About Gaussian 16

Chemistry in Solution

A substantial part of interesting chemical processes occurs in solution. The presence of a solvent can change molecular structure, molecular properties, the relative energies of isomers, the relative abundances of conformations, and many other important factors. Chemistry can also change from one solvent to another.

All available molecular properties can be predicted in solution. Solvation can be included in calculations on both ground state and excited state systems and in ONIOM models.

Structure and Property Changes in Solution

Phenolphthaline is the best known example of a change in molecular structure in solution. Its characteristic color change from clear in acidic solutions to pink in basic solutions results from a shift from a neutral lactone form to a phenolate (anion) form. In fact, the compound takes on two additional forms: in very strong acidic and in basic environments.

Solvatochromism

Solvatochromism is the ability of the solvent environment to alter the relative energies of ground and excited electronic states. This effect is typically seen in the absorbance spectrum of solutes whose excited states involve movement of electrons across the molecule. The figure plots the observed maximum absorption vs. the Onsager function of the solvent dielectric constant for three compounds in a range of solvents [Steel09]. There are two different solvatochromic behaviors. The electronic transitions in PNP and 2,6-DMPNO strongly depend on solvent polarity, while in 3,5-DMPNP λ_max is shifted much less significantly. An electronic shift to longer wavelength means that the solute’s dipole is larger in the excited state relative to the gound state, and the differences in μ predicted by TD-DFT support the observed data.

Accurate Free Energies of Solvation

The energy change going from the gas phase to solution is known as the solvation energy of a molecule. It can be computed for the same compound with several solvents in order to understand its relative solubility in different environments. The predicted free energy can also be used to predict reaction energies in solution. The SMD method is an SCRF-based solvation model from Truhlar and coworkers [Marenich09]. It was parametrized specifically to predict free energies of solvation, and includes different values for the non-electrostatic terms.

Investigating Large Systems with ONIOM

The wide variety of theoretical methods and basis sets available in Gaussian include many that are highly accurate. Unfortunately, such model chemistries scale unfavorably with the size of the molecule, resulting in a practical limit on how large a system can be studied. Gaussian’s ONIOM facility provides a means for overcoming these limitations, allowing you to study large systems that would otherwise be out of reach to all but the cheapest methods. Originally developed by Morokuma and coworkers [Dapprich99], this computational technique models large molecules by defining two or three layers within the structure that are treated at different levels of accuracy. Calibration studies [Dapprich99, Vreven06a] demonstrated that the resulting predictions are essentially equivalent to those that would be produced by the high accuracy method alone on the entire molecule.

ONIOM first appeared in Gaussian 98, and significant innovations over the years make it applicable to much larger molecules. Today, the ONIOM method is applicable to large molecules in many other areas, including enzyme reactions, reaction mechanisms for organic systems, cluster models of surfaces and surface reactions, photochemical processes of organic species, substituent effects and reactivity of organic and organometallic compounds, and homogeneous catalysis. For a recent review of the ONIOM method and many exemplary applications, see [Chung15] by Chung, Morokuma and coworkers.

In addition to modeling systems which are too large to address as a whole by a method with the desired accuracy, ONIOM calculations are also useful for other chemical situations:

• Compounds whose chemistry occurs within a protein environment. In such cases, ONIOM is needed both because of the sheer size of the molecule and because modeling, e.g., a chromophore in isolation is a poor model for its actual emission reaction.
• Steric effects arising from ligands are another example where ONIOM aids in accurately modeling the fundamental chemistry. Ligands can be bulky and flexible, and compounds containing them can be too large to optimize with a desired method. However, merely truncating the ligands can lead to poor agreement with observations since they significantly influence molecular structure and reactivity. Modeling such systems with ONIOM, using either QM:QM or QM:MM methods, is both feasible and successful.
• ONIOM may be useful for molecules whose size does not make them prohibitively expensive to model in a single form but for which there are a large number of conformations. ONIOM can aid in the conformation search process by significantly reducing the time required for each individual optimization.

ONIOM Layers for Modeling GFP

Green fluorescent protein (GFP) is the molecule responsible for fluoresence in jellyfish. When exposed to light in the proper frequency range, it emits bright green light. It is a molecule that is ideal for modeling with ONIOM. The figure illustrates one possible partitioning for an ONIOM model. The majority of the protein and the crystallographic waters are placed in the ONIOM MM region (low layer) while the chromophore and important atoms on nearby residues comprise the QM region (high layer). Including the protein environment within the calculation is essential to determining the structure of the chromophore.

