# Explicitly Correlated Methods

Several explicitly correlated methods were developed in the Werner Group

We have developed efficient explicitly correlated coupled-cluster [CCSD(T)-F12], multi-reference perturbation theory (CASPT2-F12), and multi-reference configuration interaction (MRCI-F12) methods, which strongly reduce the basis set incompleteness error by including terms that depend explicitly on the interelectronic distances. Extensive benchmarks have shown that with these methods triple-zeta basis sets are sufficient to reach better than quintuple-zeta quality for energetic quantities such as atomization energies, reaction energies, activation and excitation energies, ionization potentials, or electron affinities. Also the accuracy of other molecular properties, e.g. equilibrium structures or vibrational frequencies is significantly improved. We focus especially on combining these approaches with local correlation methods that can be applied to large molecules and to develop new programs to compute analytical energy gradients and response properties using F12 methods.

### Book Chapter:

**H.-J. Werner, C. Köppl, Q. Ma, M. Schwilk***"Explicitly Correlated **Local Electron Correlation Methods" *in:* Fragmentation: Toward Accurate Calculations on Complex Molecular Systems, *edited by Mark S. Gordon (2017)

## Review:

**T. Shiozaki, and H.-J. Werner*** Multireference explicitly correlated F12 theories*

Mol. Phys. 111, 607 (2013)

## Publications:

*Analytical energy gradients for explicitly correlated wave functions. II. Explicitly correlated coupled cluster singles and doubles with perturbative triples corrections: CCSD(T)-F12*

*Analytical energy gradients for explicitly correlated wave functions. I. Explicitly correlated second-order Møller-Plesset perturbation theory*

**Qianli Ma, Hans-Joachim Werner***Scalable Electron Correlation Methods 2: Parallel PNO-LMP2-F12 with Near Linear Scaling in the Molecular Size*

J. Chem. Theory Comput., **11,** 5291–5304 (2015)

**D**** ***Accurate thermochemistry from explicitly correlated distinguishable cluster approximation*

J. Chem. Phys. 142, 064111 (2015)

**D.H. Bross, J.G. Hill, H.-J. Werner, and K.A. Peterson *** Explicitly correlated composite thermochemistry of transition metal species*

J. Chem. Phys. 139, 094302 (2013)

**C. Krause und H.-J. Werner *** Comparison of explicitly correlated local coupled-cluster methods with various choices of virtual orbitals *

Phys. Chem. Chem. Phys. 14, 7591-7604 (2012)

** K.A. Peterson, C. Krause, H. Stoll, J.G. Hill und H.-J. Werner *** Application of explicitly correlated local coupled cluster methods to molecules containing post-3d main group elements *

Mol. Phys. 109, 2607 (2011)

** T.B. Adler and H.-J. Werner *** An explicitly correlated local coupled cluster method for calculations of large molecules close to the basis set limit *

J. Chem. Phys. 135, 144117 (2011)

** T. Shiozaki and H.-J. Werner *** Explicitly correlated multireference configuration interaction with multiple reference functions: Avoided crossings and conical intersections *

J. Chem. Phys. 134, 184104 (2011)

** T. Shiozaki, G. Knizia and H.-J. Werner *** Explicitly correlated multireference configuration interaction: MRCI-F12 *

J. Chem. Phys. 134, 034113 (2011)

** H.-J. Werner, G. Knizia and F.R. Manby *** Explicitly correlated coupled cluster methods with pair-specific geminals *

Mol. Phys. 109, 407 (2011)

**H.-J. Werner, T. B. Adler, G. Knizia, and F. R. Manby** *Efficient explicitly correlated coupled-cluster approximations* (Review)

in *Recent Progress in Coupled Cluster Methods *[Publ.: P. Čársky, J. Paldus, J. Pittner] (Springer, New York, 2010)

** T. Shiozaki and H.-J. Werner *** Communication: Second-order multireference perturbation theory with explicit correlation: CASPT2-F12 *

