We are a theoretical and computational chemistry group. We use the methods of quantum mechanics and powerful computers to study the properties of molecules and clusters. In particular, we are interested in weak intermolecular interactions and the methods that can be used to calculate the interaction energy accurately and efficiently.

Please see the Research tab for a more detailed description. If you have any questions, do not hesitate to contact Dr.McKee directly.

Introduction

1. Intermolecular interactions



    Intermolecular interactions are everywhere.  A network of intermolecular hydrogen bonds determines the properties of liquid water and aqueous solutions.  Hydrogen bonds as well as other effects (like stacking interactions of aromatic side chains) govern the structure of proteins and the catalytic abilities of enzymes.  Even the least reactive species like rare gas atoms exhibit weak mutual attraction due to a phenomenon called dispersion.  In fact, this attraction is the very reason why rare gases form liquids and solids at low temperatures.
    In a computational study of the interaction between two atoms or molecules, the key quantity is the potential energy surface (PES).  This surface represents the electronic interaction energy of the dimer as a function of the intermonomer distance and of the relative orientation of monomers.  Once the PES is known, we can calculate various quantities (spectra, virial coefficients, liquid and crystal parameters) that can be compared to experimental predictions.


2. Interaction energy from ab initio calculations



   The interaction energy at a given geometry is usually calculated in the so-called supermolecular manner: you pick your favorite quantum-chemistry electronic-structure theory, compute the energy of the dimer AB, and subtract the energies of monomers A and B.  This subtraction can be tricky - the result is orders of magnitude smaller than the energies you subtract (it is like weighing a person by placing her on a large, fully loaded ship, and weighing the ship with and without her).  Moreover, the result of the subtraction (a single number) does not really tell much about the underlying physics of the interaction.  A useful alternative to the supermolecular approach is provided by symmetry-adapted perturbation theory (SAPT) where the interaction energy is calculated directly (no subtraction) as a sum of low-order terms in a perturbation series.  Each of these terms has a clear physical interpretation and corresponds to an electrostatic, induction, dispersion, or exchange effect.  The supermolecular and SAPT methods nicely complement each other and it is often useful to employ both approaches (as well as several different electronic-structure methods) to construct and interpret accurate PESs.  Obviously, the larger the dimer, the more approximate methods have to be used.  More accurate approaches tend to scale steeply with the system size and require a lot of CPU time and memory even on powerful supercomputers.

3. SAPT: What's in the name?



SAPT is a perturbation theory. Perturbation theory is a way of obtaining an approximate solution to a hard problem if we know an exact solution to a problem that is similar but easier. In the case of SAPT, the easier problem is the electronic Schrödinger equation for two molecules that do not interact, and the hard problem is the same equation with the intermolecular interactions (the Coulomb attractions and repulsions between the nuclei and electrons of molecule A with those of molecule B) switched on. If the interactions are relatively weak, we can expect that the energies of the system will not change a lot between the two cases, and that the change in energy can be expanded in a power series (with terms that are linear, quadratic, cubic, ... with respect to the strength of the interaction).

SAPT involves symmetry adaptation. Quantum mechanics requires the wave function of a many-electron system to be antisymmetric with respect to interchanges between electrons. That is, our big and complicated wave function of two molecules (that depends on the positions of all electrons) must change its sign when the position of electron k is substituted for the position of electron l and vice versa. The antisymmetry of the wave function is the reason for the Pauli principle - no more than two electrons can occupy each orbital. In SAPT, the solution to the easier problem (no interaction) is less antisymmetric than the solutions to the hard problem (with interaction) has to be, so the wave function has to be adapted to this additional (anti)symmetry. There are different ways of performing symmetry adaptation that lead to different variants of SAPT.

4. SAPT in practice: variants and implementations



Well, we have to admit it: the problem of solving the electronic Schrödinger equation for two noninteracting molecules might be easier than the same problem when the molecules do interact, but it is by no means easy. In fact, apart from some very simple systems like He₂, we cannot describe the intramonomer electron correlation (the correlation between motions of electrons within each of the interacting molecules) in an exact way - we have to make approximations. All the SAPT approaches that are implemented for general interacting molecules (not just particularly simple cases like hydrogen or helium atoms) treat the intramonomer correlation in one of the approximate ways. The possible choices are

• SAPT(0) - monomers are described by the Hartree-Fock theory. No intramonomer correlation is included at all. This approach might give a useful general picture of the interaction but it is not accurate enough for quantitative studies.
• many-body SAPT - the intramonomer correlation is taken into account via a second perturbation theory (the energy is expanded in a two-dimensional power series) like in the popular Moller-Plesset perturbation theory (MP2, MP4, ...). This approach can lead to very accurate interaction energies but the calculations are quite computationally demanding. At the standard level of theory, the many-body SAPT computation scales like the seventh power of the system size, just like for the CCSD(T) method.
• SAPT(CC) - a newly developed method where the SAPT corrections are expressed through monomer properties calculated from the coupled-cluster theory (CCSD). This approach is even more accurate, and even more computationally demanding, than many-body SAPT.
• SAPT(DFT) (also known as DFT-SAPT) - the intramonomer correlation effects are accounted for by density functional theory (DFT). This method can match the accuracy of many-body SAPT at a fraction of its computational cost. SAPT(DFT) has been applied to systems as large as the coronene dimer (C₂₄H₁₂)₂ and a hydrogen molecule inside the C₆₀ fullerene.

