FIG 4 - uploaded by Dieter Cremer
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Schematic representation of vibrational normal modes of b 1u -, b 2g -, and b 1g -symmetry. For those modes which preferentially involve the C 6 -framework, H atoms are not shown.
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The equilibrium geometry, harmonic vibrational frequencies, and infrared transition intensities of p-benzyne were calculated at the MBPT(2), SDQ-MBPT(4), CCSD, and CCSD(T) levels of theory using different reference wave functions obtained from restricted and unrestricted Hartree-Fock (RHF and UHF), restricted Brueckner (RB) orbital, and Generalized...
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Context 1
... Fig. 4, the b 1u -, b 2g -, and b 1g -symmetrical normal Fig. 2. All orbital Hessian eigenvalues were calculated at the RHF-CCSDT/6-31G(d,p) geometry. modes of p-benzyne are shown schematically. Those modes that lead to a pronounced change in the carbon framework i.e., the folding mode 8 , the chair mode 10 , and the deformation mode 18 , in ...
Context 2
... and the overlap between the b 1u -HOMO and *(CC) orbitals Fig. 1a, should be the most sensitive with regard to a geometry-dependent orbital mixing. As is evident from Table I, this is clearly the case. Furthermore, those normal modes that preferentially involve movements of the H atoms, on the other hand e.g., modes 9, 15, 16, and 17, as shown in Fig. 4, are less affected by orbital mixing, and should therefore be less influenced by the orbital near- instability effects. Nevertheless, the orbital mixings still have some impact on these modes, as indicated by anomalous IR intensities. It should be noted however, for p-benzyne, the effects expressed within the framework of Eq. 6 depend ...
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Citations
... The benzynes are prominent examples of organic diradicals 17,18 and display increasing open-shell character (due to orbital near-degeneracy) from the ortho to the para isomer. They have been studied both experimentally [19][20][21][22][23][24] and theoretically, [25][26][27][28][29][30][31][32][33] providing a potential target for future NEXAFS measurements. Our model is employed to interpret the NEXAFS spectra of the benzynes computed with FIG. 1. ...
Theoretical simulations are critical to analyze and interpret the x-ray absorption spectrum of transient open-shell species. In this work, we propose a model of the many-body core-excited states of symmetric diradicals. We apply this model to analyze the carbon K-edge transitions of o-, m-, and p-benzyne, three organic diradicals with diverse and unusual electronic structures. The predictions of our model are compared with high-level multireference computations of the K-edge spectrum of the benzynes obtained with the driven similarity renormalization group truncated to third order. Our model shows the importance of a many-body treatment of the core-excited states of the benzynes and provides a theoretical framework to understand which properties of the ground state of these diradicals can be extracted from their x-ray spectrum.
... Model chemistry used: To describe the spin-paired open shell singlet states, we applied a single determinant broken-symmetry (BS) unrestricted ansatz, which works well for systems with small singlet-triplet gaps [38,39], combined with a density functional theory (DFT) approach. We refrained from a multi-reference description, such as CASSCF, which has been mostly applied to unsubstituted species 4 with a relatively small active space and basis sets [40]. ...
