Molpro (available at http://www.molpro.net) is a general-purpose quantum chemical program. The original focus was on high-accuracy wave function calculations for small molecules, but using local approximations combined with explicit correlation treatments, highly accurate coupled-cluster calculations are now possible for molecules with up to approximately 100 atoms. Recently, multireference correlation treatments were also made applicable to larger molecules. Furthermore, an efficient implementation of density functional theory is available.

Molpro: a general-purpose quantum chemistry program package

In this contribution to the special software-centered issue, the ORCA program package is described. We start with a short historical perspective of how the project began and go on to discuss its current feature set. ORCA has grown into a rather comprehensive general-purpose package for theoretical research in all areas of chemistry and many neighboring disciplines such as materials sciences and biochemistry. ORCA features density functional theory, a range of wavefunction based correlation methods, semi-empirical methods, and even force-field methods. A range of solvation and embedding models is featured as well as a complete intrinsic to ORCA quantum mechanics/molecular mechanics engine. A specialty of ORCA always has been a focus on transition metals and spectroscopy as well as a focus on applicability of the implemented methods to "real-life" chemical applications involving systems with a few hundred atoms. In addition to being efficient, user friendly, and, to the largest extent possible, platform independent, ORCA features a number of methods that are either unique to ORCA or have been first implemented in the course of the ORCA development. Next to a range of spectroscopic and magnetic properties, the linear- or low-order single- and multi-reference local correlation methods based on pair natural orbitals (domain based local pair natural orbital methods) should be mentioned here. Consequently, ORCA is a widely used program in various areas of chemistry and spectroscopy with a current user base of over 22 000 registered users in academic research and in industry.

The ORCA quantum chemistry program package

Combined quantum-mechanics/molecular-mechanics (QM/MM) approaches have become the method of choice for modeling reactions in biomolecular systems. Quantum-mechanical (QM) methods are required for describing chemical reactions and other electronic processes, such as charge transfer or electronic excitation. However, QM methods are restricted to systems of up to a few hundred atoms. However, the size and conformational complexity of biopolymers calls for methods capable of treating up to several 100,000 atoms and allowing for simulations over time scales of tens of nanoseconds. This is achieved by highly efficient, force-field-based molecular mechanics (MM) methods. Thus to model large biomolecules the logical approach is to combine the two techniques and to use a QM method for the chemically active region (e.g., substrates and co-factors in an enzymatic reaction) and an MM treatment for the surroundings (e.g., protein and solvent). The resulting schemes are commonly referred to as combined or hybrid QM/MM methods. They enable the modeling of reactive biomolecular systems at a reasonable computational effort while providing the necessary accuracy.

QM/MM Methods for Biomolecular Systems

The simple and efficient CCSD(T)-F12x approximations (x = a,b) we proposed in a recent communication [T. B. Adler, G. Knizia, and H.-J. Werner, J. Chem. Phys. 127, 221106 (2007)] are explained in more detail and extended to open-shell systems. Extensive benchmark calculations are presented, which demonstrate great improvements in basis set convergence for a wide variety of applications. These include reaction energies of both open- and closed-shell reactions, atomization energies, electron affinities, ionization potentials, equilibrium geometries, and harmonic vibrational frequencies. For all these quantities, results better than the AV5Z quality are obtained already with AVTZ basis sets, and usually AVDZ treatments reach at least the conventional AVQZ quality. For larger molecules, the additional cost for these improvements is only a few percent of the time for a standard CCSD(T) calculation. For the first time ever, total reaction energies with chemical accuracy are obtained using valence-double-zeta basis sets.

Simplified CCSD(T)-F12 methods: Theory and benchmarks

A simple modification of second-order Moller–Plesset perturbation theory (MP2) to improve the description of molecular ground state energies is proposed. The total MP2 correlation energy is partitioned into parallel- and antiparallel-spin components which are separately scaled. The two parameters (scaling factors), whose values can be justified by basic theoretical arguments, have been optimized on a benchmark set of 51 reaction energies composed of 74 first-row molecules. It is found, that the new method performs significantly better than standard MP2: the rms [mean absolute error (MAE)] deviation drops from 4.6 (3.3) to 2.3 (1.8) kcal/mol. The maximum error is reduced from 13.3 to 5.1 kcal/mol. Significant improvements are especially observed for cases which are usually known as MP2 pitfalls while cases already described well with MP2 remain almost unchanged. Even for 11 atomization energies not considered in the fit, uniform improvements [MAE: 8.1 kcal/mol (MP2) versus 3.2 kcal/mol (new)] are found. The results are furthermore compared with those from density functional theory (DFT/B3LYP) and quadratic configuration interaction [QCISD/QCISD(T)] calculations. Also for difficult systems including strong (nondynamical) correlation effects, the improved MP2 method clearly outperforms DFT/B3LYP and yields results of QCISD or sometimes QCISD(T) quality. Preliminary calculations of the equilibrium bond lengths and harmonic vibrational frequencies for ten diatomic molecules also show consistent enhancements. The uniformity with which the new method improves upon MP2, thereby rectifying many of its problems, indicates significant robustness and suggests it as a valuable quantum chemical method of general use.

Improved second-order Møller–Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies

A new implementation of local second-order Mo/ller-Plesset perturbation theory (LMP2) is presented for which asymptotically all computational resources (CPU, memory, and disk) scale only linearly with the molecular size. This is achieved by (i) using orbital domains for each electron pair that are independent of molecular size; (ii) classifying the pairs according to a distance criterion and neglecting very distant pairs; (iii) treating distant pairs by a multipole approximation, and (iv) using efficient prescreening algorithms in the integral transformation. The errors caused by the various approximations are negligible. LMP2 calculations on molecules including up to 500 correlated electrons and over 1500 basis functions in C1 symmetry are reported, all carried out on a single low-cost personal computer.

Low-order scaling local electron correlation methods. I. Linear scaling local MP2

Trajectory attractors of energy balance climate models with bio-feedback and latent energy flux

Multipole approximation of distant pair energies in local MP2 calculations

A novel multipole approximation for the linear scaling local second-order Moller–Plesset perturbation theory (MP2) method is presented, which is based on a splitting of the Coulomb operator into two terms. The first one contains the singularity and is rapidly decaying with increasing distance. It is treated by a conventional two-electron transformation, where the rapid decay leads to significant savings. The second term is long range, but nonsingular and can therefore be approximated by a multipole expansion. Reliability, accuracy, and efficiency of this method are demonstrated by an extensive benchmark study. It is shown that the goal to further improve the efficiency of the existing linear scaling local MP2 algorithm has been achieved. Moreover, the new method is a promising starting point for future developments, such as coupling of MP2 with density functional theory.

Low-order scaling local correlation methods II: Splitting the Coulomb operator in linear scaling local second-order Møller–Plesset perturbation theory

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Low-order scaling local electron correlation methods. I. Linear scaling local MP2

Trajectory attractors of energy balance climate models with bio-feedback and latent energy flux

Multipole approximation of distant pair energies in local MP2 calculations

Low-order scaling local correlation methods II: Splitting the Coulomb operator in linear scaling local second-order Møller–Plesset perturbation theory