Experimental near edge X-ray absorption fine structure (NEXAFS) spectra are reported for 12 ionic liquids (ILs) encompassing a range of chemical structures for both the sulfur 1s and nitrogen 1s edges and compared with time-dependent density functional theory (TD-DFT) calculations. The energy scales for the experimental data were carefully calibrated against literature data. Gas phase calculations were performed on lone ions, ion pairs and ion pair dimers, with a wide range of ion pair conformers considered. For the first time, it is demonstrated that TD-DFT is a suitable method for simulating NEXAFS spectra of ILs, although the number of ions included in the calculations and their conformations are important considerations. For most of the ILs studied, calculations on lone ions in the gas phase were sufficient to successfully reproduce the experimental NEXAFS spectra. However, for certain ILs – for example, those containing a protic ammonium cation – calculations on ion pairs were required to obtain a good agreement with experimental spectra. Furthermore, significant conformational dependence was observed for the protic ammonium ILs, providing insight into the predominant liquid phase cation–anion interactions. Among the 12 investigated ILs, we find that four have an excited state that is delocalised across both the cation and the anion, which has implications for any process that depends on the excited state, for example, radiolysis. Considering the collective experimental and theoretical data, we recommend that ion pairs should be the minimum number of ions used for the calculation of NEXAFS spectra of ILs.

Nonlinear two-dimensional infrared spectroscopy (2DIR) is most commonly simulated within the framework of the exciton method. The key parameters for these calculations include the frequency of the oscillators within their molecular environments and coupling constants that describe the strength of coupling between the oscillators. It is shown that these quantities can be obtained directly from harmonic frequency calculations by exploiting a procedure that localizes the normal modes. This approach is demonstrated using the amide I modes of polypeptides. For linear and cyclic diamides and hexapeptide Z-Aib-l-Leu-(Aib)2-Gly-Aib-OtBu, the computed parameters are compared with those from existing schemes, and the resulting 2DIR spectra are consistent with experimental observations. The incorporation of conformational averaging of structures from molecular dynamics simulations is discussed, and a hybrid scheme wherein the Hamiltonian matrix from the quantum chemical local-mode approach is combined with fluctuations from empirical schemes is shown to be consistent with experiment. The work demonstrates that localized vibrational modes can provide a foundation for the calculation of 2DIR spectra that does not rely on extensive parametrization and can be applied to a wide range of systems. For systems that are too large for quantum chemical harmonic frequency calculations, the local-mode approach provides a convenient platform for the development of site frequency and coupling maps.

The computational cost of calculations of K-edge X-ray absorption spectra using time-dependent density functional (TDDFT) within the Tamm–Dancoff approximation is significantly reduced through the introduction of a severe integral screening procedure that includes only integrals that involve the core s basis function of the absorbing atom(s) coupled with a reduced quality numerical quadrature for integrals associated with the exchange and correlation functionals. The memory required for the calculations is reduced through construction of the TDDFT matrix within the absorbing core orbitals excitation space and exploiting further truncation of the virtual orbital space. The resulting method, denoted fTDDFTs, leads to much faster calculations and makes the study of large systems tractable. The capability of the method is demonstrated through calculations of the X-ray absorption spectra at the carbon K-edge of chlorophyll a, C60 and C70.

The fluorescence of a two-dimensional supramolecular network of 5,10,15,20-tetrakis(4-carboxylphenyl)porphyrin (TCPP) adsorbed on hexagonal boron nitride (hBN) is red-shifted due to, primarily, adsorbate–substrate van der Waals interactions. TCPP is deposited from solution on hBN and forms faceted islands with typical dimensions of 100 nm and either square or hexagonal symmetry. The molecular arrangement is stabilized by in-plane hydrogen bonding as determined by a combination of molecular-resolution atomic force microscopy performed under ambient conditions and density functional theory; a similar structure is observed on MoS2 and graphite. The fluorescence spectra of submonolayers of TCPP on hBN are red-shifted by ∼30 nm due to the distortion of the molecule arising from van der Waals interactions, in agreement with time-dependent density functional theory calculations. Fluorescence intensity variations are observed due to coherent partial reflections at the hBN interface, implying that such hybrid structures have potential in photonic applications.Keywords: atomic force microscopy; boron nitride; fluorescence; molybdenum disulfide; porphyrin;