In this work, we investigated the formation of protonated hydrogen cyanide HCNH+ and methylene amine cation CH[Formula: see text] (both identified in Titan's upper atmosphere) from three different pathways which stem from the interaction between CH4 and N+(3P). As a mechanistic tool, we used the Unified Reaction Valley Approach (URVA) complemented with the Local Mode Analysis (LMA) assessing the strength of the CN bonds formed in these reactions. Our URVA studies could provide a comprehensive overview on bond formation/cleavage processes relevant to the specific mechanism of eight reactions R1- R8 that occur across the three pathways. In addition, we could explain the formation of CH[Formula: see text] and the appearance of HCNH+ and CHNH[Formula: see text] along these paths. Although only smaller molecules are involved in these reactions including isomerization, hydrogen atom abstraction, and hydrogen molecule capture, we found a number of interesting features, such as roaming in reaction R3 or the primary interaction of H2 with the carbon atom in HCNH+ in reaction R8 followed by migration of one of the H2 hydrogen atoms to the nitrogen which is more cost effective than breaking the HH bond first; a feature often found in catalysis. In all cases, charge transfer between carbon and nitrogen could be identified as a driving force for the CN bond formation. As revealed by LMA, the CN bonds formed in reactions R1-R8 cover a broad bond strength range from very weak to very strong, with the CN bond in protonated hydrogen cyanide HCNH+ identified as the strongest of all molecules investigated in this work. Our study demonstrates the large potential of both URVA and LMA to shed new light into these extraterrestrial reactions to help better understand prebiotic processes as well as develop guidelines for future investigations involving areas of complex interstellar chemistry. In particular, the formation of CN bonds as a precursor to the extraterrestrial formation of amino acids will be the focus of future investigations. Formation of CN bonds in Titan's atmosphere visualized via the reaction path curvature.
... Model chemistry used: To describe the spin-paired open shell singlet states, we applied a single determinant broken-symmetry (BS) unrestricted ansatz, which works well for systems with small singlet-triplet gaps [38,39], combined with a density functional theory (DFT) approach. We refrained from a multi-reference description, such as CASSCF, which has been mostly applied to unsubstituted species 4 with a relatively small active space and basis sets [40]. ...
From local mode stretching force constants and topological electron density analysis, computed at either the UM06/6-311G(d,p), UM06/SDD, or UM05-2X/6–31++G(d,p) level of theory, we elucidate on the nature/strength of the parallel π-stacking interactions (i.e. pancake bonding) of the 1,2-dithia-3,5-diazolyl dimer, 1,2-diselena-3,5-diazolyl dimer, 1,2-tellura-3,5-diazolyl dimer, phenalenyl dimer, 2,5,8-tri-methylphenalenyl dimer, and the 2,5,8-tri-t-butylphenalenyl dimer. We use local mode stretching force constants to derive an aromaticity delocalization index (AI) for the phenalenyl-based dimers and their monomers as to determine the effect of substitution and dimerization on aromaticity, as well as determining what bond property governs alterations in aromaticity. Our results reveal the strength of the C⋯C contacts and of the rings of the di-chalcodiazoyl dimers investigated decrease in parallel with decreasing chalcogen⋯chalcogen bond strength. Energy density values Hb suggest the S⋯S and Se⋯Se pancake bonds of 1,2-dithia-3,5-diazolyl dimer and the 1,2-diselena-3,5-diazolyl dimer are covalent in nature. We observe the pancake bonds, of all phenalenyl-based dimers investigated, to be electrostatic in nature. In contrast to their monomer counterparts, phenalenyl-based dimers increase in aromaticity primarily due to CC bond strengthening. For phenalenyl-based dimers we observed that the addition of bulky substituents steadily decreased the system aromaticity predominately due to CC bond weakening.
... In contrast, the benzyne biradical represents a molecular system exhibiting high multireference correlation. [55][56][57][58] This system was chosen to serve as a test to evaluate if the inclusion of multi-reference character from an MC-PDFT calculation makes a significant difference in both the predictions of transmission and currents in the junction. In the more multireference systems, we expect to find the greatest deviation between the standard DFT functionals and MC-PDFT. ...