Research in our group - specific topics

1. Towards general open-shell SAPT and SAPT(DFT)



We are working on the extension of the SAPT(0) and SAPT(DFT) formalism to the general open-shell case, including dimers of low-spin monomers which cannot be described by any single-determinantal wave function (we say that these monomers have a truly multireference character). So far, the SAPT and SAPT(DFT) methodology has been established and implemented for closed-shell systems and extended in the case of high-spin open-shell monomers (those that can be described by a single Slater determinant). The derivation of a multireference SAPT theory, with monomers described by the complete-active-space self-consistent field (CASSCF) method, employs and extends the ideas that have led to the development of CASSCF-based many-body perturbation theory (CASPT2, CASPT3), CASSCF linear response functions, and exchange corrections within standard SAPT utilizing a so-called single exchange approximation. The development of open-shell SAPT and SAPT(DFT) is motivated by a need for reliable and physically interpretable interaction energies for open-shell systems like transition-metal atoms and complexes, as well as radicals involved in various chemical and biochemical processes.

2. Accurate ab initio description of physisorption



Physisorption is the binding of molecules to surfaces that occurs as a result of weak intermolecular interactions, unlike the chemisorption process where the adsorbate is attached to the surface by a covalent bond. The weak binding between the surface and the physisorbed molecule is typically due to dispersion interactions. Dispersion is a purely quantum-mechanical phenomenon that involves a correlation between fluctuating dipole moments induced on both monomers. It is responsible, among others, for the attractive interactions between nonpolar systems ranging from rare gas atoms to aromatic rings.

A standard method of choice for studying medium-sized systems, the density functional theory, fails miserably for physisorption because of its inherent inability to account for dispersion interactions in a consistent way. Numerous studies have been directed at correcting this deficiency of DFT and significant progress was achieved in this field in recent years. This progress has driven a new wave of physisorption studies that employ novel dispersion-corrected variants of DFT - an emerging and promising direction of research.

With extensive previous experience in both wave function theory and dispersion-corrected DFT, our group is well qualified for pushing the description of physisorption to a new level of accuracy and understanding. In our opinion, the most complete picture can be obtained by a combination of accurate wave function calculations for small model systems and dispersion-corrected density functional theory for a larger fragment of the surface. Among the available novel DFT methods, the "dispersionless density functional" approach, co-developed by our group leader, is the method of first choice due to the unambiguous distinction between dispersion and the rest of the interaction energy.

A classic example of a system bound by physisorption are molecules (hydrogen, water, alkanes, ...) attached to a graphite surface or to a graphene sheet. With the curvature of the surface taken into account, the adsorption on inner and outer walls of carbon nanotubes can also be described. Molecules adsorbed on quartz and metallic oxide surfaces are another class of technologically important systems to be studied.

3. Ultra-accurate potentials and properties of small dimers and trimers



When the standard supermolecular CCSD(T) theory with large basis sets and complete basis set extrapolation usually gives interaction energies accurate to about 1-2%, is there any point to go beyond this accuracy? Quite often, there is.

First of all, there are systems for which CCSD(T) is not nearly as accurate. For example, for the beryllium dimer the CCSD(T) interaction energy is in error by more than 20% - the reason is the near-degenerate character of the beryllium atom.

Even when CCSD(T) is as accurate as usual, some applications of intermolecular potentials demand an even higher accuracy, and some quantities, most notably those associated with scattering processes, are extremely sensitive to the quality of the potential. For two interacting helium atoms, the needs of the metrology community (a task of establishing new, improved temperature and pressure standards) have called for, and received, an interaction potential that is accurate to 100 ppm.

Last but not least, experimental measurements provide, together with any measured value, an estimate of its uncertainty. Can we theorists do the same? Obtaining an estimated uncertainty of an ab initio result is not an easy task and has to include contributions due to the inexactness of the theory employed (have we managed to do FCI? CCSDTQ? CCSDT?), the incompleteness of the basis set (how well do extrapolated and nonextrapolated results converge?), and the effects that have been neglected or approximated (relativistic effects? core-core and core-valence correlation?) Estimating the theoretical uncertainties calls for a well-designed set of high-level ab initio calculations.