The electronic structure and photoinduced electron transfer processes in a K+ fluorescent sensor that comprises a 4-amino-naphthalimide derived fluorophore with a triazacryptand ligand is investigated using density functional theory (DFT) and time-dependent density functional theory (TDDFT) in order to rationalize the function of the sensor. The absorption and emission energies of the intense electronic excitation localized on the fluorophore are accurately described using a ΔSCF Kohn–Sham DFT approach, which gives excitation energies closer to experiment than TDDFT. Analysis of the molecular orbital diagram arising from DFT calculations for the isolated molecule or with implicit solvent cannot account for the function of the sensor, and it is necessary to consider the relative energies of the electronic states formed from the local excitation on the fluorophore and the lowest fluorophore → chelator charge transfer state. The inclusion of solvent in these calculations is critical since the strong interaction of the charge transfer state with the solvent lowers its energy below the local fluorophore excited state making a reductive photoinduced electron transfer possible in the absence of K+, while no such process is possible when the sensor is bound to K+. The rate of electron transfer is quantified using Marcus theory, which gives a rate of electron transfer of kET = 5.98 × 106 s–1.

The calculation of X-ray emission spectroscopy with equation of motion coupled cluster theory (EOM-CCSD), time-dependent density functional theory (TDDFT), and resolution of the identity single excitation configuration interaction with second-order perturbation theory (RI-CIS(D)) is studied. These methods can be applied to calculate X-ray emission transitions by using a reference determinant with a core-hole, and they provide a convenient approach to compute the X-ray emission spectroscopy of large systems since all of the required states can be obtained within a single calculation, removing the need to perform a separate calculation for each state. For all of the methods, basis sets with the inclusion of additional basis functions to describe core orbitals are necessary, particularly when studying transitions involving the 1s orbitals of heavier nuclei. EOM-CCSD predicts accurate transition energies when compared with experiment; however, its application to larger systems is restricted by its computational cost and difficulty in converging the CCSD equations for a core-hole reference determinant, which become increasing problematic as the size of the system studied increases. While RI-CIS(D) gives accurate transition energies for small molecules containing first row nuclei, its application to larger systems is limited by the CIS states providing a poor zeroth-order reference for perturbation theory which leads to very large errors in the computed transition energies for some states. TDDFT with standard exchange-correlation functionals predicts transition energies that are much larger than experiment. Optimization of a hybrid and short-range corrected functional to predict the X-ray emission transitions results in much closer agreement with EOM-CCSD. The most accurate exchange-correlation functional identified is a modified B3LYP hybrid functional with 66% Hartree–Fock exchange, denoted B66LYP, which predicts X-ray emission spectra for a range of molecules including fluorobenzene, nitrobenzene, acetone, dimethyl sulfoxide, and CF3Cl in good agreement with experiment.

The binding within the ethene–argon and formaldehyde–methane complexes in the ground and electronically excited states is studied with equation of motion coupled cluster theory (EOM-CCSD), second-order Møller–Plesset perturbation theory (MP2) and density functional theory with dispersion corrections (DFT-D). Electronically excited states are studied within MP2 and Kohn–Sham DFT formalisms by exploiting a procedure called the maximum overlap method that allows convergence of the relevant self-consistent field equations to higher energy (or excited state) solutions. Potential energy curves computed using MP2 are in good agreement with the EOM-CCSD calculations for both the valence and Rydberg excited states studied. For the DFT-D approach, B3LYP-D3/aug-cc-pVTZ calculations are found to be in agreement with EOM-CCSD for the ground and valence excited states. However, for the π3s Rydberg state of ethene–argon and the n3s Rydberg state of formaldehyde–methane significant deviation is observed, and this disagreement with EOM-CCSD is present for a variety of DFT-D based approaches. Variation of the parameters within the D2 dispersion correction results in closer agreement with EOM-CCSD for the Rydberg states but demonstrates that a different parameterisation from the ground state is required for these states. This indicates that time-dependent density functional theory calculations based upon a DFT-D reference may be satisfactory for excitations to valence states, but will potentially be inaccurate for excitations to Rydberg states, or more generally states where the nature of the electron density is significantly different from the ground state.