Due to their small size and unique properties, single-molecule electronics have long seen research interest from experimentalists and theoreticians alike. From a theoretical standpoint, modeling these systems using electronic structure theory can be difficult due to the importance of electron correlation in the determination of molecular properties, and this electron correlation can be computationally expensive to consider, particularly multiconfigurational correlation energy. In this work, we develop a new approach for the study of single-molecule electronic systems, denoted NEGF-MCPDFT, which combines multiconfiguration pair-density functional theory (MC-PDFT) with the non-equilibrium Green's function formalism (NEGF). The use of MC-PDFT with NEGF allows for the efficient inclusion of both static and dynamic electron correlation in the description of the junction's electronic structure. CASSCF wave functions are used as references in the MC-PDFT calculation, and like with any active space method, effort must be made to determine the proper orbital character to include in the active space. We perform conductance and transmission calculations on a series of alkanes (predominantly single-configurational character) and benzyne (multiconfigurational character), exploring the role that active space selection has on the computed results. For the alkane junctions explored (where dynamic electron correlation dominates), the MCPDFT-NEGF results agree well with DFT-NEGF results. For the benzyne junction (which has significant static correlation), we see clear differences in the MCPDFT-NEGF and DFT-NEGF results, and evidence that NEGF-MCPDFT is capturing additional electron correlation effects beyond those provided by the PBE functional.
... The para-benzyne radical presents as a more challenging case and has been the focus in comparing the ST gap obtained from various highly accurate theoretical methods to the available experimental result [98][99][100]103,[103][104][105] . The discrepency between experimental and theoretical results have been discussed in earlier works on the diradical 99,103 . ...
We present a practical approach to treat static and dynamical correlation accurately in large multi-configurational systems. The static correlation is accounted for using the spin-flip approach which is well known for capturing static correlation accurately at low-computational expense. Unlike previous approaches to add dynamical correlation to spin-flip models which use perturbation theory or coupled-cluster theory, we explore the ability to use the on-top pair-density functional theory approaches recently developed by Gagliardi and co-workers (JCTC, 10, 3669, 2014). External relaxations are carried out in the spin-flip calculations though a restricted active space framework for which a truncation scheme for the orbitals used in the external excitation is presented. The performance of the approach is demonstrated by computing energy gaps between ground and excited states for diradicals, triradicals and linear polyacene chains ranging from naphthalene to dodecacene. Accurate results are obtained using the new approach for these challenging open-shell molecular systems.
... The largest value of the diradical characteristic reached in diradicaloids is n s = 0.65 for p-By. Indeed, p-By is known to display pronounced diradical character 13,77,78 and the present result is consistent with the previous studies. ...
... 82 In the case of p-By, the C−C distance is 2.66 Å and is close to 2.69 Å from SF-CCSD/cc-pVTZ 46 and 2.71 Å from CCSD(T)/cc-pVTZ. 78 For o-By and m-By, there is a difference between the equilibrium C−C distances in the singlet and triplet states of ∼0.14 and ∼0.30 Å, respectively, which is larger than 0.06 Å for p-By. ...
Due to their multiconfigurational nature featuring strong electron correlation, accurate description of diradicals and diradicaloids is a challenge for quantum chemical methods. The recently developed mixed-reference spin-flip (MRSF)-TDDFT method is capable of describing the multiconfigurational electronic states of these systems while avoiding the spin-contamination pitfalls of SF-TDDFT. Here, we apply MRSF-TDDFT to study the adiabatic singlet–triplet (ST) gaps in a series of well-known diradicals and diradicaloids. On average, MRSF displays a very high prediction accuracy of the adiabatic ST gaps with the mean absolute error (MAE) amounting to 0.14 eV. In addition, MRSF is capable of accurately describing the effect of the Jahn–Teller distortion occurring in the trimethylenemethane diradical, the violation of the Hund rule in a series of the didehydrotoluene diradicals, and the potential energy surfaces of the didehydrobenzene (benzyne) diradicals. A convenient criterion for distinguishing diradicals and diradicaloids is suggested on the basis of the easily obtainable quantities. In all of these cases, which are difficult for the conventional methods of density functional theory (DFT), MRSF shows results consistent with the experiment and the high-level ab initio computations. Hence, the present study documents the reliability and accuracy of MRSF and lays out the guidelines for its application to strongly correlated molecular systems.