24. Patkowski, K.; Szalewicz, K. "Argon pair potential at basis set and excitation limits" J. Chem. Phys., 2010, 133, 094304.

23. Patkowski, K.; Szalewicz, K.; Jeziorski, B. "Orbital relaxation and the third-order induction energy in symmetry-adapted perturbation theory" Theor. Chem. Acc., 2010, 127, 211.

22. Podeszwa, R.; Patkowski, K.; Szalewicz, K. "Improved interaction energy benchmarks for dimers of biological relevance" Phys. Chem. Chem. Phys., 2010, 12, 5974.

21. Podeszwa, R.; Pernal, K.; Patkowski, K.; Szalewicz, K. "Extension of the Hartree-Fock plus dispersion method by first-order correlation effects" J. Phys. Chem. Lett., 2010, 1, 550.

20. Pernal, K.; Podeszwa, R.; Patkowski, K.; Szalewicz, K. "Dispersionless density functional theory" Phys. Rev. Lett., 2009, 103, 263201.

19. Patkowski, K.; Spirko, V.; Szalewicz, K. "On the Elusive Twelfth Vibrational State of Beryllium Dimer" Science, 2009, 326, 1382. University of Delaware press release

18. Cencek, W.; Patkowski, K.; Szalewicz, K. "Full configuration-interaction calculation of three-body nonadditive contribution to helium interaction potential," J. Chem. Phys., 2009, 131, 064105.

17. Patkowski, K.; Cencek, W.; Jankowski, P.; Szalewicz, K.; Mehl, J.B.; Garberoglio, G.; Harvey, A.H. "Potential energy surface for interactions between two hydrogen molecules" J. Chem. Phys., 2008, 129, 094304.

16. Jeziorska, M.; Cencek, W.; Patkowski, K.; Jeziorski, B.; Szalewicz, K. "Complete basis set extrapolations of dispersion, exchange, and coupled-clusters contributions to the interaction energy: a helium dimer study," Int. J. Quantum Chem., 2008, 108, 2053.

15. Patkowski, K.; Podeszwa, R.; Szalewicz, K. "Interactions in diatomic dimers involving closed-shell metals" J. Phys. Chem. A, 2007, 111, 12822.

14. Patkowski, K.; Szalewicz, K. "Frozen core and effective core potentials in symmetry-adapted perturbation theory" J. Chem. Phys., 2007, 127, 164103.

13. Jeziorska, M.; Cencek, W.; Patkowski, K.; Jeziorski, B.; Szalewicz, K. "Pair potential for helium from symmetry-adapted perturbation theory calculations and from supermolecular data" J. Chem. Phys., 2007, 127, 124303.

12. Patkowski, K.; Cencek, W.; Jeziorska, M.; Jeziorski, B.; Szalewicz, K. "Accurate pair interaction energies for helium from supermolecular Gaussian geminal calculations" J. Phys. Chem. A, 2007, 111, 7611.

11. Patkowski, K.; Szalewicz, K.; Jeziorski, B. "Third-order interactions in symmetry-adapted perturbation theory" J. Chem. Phys., 2006, 125, 154107.

10. Bukowski, R.; Cencek, W.; Patkowski, K.; Jankowski, P.; Jeziorska, M.; Kolaski, M.; Szalewicz, K. "Portable parallel implementation of symmetry-adapted perturbation theory code" Mol. Phys., 2006, 104, 2241.

9. Szalewicz, K.; Patkowski, K.; Jeziorski, B. "Intermolecular interactions via perturbation theory: from diatoms to biomolecules" Struct. Bonding (Berlin), 2005, 116, 43.

8. Patkowski, K.; Murdachaew, G.; Fou, C.-M.; Szalewicz, K. "Accurate ab initio potential for argon dimer including highly repulsive region," Mol. Phys., 2005, 103, 2031.

7. Patkowski, K.; Jeziorski, B.; Szalewicz, K. "Unified treatment of chemical and van der Waals forces via symmetry-adapted perturbation expansion" J. Chem. Phys., 2004, 120, 6849.

6. Przybytek, M.; Patkowski, K.; Jeziorski, B. "Convergence behavior of symmetry-adapted perturbation expansions for excited states. A model study of interactions involving a triplet helium atom" Collect. Czech. Chem. Commun., 2004, 69, 141.

5. Brudermann, J.; Steinbach, C.; Buck, U.; Patkowski, K.; Moszynski, R. "Elastic and rotationally inelastic differential cross sections for He + H2O collisions" J. Chem. Phys., 2002, 117, 11166.

4. Patkowski, K.; Jeziorski, B.; Korona, T.; Szalewicz, K. "Symmetry-forcing procedure and convergence behavior of perturbation expansions for molecular interaction energies" J. Chem. Phys., 2002, 117, 5124.