•Low energy isomers of mixed component radical cation clusters identified.•Basin hopping search method used in conjunction with MP2.•Hemibonding and proton transfer based structures observed.Basin hopping in conjunction with second order Møller–Plesset perturbation theory is used to characterise the lowest energy isomers of mixed component radical cation clusters of the form [H2O-X]+, [(H2O)2-X]+ and [H2O-X2]+, where X = PH3, H2S and HCl, with the relative energies refined using coupled cluster theory calculations. For the dimers where X = H2S or HCl, a proton transfer based structure comprising H3O+ and SH or Cl radicals has the lowest energy structure whereas for X = PH3 a hemibonded structure is most stable. For the trimers, a much wider range of possible isomers based upon both proton transfer and hemibonded structural motifs is observed.

The basin hopping search algorithm in conjunction with second-order Møller–Plesset perturbation theory is used to determine the lowest energy structures of the radical cation clusters (NH3)n˙+, (H2O)n˙+, (HF)n˙+, (PH3)n˙+, (H2S)n˙+ and (HCl)n˙+, where n = 2–4. The energies of the most stable structures are subsequently evaluated using coupled cluster theory in conjunction with the aug-cc-pVTZ basis set. These cationic clusters can adopt two distinct structural types, with some clusters showing an unusual type of bonding, often referred to as hemibonding, while other clusters undergo proton transfer to give an ion and radical. It is found that proton transfer based structures are preferred by the (NH3)n˙+, (H2O)n˙+ and (HF)n˙+ clusters while hemibonded structures are favoured by (PH3)n˙+, (H2S)n˙+ and (HCl)n˙+. These trends can be attributed to the relative strengths of the molecules and molecular cations as Brønsted bases and acids, respectively, and the strength of the interaction between the ion and radical in the ion–radical clusters.

The calculation of the electronic circular dichroism (CD) spectra of the oxidized form of the blue copper proteins plastocyanin and cucumber basic protein and the relationship between the observed spectral features and the structure of the active site of the protein is investigated. Excitation energies and transition strengths are computed using multireference configuration interaction, and it is shown that computed spectra based on coordinates from the crystal structure or a single structure optimized in quantum mechanics/molecular mechanics (QM/MM) or ligand field molecular mechanics (LFMM) are qualitatively incorrect. In particular, the rotational strength of the ligand to metal charge transfer band is predicted to be too small or have the incorrect sign. By considering calculations on active site models with modified structures, it is shown that the intensity of this band is sensitive to the nonplanarity of the histidine and cysteine ligands coordinated to copper. Calculation of the ultraviolet absorption and CD spectra based upon averaging over many structures drawn from a LFMM molecular dynamics simulation are in good agreement with experiment, and superior to analogous calculations based upon structures from a classical molecular dynamics simulation. This provides evidence that the LFMM force field provides an accurate description of the molecular dynamics of these proteins.

The structure and bonding in ionized water clusters, (H2O)n+ (n = 3–9), has been studied using the basin hopping search algorithm in combination with quantum chemical calculations. Initially candidate low energy isomers were generated using basin hopping in conjunction with density functional theory. Subsequently, the structures and energies were refined using second order Møller–Plesset perturbation theory and coupled cluster theory, respectively. The lowest energy isomers are found to involve proton transfer to give H3O+ and a OH radical, which are more stable than isomers containing the hemibonded hydrazine-like fragment (H2O–OH2), with the calculated infrared spectra consistent with experimental data. For (H2O)9+ the observation of a new structural motif comprising proton transfer to form H3O+ and OH, but with the OH radical involved in hemibonding to another water molecule is discussed.