A Novel Yttrium-Phosphinidene Complex

Zhang and coworkers recently synthesized two novel trinuclear rare-earth metal phosphinidene complexes [Wang15]. The illustration focuses on the compound containing yttrium (the other complex contains lutetium). The central part of the newly-synthesized compound appears on the left, with the phenol group and the ligands truncated for clarity. The molecule on the right shows the partitioning used for their related ONIOM calculations; it depicts the first step of their proposed pathway, the reaction of the phosphinidene complex {[PhC(NC₆H₄iPr₂-2,6)₂]^–(Y)(μ₂-Me)}₃(μ₃-Me)(μ₃-PPh) with CS₂ in toluene. The high accuracy region contains the Y and P atoms and the most important groups bonded to them, the CS₂ molecule weakly bound to the cluster, as well as the N-C-N group from each ligand. ONIOM (QM:QM) calculations allowed this very large molecule to be studied with accurate methods; the high layer used a DFT model, while Hartree-Fock was used for the bulk of the ligands. On the basis of their calculations, these researchers identified a potential pathway for the complete synthesis.

Modeling Spectroscopy

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 to compare peak locations and intensities with experimental data. Gaussian 16 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 16 can predict a variety of spectra, in both the gas phase and in solution, including:

• IR and Raman
• NMR spectra and spin-spin coupling constants
• Vibrational circular dichroism (VCD)
• Raman optical activity (ROA)
• Resonance Raman
• UV/Visible
• Vibronic absorption and emission spectra for excited states, via Franck-Condon and/or Herzberg-Teller analysis
• Electronic circular dichroism (ECD) and circularly polarized luminescence (CPL)
• Optical rotatory dispersion (ORD)
• Hyperfine (microwave spectroscopy)
• Anharmonic analysis is available for IR, Raman, VCD and ROA spectra.

Harmonic vs. Anharmonic IR Spectrum of Naphthalene

Vibrational frequency analysis performed by default uses the harmonic approximation for performance reasons; it assumes that there are no interactions between vibrational modes. As a result, such analysis can only predict fundamental bands. However, observed spectra also often include overtone and combination bands. Anharmonic frequency analysis must be used to predict the latter band types and to achieve agreement with experiment in many cases. This figure illustrates the predicted IR spectrum for naphthalene. The harmonic (blue) and anharmonic (red) spectra are compared; in addition to shifting the location of several peaks, the anharmonic spectrum exhibits considerably more complexity (see, e.g., the 1600-2000 cm^–1 range and the region above ~3000 cm^–1). The anharmonic spectrum is plotted against experiment in the inset. The bottom plot focuses on the 2950-3250 cm^–1 region and shows the contributions of fundamental, 2-quanta and 3-quanta modes to the overall spectrum.

Modeling NMR Spin-Spin Coupling Constants

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 [Deng06]. Gaussian 16 can 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.

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.

Studying Chirality

Chiral molecules are of great importance in many research contexts. Gaussian 16 can study chirality with several techniques including two spectroscopic classes: VCD and ROA. Both types of spectra can be predicted including anharmonic vibrational analysis.

Distinguishing Chiral Products with VCD

The Baeyer-Villiger oxidation of (+)-(1R,5S)-bicyclo[3.3.1]nonane-2,7-dione has four possible keto-lactone products. VCD calculations can determine which one is the actual product by comparing their predicted spectra to the observed one. We’ve overlaid the observed spectrum (yellow, from [Stephens05a]) on each of the plots. Isomer 1 can be identified as the product structure, and there is excellent agreement between theory and experiment.

ORD Spectra of Substituted Oxiranes

When polarized light travels through some materials, it is rotated with respect to the direction of motion. Such materials include crystals, spin-polarized molecules in the gas phase and chiral molecules. As with other observed effects of chirality, optical rotation differs for left and right circularly polarized light, and it can give important information about molecular structure for chiral molecules. Observed optical rotations vary for the same substance according to the wavelength of the incident light. This variation is known as optical rotatory dispersion (ORD). ORD results plot the observed rotation for various incident light wavelengths. This plot shows the predicted optical rotations for a series of substituted oxirane compounds for a series of incident light frequencies in the range 350-650 nm [Wilson05, Wiberg07]. In general, the curves exhibit increased specific rotations with decreasing incident light frequency. The chlorine compound is an exception, and it exhibits an opposite change, an example of the anomeric effect; here, electron density moves from the lone pair to the σ* orbital of the C–Cl bond, resulting in a longer bond length and energetic stabilization [Wiberg07].

