1 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. Using recently developed integral-direct 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.

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 (1985) 5053. 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. Letters 115 (1985) 259.
• 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 (1988) 5803 and Chem. Phys. Lett. 145 (1988) 514. 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).

• Multireference second-order and third-order perturbation theory (MR-PT2, MR-PT3) as described in Mol. Phys. 89, 645 (1996) and J. Chem. Phys. 112, 5546 (2000).

• 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 (1992) 1. Perturbative corrections for triple excitations can also be calculated (Chem. Phys. Letters 227 (1994) 321).

• Open-shell coupled cluster theories as described in J. Chem. Phys. 99 (1993) 5219, Chem. Phys. Letters 227 (1994) 321.

• 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 and QCISD(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.

• Spin-orbit coupling, as described in Mol. Phys., 98, 1823 (2000).

• Some two-electron transition properties for MCSCF wavefunctions (e.g., $L_x^2$ etc.).
• Population analysis.
• Orbital localization.
• Distributed Multipole Analysis (A. J. Stone).

• Automatic geometry optimization as described in J. Comp. Chem. 18, (1997), 1473.

• Automatic calculation of vibrational frequencies, intensities, and thermodynamic properties.

• Reaction path following, as described in Theor. Chem. Acc. 100, (1998), 21.

• 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. Letters 318, 370 (2000), J. Chem. Phys. 114, 661 (2001), Phys. Chem. Chem. Phys. 4, 3941 (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 and DF-LMP2, as described in J. Chem. Phys. 108, 5185, (1998), J. Chem. Phys. 121, 737 (2004).

• Explicit correlation 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).

• Parallel execution on distributed memory machines, as described in J. Comp. Chem. 19, (1998), 1215. At present, SCF, DFT, MRCI, MP2, LMP2, CCSD(T) energies and SCF, DFT gradients are parallelized when running with conventional integral evaluation; integral-direct and density fitted SCF, DFT, LMP2, and LCCSD(T) are also parallel.

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 IBM RS/6000, Hewlett-Packard, Silicon Graphics, Compaq, and Linux systems. A fuller description of the hardware and operating systems of these machines can be found at http://www.molpro.net/supported. The program additionally runs on Cray, Sun, Convex, Fujitsu and NEC SX4 platforms, as well as older architectures and/or operating systems from the primary list; however, testing is not carried out regularly on these systems, and hand-tuning of code may be necessary on porting. A large library of commonly used orbital basis sets is available, which can be extended as required. There is a comprehensive users' manual, which includes installation instructions. The manual is available in PostScript, PDF and also in HTML for mounting on a Worldwide Web server.

New methods and enhancements in Version 2006.1 include:

1. More consistent input language and input pre-checking.
2. More flexible basis input, allowing to handle multiple basis sets.
3. New more efficient density functional implementation, additional density functionals.
4. Low-order scaling local coupled cluster methods with perturbative treatment of triples excitations (LCCSD(T) and variants like LQCISD(T))
5. Efficient density fitting (DF) programs for Hartree-Fock (DF-HF), Density functional Kohn-Sham theory (DF-KS), Second-order Møller-Plesset perturbation theory (DF-MP2), as well as for all local methods (DF-LMP2, DF-LMP4, DF-LQCISD(T), DF-LCCSD(T))
6. Analytical QCISD(T) gradients
7. Analytical MRPT2 (CASPT2) and multi-state CASPT2 gradients, using state averaged MCSCF reference functions
8. Analytical DF-HF, DF-KS, DF-LMP2, and DF-SCS-LMP2 gradients
9. Explicitly correlated methods with density fitting: DF-MP2-R12/2A', DF-MP2-F12/2A' as well as the local variants DF-LMP2-R12/2*A(loc) and DF-LMP2-F12/2*A(loc).
10. Multi-state MRPT2, MS-CASPT2
11. Coupling of multi-reference perturbation theory and configuration interaction (CIPT2)
12. DFT-SAPT
13. Transition moments and transition Hamiltonian between CASSCF and MRCI wavefunctions with different orbitals.
14. Douglas-Kroll-Hess Hamiltonian up to arbitrary order.
15. A new spin-orbit integral program for generally contracted basis sets.
16. Improved procedures for geometry optimization and numerical Hessian calculations, including constrained optimization.
17. Improved facilities to treat large lattices of point charges for QM/MM calculations, including lattice gradients.
18. An interface to the MRCC program of M. Kallay, allowing coupled-cluster calculations with arbitrary excitation level.
19. Automatic embarrassingly parallel computation of numerical gradients and Hessians (mppx Version).
20. Additional parallel codes, e.g. DF-HF, DF-KS, DF-LCCSD(T) (partly, including triples).

Future enhancements presently under development include

• Automatic calculation of anharmonic vibrational spectra using vibrational CI.
• Coupling of DFT and coupled cluster methods.
• Open-shell local coupled cluster methods.
• Explicitly correlated local coupled cluster methods.
• Local response methods (CC2, EOM-CCSD) for computing excitation energies and transition properties in large molecules.
• Analytical energy gradients for CCSD(T)
• Analytic second derivatives for DFT

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.