J. Chem. Phys. 133, 141103 (2010)

** H.-J. Werner, G. Knizia, T.B. Adler and O. Marchetti *** Benchmark Studies for Explicitly Correlated Perturbation- and Coupled Cluster Theories *

Z. Phys. Chem. 224, 493 (2010)

**O. Marchetti and H.-J. Werner***Accurate Calculations of Intermolecular Interaction Energies Using Explicitly Correlated Coupled Cluster Wave Functions and a Dispersion-Weighted MP2 Method *

J. Phys. Chem. A 113, 11580 (2009)

** J.G. Hill, K.A. Peterson, G. Knizia and H.-J. Werner *** Extrapolating MP2 and CCSD explicitly correlated correlation energies to the complete basis set limit with first and second row correlation consistent basis sets *

J. Chem. Phys. 131, 194105 (2009)

** T. B. Adler and H.-J. Werner *** Local explicitly correlated coupled-cluster methods: Efficient removal of the basis set incompleteness and domain errors *

J. Chem. Phys. 130, 241101 (2009)

** T. B. Adler, H.-J. Werner and F. R. Manby *** Local explicitly correlated second-order perturbation theory for the accurate treatment of large molecules *

J. Chem. Phys. 130, 054106 (2009)

** G. Knizia, T. B. Adler and H.-J. Werner *** Simplified CCSD(T)-F12 methods: Theory and benchmarks *

J. Chem. Phys. 130, 054104 (2009)

**O. Marchetti and H.-J. Werner *** Accurate calculations of intermolecular interaction energies using explicitly correlated wave functions *

Phys. Chem. Chem. Phys. 10, 3400 (2008)

** H.-J. Werner *** Eliminating the domain error in local explicitly correlated second-order Møller-Plesset perturbation theory *

J. Chem. Phys. 129, 101103 (2008)

** G. Knizia and H.-J. Werner *** Explicitly correlated RMP2 for high-spin open-shell reference states*

J. Chem. Phys. 128, 154103 (2008)

** K. A. Peterson, T. B. Adler and H.-J. Werner *** Systematically convergent basis sets for explicitly correlated wavefunctions: The atoms H, He, B-Ne, and Al-Ar*

J. Chem. Phys. 128, 084102 (2008)

**T. B. Adler, G. Knizia and H.-J. Werner *** A simple and efficient CCSD(T)-F12 approximation*

J. Chem. Phys. 127, 221106 (2007)

**H.-J. Werner, T. B. Adler and F. R. Manby***General orbital invariant MP2-F12 theory*

J. Chem. Phys. 126, 164102 (2007)

**R. Polly, H.-J. Werner, P. Dahle and P. Taylor***Application of Gaussian-type geminals in local second-order Møller-Plesset perturbation theory*

J. Chem. Phys. 124, 234107 (2006)

**F. R. Manby, H.-J. Werner, T. B. Adler and A. J. May***Explicitly correlated local second-order perturbation theory with a frozen geminal correlation factor*

J. Chem. Phys. 124, 094103 (2006)

**F. R. Manby and H.-J. Werner***Explicitly correlated second-order perturbation theory using density fitting and local approximations*

J. Chem. Phys. 124, 054114 (2006)

### Benchmarks and applications

** P. Botschwina, R. Oswald, G. Knizia and H.-J. Werner *** High-level ab initio calculations for astrochemically relevant polyynes (HC _{2n}H),their isomers (C_{2n}H_{2}) and their anions (C_{2n}H^{-}) *

Z. Phys. Chem. 223, 447 (2009)

** G. Rauhut, G. Knizia and H.-J. Werner *** Accurate calculation of vibrational frequencies using explicitly correlated coupled-cluster theory *

J. Chem. Phys. 130, 054105 (2009)

** O. Marchetti and H.-J. Werner *** Accurate calculations of intermolecular interaction energies using explicitly correlated wave functions *

Phys. Chem. Chem. Phys. 10, 3400 (2008)

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