Gaussian 09: Expanding the limits of computational chemistry

Gaussian 09 is the latest version of the Gaussian® series of electronic structure programs, used by chemists, chemical engineers, biochemists, physicists and other scientists worldwide. Starting from the fundamental laws of quantum mechanics, Gaussian 09 predicts the energies, molecular structures, vibrational frequencies and molecular properties of molecules and reactions in a wide variety of chemical environments. Gaussian 09’s models can be applied to both stable species and compounds which are difficult or impossible to observe experimentally (e.g., short-lived intermediates and transition structures).

Gaussian 09 provides the most advanced modeling capabilities available today, and it includes many new features and enhancements which significantly expand the range of problems and systems which can be studied. With Gaussian 09, you can model larger systems and more complex problems than ever before, even on modest computer hardware.

Comprehensive Investigations of Molecules and Reactions

With Gaussian 09, you can thoroughly investigate the chemical problems that interest you. For example, not only can you minimize molecular structures rapidly and reliably, you can also predict the structures of transition states, and verify that the located stationary points are in fact minima and transition states. You can go on to compute the reaction path by following the intrinsic reaction coordinate (IRC) and determine which reactants and products are connected by a given transition structure. Once you have a complete picture of the potential energy surface, reaction energies and barriers can be accurately predicted.

Researchers have used these fundamental capabilities of Gaussian 09 to study isopenicillin N synthase (IPNS), a member of a family of mononuclear nonheme iron enzymes (illustrated at the bottom right of the next image). Transition metal enzymes catalyze some of the most important biochemical processes, and they can also serve as inspiration for novel biomimetic catalysis. In the latter context, these researchers wanted to determine how the metal center and the protein matrix separately contribute to the enzyme system’s catalytic activity. They analyzed the catalytic mechanism of IPNS, exploring the potential energy surface for the transformation of the tripeptide substrate δ-(l-α-aminoadipoyl)-l-cysteinyl-d-valine (ACV) to isopenicillin N (IPN). The ONIOM facility in Gaussian 09 enables the transition structures and reaction paths to be computed for the reactions involving large proteins like this system.

IRC reaction path

The reactants (left), transition structure (center) and products (right), as well as the IRC reaction path, are all computed using the ONIOM facility. The highlighted inset focuses on the active atoms in the high accuracy layer, treated with density functional theory. The grey region outside is a tiny portion of the low accuracy layer, treated with molecular mechanics in the integrated QM:MM method.

Reference: M. Lundberg, T. Kawatsu, T. Vreven,
M.J. Frisch & K. Morokuma, JCTC 5 (2009) 222.

A small part of their results are shown in the illustration above depicting the reactants, products and transition structure for a proton transfer reaction. Overall, their analysis suggests that the main catalytic effect comes from the metal center while the protein environment controls the high product specificity.

Predicting and Interpreting Spectra

Spectroscopy is a fundamental tool for investigating molecular structures and properties. However, observed spectra are often difficult to interpret. The results of electronic structure calculations can be vital to this process. For example, predicted spectra can be examined in order to determine peak assignments in observed spectra as well as comparing peak locations and intensities with experimental data. Gaussian 09 can also compute relevant spectroscopic constants and related molecular properties with excellent accuracy. This combination of experimental observation and theoretical computation can yield very accurate structural and spectral data for compounds of interest.

Gaussian 09 can predict a variety of spectra including IR and Raman, NMR, UV/Visible, Vibrational circular dichroism (VCD), Raman optical activity (ROA), Electronic circular dichroism (ECD), Optical rotary dispersion (ORD), Hyperfine spectra (microwave spectroscopy), Franck-Condon, Herzberg-Teller and Franck-Condon/Herzberg-Teller analyses.

Modeling NMR. Gaussian 09 continues to enhance the program’s NMR capabilities. Spin-spin coupling constants are one of the most difficult spectral data to produce quantitatively. The accuracy of calculations is highly dependent on the basis set used. While the standard basis sets of quantum chemistry are well developed for valence electrons, a more sophisticated description of the electron density closer to the nuclei is needed for predicting the Fermi contact (FC) term (often the spin-spin coupling constants’ largest component). Researchers at Gaussian, Inc. have explored this problem in depth and have developed modified basis sets suitable for modeling these quantities within a DFT framework; their results are summarized below. When requested, Gaussian 09 will automatically perform a two-step calculation for NMR spin-spin coupling, using the standard basis set for the general calculation and the corresponding modified basis set for the FC term.

Basis Sets for Computing NMR Spin-Spin Coupling Constants

Basis Set Derived from Accuracy Improvement
uTZ-w aug-cc-pVTZ 650% (ΔAAE=-20 Hz, AAE=3.6 Hz)
uDZ-w aug-cc-pVDZ 590% (ΔAAE=-41 Hz, AAE=8.7 Hz)
uG-w 6-311+G(d,p) 415% (ΔAAE=-33 Hz, AAE=10.3 Hz)

Larger improvement percentages are better (AAE: average absolute error with respect to the basis set limit). Recommended basis sets are arranged from largest (top) to smallest.