... In cases where the diradical character is significant, the frontier molecular orbitals should be nearly degenerate, so there must be more than one determinant of significant weight in the description of the electronic configuration [32,33]. However, although multi-reference methods should preferably be employed for treating systems with strongly correlated electrons [34][35][36], diradical character has already been evaluated from spin-unrestricted mono-reference methods [37], such as DFT [38][39][40][41][42]. In the unrestricted formalism of mono-reference methods the diradical character can be evaluated from (i) the frontier orbital energy gaps [43][44][45], (ii) the energy difference between singlet and triplet wave functions [46,47], and (iii) the occupation numbers of frontier natural orbitals (HONO and LUNO), from which the multiple diradical characters y i are defined as [28][29][30][31][48][49][50][51][52][53]: ...
Mesoionics are neutral compounds that cannot be represented by a fully covalent or purely ionic structure. Among the possible mesomeric structures of these compounds are the diradical electronic configurations. Theoretical and experimental studies indicate that some mesoionic rings are unstable, which may be related to a significant diradical character, that until then is not quantified. In this work, we investigated the diradical character of four heterocycles: 1,3-oxazol-5-one, 1,3-oxazol-5-thione, 1,3-thiazole-5-one, and 1,3-thiazole-5-thione. The oxazoles are known to be significatively less stable than thiazoles. DFT and ab initio single (B3LYP, MP2, CCSD, and QCISD) and ab initio multi-reference (MR-CISD) methods with three basis sets (6-311+G(d), aug-cc-pVDZ, and aug-cc-pVTZ) were employed to assess the diradical character of the investigated systems, in gas phase and DMSO solvent, from three criteria: (i) HOMO-LUMO energy gap, (ii) determination of energy difference between singlet and triplet wave functions, and (iii) quantification of the most significant diradical character (y0, determined in the unrestricted formalism). All of the results showed that the diradical character of the investigated systems is very small. However, the calculated electronic structures made it possible to identify the possible origin of the oxazoles instability, which can help the design of mesoionic systems with the desired properties.
... Better results are obtained with the broken-symmetry UHF reference, with complete spin symmetry-restoration via, e.g., subsequent CCSD calculation. 74 With this in mind, we explore UHF and UB3LYP trial wavefunctions for ph-AFQMC, in addition to multi-determinant trial wavefunctions from CASSCF. ...
The energy gap between the lowest-lying singlet and triplet states is an important quantity in chemical photocatalysis, with relevant applications ranging from triplet fusion in optical upconversion to the design of organic light-emitting devices. The ab initio prediction of singlet-triplet (ST) gaps is challenging due to the potentially biradical nature of the involved states, combined with the potentially large size of relevant molecules. In this work, we show that phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) can accurately predict ST gaps for chemical systems with singlet states of highly biradical nature, including a set of 13 small molecules and the ortho-, meta-, and para-isomers of benzyne. With respect to gas-phase experiments, ph-AFQMC using CASSCF trial wavefunctions achieves a mean averaged error of ~1 kcal/mol. Furthermore, we find that in the context of a spin-projection technique, ph-AFQMC using unrestricted single-determinant trial wavefunctions, which can be readily obtained for even very large systems, produces equivalently high accuracy. We proceed to show that this scalable methodology is capable of yielding accurate ST gaps for all linear polyacenes for which experimental measurements exist, i.e. naphthalene, anthracene, tetracene, and pentacene. Our results suggest a protocol for selecting either unrestricted Hartree-Fock or Kohn-Sham orbitals for the single-determinant trial wavefunction, based on the extent of spin-contamination. These findings pave the way for future investigations of specific photochemical processes involving large molecules with substantial biradical character.
... We have also carried out frequency calculations to confirm that the resulting geometries provided by IVO-SSMRPT(2,2) describe a local minimum. Crawford et al. [92] argued that, at the equilibrium (optimized) structure of singlet p-benzyne, RHF-based dynamical correlated calculations generate two large imaginary frequencies. Table 5 describes the computed harmonic vibrational frequencies for the singlet p-benzyne as obtained by the IVO-SSMRPT/cc-pVTZ gradient scheme along with the available experimental values. ...