3. Patkowski, K.; Korona, T.; Moszynski, R.; Jeziorski, B.; Szalewicz, K. "Ab initio potential energy surface and second virial coefficient for He-H2O complex" J. Mol. Struct. (Theochem), 2002, 591, 231.

2. Patkowski, K.; Korona, T.; Jeziorski, B. "Convergence behavior of the symmetry-adapted perturbation theory for states submerged in Pauli forbidden continuum" J. Chem. Phys., 2001, 115, 1137.

1. Patkowski, K.; Jeziorski, B.; Szalewicz, K. "Symmetry-adapted perturbation theory with regularized Coulomb potential" J. Mol. Struct. (Theochem), 2001, 547, 293.

• Spring 2011: CHEM3160 - Survey of Physical Chemistry

• June 2011: Our very own computer cluster just arrived. Thanks to Auburn University for the startup funding!



• May 2011: Dr. Patkowski gave a talk "Limits of accuracy in interatomic and intermolecular potentials" at the 2011 Southeast Theoretical Chemistry Association (SETCA) Annual Meeting at Mississippi State.


• February 2011: This page is created. Group news will be posted here.

1. What is quantum chemistry?



Quantum chemistry is a science that applies the methods of quantum mechanics and applies them to systems of interest to chemistry - molecules, clusters, and chemical reactions. By solving the central formula of quantum mechanics - the Schrodinger equation - we obtain molecular wave functions and energy levels, which we then can use to calculate geometries, spectroscopical properties, and other quantities that can be compared with experiment.

2. OK, so we have an equation to solve. Does that mean that quantum chemistry is a pen-and-paper science?



Not at all. The most complicated system for which the Schrödinger equation can be solved exactly is the hydrogen atom (and even that only if we do not take into account the effects of quantum electrodynamics). Anything that has more than one electron and/or more than one nucleus has to be treated approximately, and there is no better way to do these approximate calculations than using computers.

3. The computers are so fast and powerful these days. Can't all the quantum chemistry problems be solved right away?



Not quite. There are many approximate methods in quantum chemistry. Some of them are more approximate but very fast, some are more accurate but much more computationally expensive. To compare the computational cost of different algorithms, people like to talk about scaling of a method with a system size N. For example, if a method scales quadratically (N²) with system size, if the molecule is made twice as large, it takes the computer 4=2² more times to perform the calculation. Some accurate methods of quantum chemistry (like the popular and reliable CCSD(T) approach) scale like the seventh or even higher power of the system size. That means if we want to be able to apply the method to a molecule that is twice as large, we need a computer that is 2⁷=128 times more powerful!

4. What programs do you use?



There are several popular quantum-chemistry codes on the market, including GAUSSIAN, MOLPRO, Q-Chem, and DALTON. Each of them can perform calculations using a large variety of methods and algorithms. Still, none of them can do everything that we possibly need, and every now and then one has to write their own code to solve a particular problem.

5. Do I need to know how to program to be a quantum chemist?



You do not need to be able to program initially. However, in the course of a graduate study in quantum chemistry you will surely learn how to read the code written in several programming languages and how to write a code in at least one of them. At the same time, you will gain a good working knowledge of the Linux/Unix operating system - this is the system which all our big computers are running.

6. What computers are available for your group?



We have our own cluster with a small number of powerful nodes (with four 12-core AMD Opteron CPUs, 128 GB of memory, and 5 TB of disk space on each node) that will be extended and upgraded in the next years. Our group can also run calculations using the machines in the Alabama Supercomputer Center, a supercomputing facility (located in Huntsville) shared by all educational institutions of Alabama.

Quantum chemistry software

• SAPT code coauthored by Dr. Patkowski (University of Delaware and University of Warsaw)
• MOLPRO package of ab initio programs
• GAUSSIAN suite of programs
• DALTON electronic structure and molecular properties program
• CFOUR (Coupled-Cluster techniques for Computational Chemistry) - formerly known as ACESII(Mainz-Austin-Budapest)
• Mihály Kállay's MRCC program interfaced to MOLPRO and CFOUR
• Q-Chem suite of programs
• NWChem computational chemistry package
• PSI3 ab initio quantum chemistry package

Other scientific stuff

• NIST Chemistry WebBook - if you need molecular reference data, this is the place.
• EMSL Basis Set Exchange - if you need basis sets... well, you know.
• PyMOL - a Python-based molecular visualization system
• Quantum Chemistry Laboratory, University of Warsaw
• Dr. Krzysztof Szalewicz's group, University of Delaware
• Notes on Quantum Chemistry written by Dr. C. David Sherrill
• Python Documentation HQ

Non-scientific stuff

• The Wikimapia project - let's describe the whole world!
• Google Sightseeing - interesting places and odd sightings on Google Maps and Google Street View
• Polish Scrabble Federation (mostly in Polish)