second derivatives for DFT.
• New, more efficient MRCI methods for larger molecules.

These features will be included in the base version at later stages. The above list is for information only, and no representation is made that any of the above will be available within any particular time.