... Accordance between our computed and experimental frequencies is satisfactory for seven experimentally measured frequencies. The agreement between IVO-SSMRPT and spin-unrestricted-CCSD (T) description [92] is acceptably good. The 2R-RMRCCSD and 2R-RMRCCSD(T), as well as the 2R-Mk-MRCCSD values, agree well with IVO-SSMRPT(2,2), the deviations amounting to 5-250 cm −1 . ...
... The 2R-RMRCCSD and 2R-RMRCCSD(T), as well as the 2R-Mk-MRCCSD values, agree well with IVO-SSMRPT(2,2), the deviations amounting to 5-250 cm −1 . It should be noted that although R-CCSD(T) yields very large imaginary frequencies for ω 13 and ω 12 , [92] the present IVO-SSMRPT yield real frequencies for these two challenging modes as that of the MRCC, SF-based and U-CCSD bers closely, the deviation amounting to 49 cm −1 [84] . Thus, the result is improved noticeably using the MCSSCF orbitals instead of RHF ones. ...
IVO‐SSMRPT is an affordable and accurate type of state‐specific multireference perturbation (SSMRPT) theory that adds dynamic correlation energy to improved virtual orbital (IVO) complete active space configuration interaction (CASCI) wave functions using a single‐root parametrization of multi‐root Hilbert‐space ansatz. We applied it to many chemically important di‐ and tri‐radicals to analyze the geometries and electronic properties of spectroscopic interest for both closed‐ and open‐shell singlet‐ and nonsinglet ground as well as excited states. We observed that IVO‐SSMRPT identifies optimized geometries, splitting between multiplets and frequencies for several radicals that are similar to those displayed by current generation state‐of‐the‐art methods but with admiringly decreased computational effort. This study illustrates the importance of having an accurate treatment of both nondynamical and dynamical correlation effects when examining multiradical species. Chemically and spectroscopically relevant answers can be obtained using our computationally tractable method. Our method will be a serviceable avenue for portraying open‐shell interactions in other radicals. Interest in organic radicals is fuelled by their potential role in designing organic materials and complex electronic structure. A multireference perturbative method with improved virtual orbitals has been used as an affordable, efficient and robust device for studying radicals. The method is tailored to tackle open‐ and closed‐shell states with the same accuracy. An intricate balance between different correlation effects is tangled in the accurate description of multiple states and their gaps.
... They occur, for example, in most molecular dissociations to open-shell fragments. At the mean-field level, these degeneracies are associated with symmetry breaking, and can be detected by examining the eigenvalues of the symmetry adapted molecular orbital (MO) Hessian where they lead to wellstudied instabilities of singlet, triplet and complex character [4,5]. Already, we have shown that symmetry projected methods in their variation after projection version [6][7][8] are capable of dealing with accidental degeneracies in a variety of practical contexts [9][10][11]. ...
We study the behavior of Hartree-Fock (HF) solutions in the vicinity of conical intersections. These are here understood as regions of a molecular potential energy surface characterized by degenerate or nearly-degenerate eigenfunctions with identical quantum numbers (point group, spin, and electron number). Accidental degeneracies between states with different quantum numbers are known to induce symmetry breaking in HF. The most common closed-shell restricted HF instability is related to singlet-triplet spin degeneracies that lead to collinear unrestricted HF (UHF) solutions. Adding geometric frustration to the mix usually results in noncollinear generalized HF (GHF) solutions, identified by orbitals that are linear combinations of up and down spins. Near conical intersections, we observe the appearance of coplanar GHF solutions that break all symmetries, including complex conjugation and time-reversal, which do not carry good quantum numbers. We discuss several prototypical examples taken from the conical intersection literature. Additionally, we utilize a recently introduced a magnetization diagnostic to characterize these solutions, as well as a solution of a Jahn-Teller active geometry of H$_8^{+2}$.