Modeling Microwave Spectroscopy

Molecular rotational transitions are split by a variety of interactions between the overall rotational motion of the molecule and both the electron distribution and spins of the nuclei, yielding the so-called fine structure, which can be measured with very great accuracy. For molecules with unpaired electrons, the fine structure itself can be further split as a result of additional factors including the magnetic interactions between the magnetic moment and induced fields of the electron with those of the nucleus. The effect is known as hyperfine coupling, and it is studied experimentally with microwave spectroscopy. It can also be modeled by Gaussian.

Calculations can also aid in interpreting experimental data. They 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.

Hyperfine Spectrum for H₂C₆N

This plot compares the observed (top) and computed (bottom) hyperfine spectra for H₂C₆N, showing very good agreement between the two (experimental data provided by S. E. Novick, W. Chen, M. C. McCarthy and P. Thaddeus).

F₂CC≡CH Hyperfine Coupling Constants and Spin Density

Researchers have also 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 at the top compares the predicted values of many constants for this compound with those fitted from experimental data [Kang06], showing excellent agreement between them. The figure below the table shows the spin density for the molecule, with the α spin density in teal and the β spin density in yellow, situated perpendicular (top) and parallel to the plane of the molecule. Note the abundance of α spin density in both potential locations for the unpaired electron—the two end carbon atoms—as well as the small amount of β spin density on the H atom.

Studying Excited State Chemistry

Excited states are relevant to the study of a wide variety of phenomenon, including photosynthesis, photodecomposition, photochemical generation of electricity, perception of light in animals, fluorescence, bioluminescence, and more. Gaussian can calculate UV-Visible spectra, model processes and reactions on excited state potential energy surfaces and predict vibronic absorption and emission spectra. Calculations can be performed in the gas phase and in solution.

Excited state methods and properties received a lot of attention as we developed Gaussian 16. With its analytic TD-DFT frequencies, you can efficiently optimize excited state transition structures, perform IRC calculations and predict vibronic spectra. Analytic EOM-CCSD gradients let you optimize the structures of molecules that require a high accuracy excited state treatment. CASSCF calculations can be performed to model structures for which multireference effects are vital; active spaces of up to 16 orbitals are supported.

Firefly Bioluminescence

Bioluminescence is a fascinating phenomenon: light emission arising from chemical reactions within the bodies of animals (without photon absorption). In fireflies, the best known example of bioluminescence, the luciferin molecule undergoes a two-step enzyme-catalyzed reaction yielding oxyluciferin, a species formed in its excited state; oxyluciferin then decays to its ground state, emitting a yellow-green photon. In some circumstances, the emitted photon is shifted in color to red (the result of an acid environment for the reaction). Theoretical studies of firefly bioluminescence span almost 2 decades, and they use ever more accurate methods for studying it: semi-empirical methods, CI-Singles and, most recently, TD-DFT. Many important questions remain unresolved, though. For example, there are six forms of the bioluminophore oxyluciferin, and the question as to which is the light-emitting molecule is not completely resolved (see, e.g., [Cheng15, daSilva15]). Gaussian 16’s TD-DFT capabilites including analytic frequencies and ONIOM capabilities are ideal for the continued study of this phenomenon.

GFP Proton Shuttle Reaction IRC

These plots show idealized intrinsic reaction coordinate paths on the ground state and excited state PESs for the proton shuttle process in green fluorescent protein (GFP) studied by the Rega group (see [Petrone16] for the predicted paths). The S₀ and S₁ transition structures are illustrated, and the proton shuttling is highlighted. In both the ground state and the excited state, all three proton transfers are concerted and proceed via a single transition state. In the organism, the reaction occurs on the lower energy excited state PES (on average, ~2-3 kcal/mol below the ground state PES). The entire hydrogen bond network is more planar in the excited state, resulting in a tighter chromophore-water-residues packet. While the published results studied a model of the chromophore region, the TD-DFT analytic frequency feature in Gaussian 16 makes it possible to study the reaction in the protein environment with ONIOM.

One Photon Absorption Spectrum

This plot shows the predicted (red) and experimental (blue) one photon absorption spectrum for trans,trans-1,4-diphenyl-1,3-butadiene [Foresman15]. The transitions requested in the calculation are represented by the vertical green lines which we have labeled with their specific transition. There is excellent agreement between calculation and experiment.

Resonance Raman Spectrum of the tris(2,2’-bipyridyl)-ruthenium(II) Complex

Each curve shows the intensity of the Raman shift produced by various frequencies of incident light. The area under each curve is filled, colored by the magnitude of the intensity (blue to red as the intensity increases). The spectrum was computed in acetonitrile solution [Baiardi14].