Reference: W. Deng, J.R. Cheeseman & M.J. Frisch, JCTC 2 (2006) 1028.

Standard basis sets produce large errors when computing Fermi contact contributions to NMR spin-spin coupling constants. Gaussian 09 provides specialized basis sets which produce very good agreement with experiment for these quantities.

alanine

Studying Chirality. Chiral molecules are of great importance in many research contexts. Gaussian 09 can study chirality with several techniques including two of the latest spectroscopic classes: VCD and ROA. For example, researchers have used the VCD facility to model helical peptides. The structures of peptides composed of alanine are dominantly α-helical with the C terminus being coil-like. VCD experiments used isotopic labeling to demonstrate that the α-helix in Ala20 and in Ala25 (shown right) noncooperatively unwinds from the ends with increasing temperature.

The IR and VCD spectra for these systems were studied in solution with Gaussian 09. Results for Ala25 appear below. The calculations successfully reproduce the experimental observations and are additionally able to quantify the degree of “fraying.” They also indicate that confidence can be placed in the reported molecular structures.

IR and VCD spectra

 

Experimental References: R. Silva, J. Kubelka, P. Bour, S. Decatur and T. Keiderling,
PNAS 97 (2000) 8313; R. Huang, J. Kubelka, W. Barber-Armstrong, R. Silva, S. Decatur
and T. Keiderling, JACS 126 (2004) 2346. Computational reference in preparation.

Predicting Optical Spectra. Steady-state spectroscopy is one of the most fundamental tools for investigating equilibrium structures and potential energy surfaces for different electronic states. However, interpreting such experimental data is often not straightforward. Such situations often benefit greatly from calculations which aid in interpreting and assigning each spectral feature.

Several Gaussian 09 capabilities in such studies. For example, the time-dependent DFT method produces high quality descriptions of excited state systems (comparable to DFT for the ground state), and Franck-Condon and Herzberg-Teller analyses can be used for computing the amplitudes for electronic transitions from the ground and excited state frequency analyses. The combination of the two can be used to effectively treat both transitions with large oscillator strengths and forbidden transitions. Solvation effects can be included in these models.

These methods have been used to compute the Herzberg-Teller absorption and fluorescence Qx spectra of free-base porphyrin. Their results are shown to the right. These graphs compare the high definition quasiline absorption and emission bands, plotting the computed and experimental intensities divided by ω (absorption) or ω3 (emission), and demonstrate excellent agreement.

absorption and fluorescence

Reference: F. Santoro, A. Lami, R. Improta, J. Bloino & V. Barone, J. Chem. Phys. 128 (2008) 224311.

Predicting Hyperfine Spectra. Gaussian 09 computes the most important tensors which contribute to hyperfine spectra. Calculations can suggest regions in which to look for transitions, which can make experiments more efficient. Theoretical results are also useful for making spectral assignments for observed peaks, which can be difficult or impossible to determine solely from the raw experimental data. Computed tensors can also be combined with observations in fitting operations. Using computations to aid in interpreting and fitting observed results should make non-linear molecules as amenable to study as linear ones.

The plot below compares the observed (top) and computed (bottom) hyperfine spectra for H2C6N, showing very good agreement between the two.

observed & computed spectra

Experimental data provided by S. E. Novick, W. Chen, M. C. McCarthy and P. Thaddeus.

Open shell species have particularly rich and complex spectra when studied with microwave spectroscopy. Such compounds are important in many contexts, including the chemistry of interstellar media. Researchers have studied the 1,1-difluoroprop-2-ynyl radical, F2CC≡CH, a partially fluorinated variant of the propargyl radical. The combination of the observed microwave spectral data and calculation of various hyperfine tensors determined that the compound has a planar structure, a somewhat unexpected result.

The table below compares the values for several quantities from the theoretical calculation and derived from the experimental data, illustrating the very good agreement between the two.

spin density
Constant Calc. Comb. Fit Constant Calc. Comb. Fit
A0 11.108 11.126 εaa -43.236 -43.674
B0 3.926 3.927 εbb 20.852 16.159
C0 2.901 2.904 εcc 2.158 0.359
ΔNx103 0.44 0.57 aF(H) -43.226 -32.542
ΔNKx103 17.0 19.1 aF(F) 97.52 145.73
ΔKx103 -1.5 -30.0 Taa(H) 20.852 16.159
δNx103 0.13 0.19 Taa(F) 97.52 145.73
δKx103 9.6 14.6 Tab(F) 16.1 13.4

Calculation performed at UB3LYP/aug-cc-PVQZ. Combined fit IF=0,1.

Reference: L. Kang & S.E. Novick, J. Chem. Phys. 125 (2006) 054309.

The plots at the right depict the spin density for F2CC≡CH (with the α spin density in burgundy and the β spin density in teal), situated perpendicular (top) and parallel to the plane of the molecule. Note the small amount of β spin density on the H atom.

Explore Diverse Chemical Arenas

Gaussian 09’s predictive powers are just as extensive in other chemical contexts as they are in spectroscopy.