The copper–sulfur bond that binds cysteinate to the metal center is a key factor in the spectroscopy of blue copper proteins. We present theoretical calculations describing the electronically excited states of small molecules, including CuSH, CuSCH3, (CH3)2SCuSH, (imidazole)–CuSH, and (imidazole)2–CuSH, derived from the active site of blue copper proteins that contain the copper–sulfur bond in order to identify small molecular systems that have electronic structure that is analogous to the active site of the proteins. Both neutral and cationic forms are studied since these represent the reduced and oxidized forms of the protein, respectively. For CuSH and CuSH+, excitation energies from time-dependent density functional theory with the B97-1 exchange-correlation functional agree well with the available experimental data and multireference configuration interaction calculations. For the positive ions, the singly occupied molecular orbital is formed from an antibonding combination of a 3d orbital on copper and a 3pπ orbital on sulfur, which is analogous to the protein. This leads several of the molecules to have qualitatively similar electronic spectra to the proteins. For the neutral molecules, changes in the nature of the low lying virtual orbitals leads the predicted electronic spectra to vary substantially between the different molecules. In particular, addition of a ligand bonded directly to copper results in the low-lying excited states observed in CuSH and CuSCH3 to be absent or shifted to higher energies.

The calculation of anharmonic vibrational frequencies for a set of small molecules has been examined to explore the merit of applying such computationally expensive approaches for large molecules with density functional theory. The performance of different hybrid and gradient-corrected exchange-correlation functionals has been assessed for the calculation of anharmonic vibrational frequencies using second-order vibrational perturbation theory with two- and four-mode couplings and compared to the recently developed transition optimized shifted Hermite method. A range of exchange-correlation functionals (B3LYP, BLYP, EDF1, EDF2, B97-1, B97-2, HCTH-93, HCTH-120, HCTH-147, and HCTH-407) have been evaluated with reference to a large experimental data set comprising 88 species and 655 modes as well as a smaller set of shifts in frequency because of anharmonicity derived from experimental data. The anharmonic frequencies calculated using hybrid functionals provide the best agreement with experiment, and are not significantly improved by frequency scaling factors, indicating an absence of significant systematic error. For the molecules studied, the B97-1 and B97-2 functionals give the closest overall agreement with experiment, although the improvement over the best case for pure harmonic frequencies is modest. Predictions of the experimental anharmonic shifts are closest for the B3LYP and EDF2 functionals, with B97-1 performing well because of a good description of the harmonic force field. Investigations using modified hybrid functionals with increased fractions of Hartree–Fock exchange indicate that approximately 20% Hartree–Fock exchange is optimal.

It is shown that by using a numerical integration grid of low quality and large two-electron pre-screening threshold, the computational cost of computing near-edge X-ray absorption fine structure (NEXAFS) spectra within time-dependent density functional theory can be reduced significantly with a very small loss in accuracy. This allows accurate NEXAFS spectra to be computed for relatively large molecules involving excitations from a large number of core orbitals using short-range corrected exchange-correlation functionals. The approach is illustrated by calculations of the carbon K-edge NEXAFS spectra of coronene and two semi-conducting polymers, where the calculations give good agreement with experiment and allow the origin of the different spectral features to be assigned.

The electronic absorption, electronic circular dichroism and X-ray absorption spectroscopy of the blue copper protein plastocyanin is studied with density functional theory, time-dependent density functional theory and multireference configuration interaction in conjunction with classical molecular dynamics simulations. A strong correlation is observed between the excitation energy of the intense ligand to metal charge transfer band and the copper–cysteine sulfur bond length. The results suggest that the copper–cysteine sulfur bond length in the crystal structure of plastocyanin is too short and should be closer to the corresponding bond lengths in related blue copper proteins. Averaging over many structural conformations is required to reproduce the major features of the experimental circular dichroism spectra. A correlation between the rotational strength of the ligand to metal charge transfer band and the distortion of the copper atom from the plane of the cysteine sulfur and histidine nitrogen atoms is found. X-ray absorption calculations show a smaller sulfur p orbital character in the singly occupied molecular orbital of cucumber basic protein compared to plastocyanin.