Thermochemistry. Accurate predictions of ΔG are vital to understanding many chemical reactions. Gaussian 09 offers a variety of very accurate energy methods for predicting thermochemical quantities, including the Complete Basis Set (CBS) methods, the Gaussian-1 through Gaussian-4 method families, and the W1 methods. In addition to ΔG and ΔH, you can predict heats of formation, atomization energies, ionization potentials, electron affinities and proton affinities for a wide range of compounds at the highest available accuracy.

Photochemistry and other Excited State Processes. In addition to the spectroscopic features considered earlier, Gaussian 09 also provides several other features for studying systems in their excited states. Using these capabilities, you can study the absorption properties of dyes and other chromophores, the photodecomposition rates of pesticides and other compounds, the properties of materials of potential use for solar energy, and many other equally important research problems.

Gaussian 09 offers many methods for studying such reactions, suitable for systems of varying sizes, including the time-dependent DFT method, the EOM-CCSD method (comparable in accuracy and cost to coupled cluster singles and doubles ground state calculations), and the CASSCF method which provides a multireference description of molecular systems and can also be used to locate conical intersections on excited state-ground state potential energy surfaces.

Solvent Effects can be taken into account when optimizing structures and predicting most molecular properties. For example, the VCD investigation of the alanine peptide chain we considered on pages 4-5 was carried out in solution. In fact, in this case, the gas phase results are very different and solvent effects are crucial to studying this system. Gaussian 09’s solvation capabilities are the most advanced available, and they provide roughly comparable performance to gas phase studies for many computation types.

Complex Modeling, Yet Easy-to-Use Features

Gaussian 09 is a powerful program offering sophisticated modeling capabilities. It is nevertheless very easy to use, even for new users. There are many ways that Gaussian 09 makes studying molecules and reactions simple and straightforward. For example, its consistent and intuitive user input and carefully chosen default settings hide algorithmic and procedural complexity, allowing you to focus on the chemistry.

Automation. Gaussian 09 also automates many compound calculation types whose steps traditionally have to be performed separately and explicitly:

  • The quadratic synchronous transit (QST) approach automates transition structure optimization. You need simply provide the reactants, products and optionally a starting guess for the transition state.
  • The high accuracy energy models in the CBS, Gaussian-1 through Gaussian-4, and W1 families consist of many diverse calculations whose results must be combined for the final energy value. Gaussian 09 automates all of these methods and reports the final model energy.
  • Gaussian 09 now provides a fragment guess capability which allows you to define fragments within the molecule whose separate initial guesses can be used to form the initial guess for the calculation. Previously, considerable effort was required to examine and reorder molecular orbitals in order to set up an appropriate initial guess for systems like antiferromagnetic transition metal complexes.

Antiferromagnetic coupling is an effect that is often important for molecules with high spin multiplicity like the bridged manganese complex below. This is a typical transition metal system in which this phenomenon is of interest: Mn2O2(NH3)8. In the neutral molecule, in which the Mn atoms are nominally Mn(II), there are 5 d electrons on each Mn, and the antiferromagnetic singlet (5 alpha d electrons on one Mn and 5 beta d electrons on the other) may be the ground state wavefunction. For this system, we define four fragments as indicated by the colored shading. The results of our complete study of this system indicate that the antiferromagnetic singlet is in fact the ground state wavefunction for this molecule (see www.gaussian.com/g_tech/afc.htm for full details on the calculations).

Electronic state ΔE
Antiferromagnetic singlet ground state
Spin multiplicity 11 4.4 kcal/mol  
Open shell singlet 60.2 kcal/mol  
Closed shell singlet 154.5 kcal/mol  
antiferromagnetic coupling
  • Gaussian 09 provides the ability to test wavefunctions for instability and to automatically reoptimize non-ground state wavefunctions. This capability is very important for open shell systems, to ensure that the desired electronic state is in fact being modeled. We used it extensively in the study of the manganese complex described just previously.
molecular orbitals

Intuitive Presentation of Results. Gaussian 09 presents results in as straightforward and comprehensible a manner as possible. First and foremost, the GaussView 5 graphical interface makes setting up jobs and examining results visually easy. In addition, Gaussian 09 provides many convenience features which convey the computational outcome and the associated chemistry in forms which are familiar and recognizable to experimental researchers.

An example of the latter introduced in Gaussian 09 is illustrated at the right. The figure shows two sets of orbitals for FeO+. This system is a quartet, and it is accordingly modeled using an unrestricted method.

The first set of orbitals (top) are the default canonical orbitals. They can be difficult to interpret for molecules like this one since they are spin polarized.

Understanding the bottom set of orbitals is much more straightforward. These orbitals have been biorthogonalized—transformed via an energy-invariant rotation—in order to produce the “corresponding orbitals.” With this representation, it is clear that the molecule contains five singly occupied orbitals: four α unpaired electrons localized on the iron atom, and one β unpaired electron localized on the oxygen atom.

Gaussian 09 can also report the atomic contributions to the molecular orbitals. For example, the α HOMO in the canonical orbital set is composed of about 70% p-orbital on the oxygen and about 20% s-orbital on the iron.

Spin density itself can also be computed and visualized. We saw an example of this previously above.

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Last update: 23 April 2013