Recent advances in X-ray sources have led to a renaissance in spectroscopic techniques in the X-ray region. These techniques that involve the excitation of core electrons can provide an atom specific probe of electronic structure and provide powerful analytical tools that are used in many fields of research. Theoretical calculations can often play an important role in the analysis and interpretation of experimental spectra. In this perspective, we review recent developments in quantum chemical calculations of X-ray absorption spectra, focusing on the use of time-dependent density functional theory to study core excitations. The practical application of these calculations is illustrated with examples drawn from surface science and bioinorganic chemistry, and the application of these methods to study X-ray emission spectroscopy is explored.

We report calculations of core excitation energies and near-edge X-ray absorption fine structure (NEXAFS) spectra computed with time-dependent density functional theory (TDDFT). TDDFT with generalized gradient approximation and standard hybrid exchange–correlation functionals is known to underestimate core excitation energies. This failure is shown to be associated with the self-interaction error at short interelectronic distances. Short-range corrected hybrid functionals are shown to reduce the error in the computed core excitation energies for first and second row nuclei in a range of molecules to a level approaching that observed in more traditional excited states calculations in the ultraviolet region. NEXAFS spectra computed with the new functionals agree well with experiment and the pre-edge features in the NEXAFS spectra of plastocyanin are correctly predicted.

The near edge X-ray absorption fine structure and infrared spectroscopy of acetylene and benzene adsorbed on C(1 0 0)-2 × 1, Si(1 0 0)-2 × 1 and Ge(1 0 0)-2 × 1 surfaces is studied with density functional theory calculations. Time dependent density functional theory calculations of the near edge X-ray absorption fine structure with a modified exchange-correlation functional agree well with experiment, and show that the spectral features arise from excitation to π∗, σCH∗ and σXC∗ orbitals, where X represents C, Si or Ge. The σXC∗ excitation energies are dependent on the surface, and for acetylene, the location of the π∗ band also varies with the surface. Calculations of the vibrational modes show the CH stretching frequencies for carbon atoms bonded directly to the surface vary significantly between the three surfaces, while those for carbon atoms not bonded to the surface do not change significantly.

An empirical force field for carbon based upon the Murrell-Mottram potential is developed for the calculation of the vibrational frequencies of carbon nanomaterials. The potential is reparameterised using data from density functional theory calculations through a Monte-Carlo hessian-matching approach, and when used in conjunction with the empirical bond polarisability model provides an accurate description of the non-resonant Raman spectroscopy of carbon nanotubes and graphene. With the availability of analytical first and second derivatives, the computational cost of evaluating harmonic vibrational frequencies is a fraction of the cost of corresponding quantum chemical calculations, and makes the accurate atomistic vibrational analysis of systems with thousands of atoms possible. Subsequently, the non-resonant Raman spectroscopy of carbon nanotubes and graphene, including the role of defects and carbon nanotube junctions is explored.

The near edge X-ray absorption fine structure and infrared spectroscopy of acetylene and benzene adsorbed on C(1 0 0)-2 × 1, Si(1 0 0)-2 × 1 and Ge(1 0 0)-2 × 1 surfaces is studied with density functional theory calculations. Time dependent density functional theory calculations of the near edge X-ray absorption fine structure with a modified exchange-correlation functional agree well with experiment, and show that the spectral features arise from excitation to π∗, σCH∗ and σXC∗ orbitals, where X represents C, Si or Ge. The σXC∗ excitation energies are dependent on the surface, and for acetylene, the location of the π∗ band also varies with the surface. Calculations of the vibrational modes show the CH stretching frequencies for carbon atoms bonded directly to the surface vary significantly between the three surfaces, while those for carbon atoms not bonded to the surface do not change significantly.

The binding within the ethene–argon and formaldehyde–methane complexes in the ground and electronically excited states is studied with equation of motion coupled cluster theory (EOM-CCSD), second-order Møller–Plesset perturbation theory (MP2) and density functional theory with dispersion corrections (DFT-D). Electronically excited states are studied within MP2 and Kohn–Sham DFT formalisms by exploiting a procedure called the maximum overlap method that allows convergence of the relevant self-consistent field equations to higher energy (or excited state) solutions. Potential energy curves computed using MP2 are in good agreement with the EOM-CCSD calculations for both the valence and Rydberg excited states studied. For the DFT-D approach, B3LYP-D3/aug-cc-pVTZ calculations are found to be in agreement with EOM-CCSD for the ground and valence excited states. However, for the π3s Rydberg state of ethene–argon and the n3s Rydberg state of formaldehyde–methane significant deviation is observed, and this disagreement with EOM-CCSD is present for a variety of DFT-D based approaches. Variation of the parameters within the D2 dispersion correction results in closer agreement with EOM-CCSD for the Rydberg states but demonstrates that a different parameterisation from the ground state is required for these states. This indicates that time-dependent density functional theory calculations based upon a DFT-D reference may be satisfactory for excitations to valence states, but will potentially be inaccurate for excitations to Rydberg states, or more generally states where the nature of the electron density is significantly different from the ground state.

We report calculations of core excitation energies and near-edge X-ray absorption fine structure (NEXAFS) spectra computed with time-dependent density functional theory (TDDFT). TDDFT with generalized gradient approximation and standard hybrid exchange–correlation functionals is known to underestimate core excitation energies. This failure is shown to be associated with the self-interaction error at short interelectronic distances. Short-range corrected hybrid functionals are shown to reduce the error in the computed core excitation energies for first and second row nuclei in a range of molecules to a level approaching that observed in more traditional excited states calculations in the ultraviolet region. NEXAFS spectra computed with the new functionals agree well with experiment and the pre-edge features in the NEXAFS spectra of plastocyanin are correctly predicted.

The electronic absorption, electronic circular dichroism and X-ray absorption spectroscopy of the blue copper protein plastocyanin is studied with density functional theory, time-dependent density functional theory and multireference configuration interaction in conjunction with classical molecular dynamics simulations. A strong correlation is observed between the excitation energy of the intense ligand to metal charge transfer band and the copper–cysteine sulfur bond length. The results suggest that the copper–cysteine sulfur bond length in the crystal structure of plastocyanin is too short and should be closer to the corresponding bond lengths in related blue copper proteins. Averaging over many structural conformations is required to reproduce the major features of the experimental circular dichroism spectra. A correlation between the rotational strength of the ligand to metal charge transfer band and the distortion of the copper atom from the plane of the cysteine sulfur and histidine nitrogen atoms is found. X-ray absorption calculations show a smaller sulfur p orbital character in the singly occupied molecular orbital of cucumber basic protein compared to plastocyanin.

Recent advances in X-ray sources have led to a renaissance in spectroscopic techniques in the X-ray region. These techniques that involve the excitation of core electrons can provide an atom specific probe of electronic structure and provide powerful analytical tools that are used in many fields of research. Theoretical calculations can often play an important role in the analysis and interpretation of experimental spectra. In this perspective, we review recent developments in quantum chemical calculations of X-ray absorption spectra, focusing on the use of time-dependent density functional theory to study core excitations. The practical application of these calculations is illustrated with examples drawn from surface science and bioinorganic chemistry, and the application of these methods to study X-ray emission spectroscopy is explored.

The basin hopping search algorithm in conjunction with second-order Møller–Plesset perturbation theory is used to determine the lowest energy structures of the radical cation clusters (NH3)n˙+, (H2O)n˙+, (HF)n˙+, (PH3)n˙+, (H2S)n˙+ and (HCl)n˙+, where n = 2–4. The energies of the most stable structures are subsequently evaluated using coupled cluster theory in conjunction with the aug-cc-pVTZ basis set. These cationic clusters can adopt two distinct structural types, with some clusters showing an unusual type of bonding, often referred to as hemibonding, while other clusters undergo proton transfer to give an ion and radical. It is found that proton transfer based structures are preferred by the (NH3)n˙+, (H2O)n˙+ and (HF)n˙+ clusters while hemibonded structures are favoured by (PH3)n˙+, (H2S)n˙+ and (HCl)n˙+. These trends can be attributed to the relative strengths of the molecules and molecular cations as Brønsted bases and acids, respectively, and the strength of the interaction between the ion and radical in the ion–radical clusters.