Ab initio calculation of the electronic structures of the 3Phi ground and 5Phi excited states of CoH

The electronic structures and the spectroscopic constants of the electronic ground 3Phi and low-lying 5Phi electronic excited states of the CoH molecule were studied by multireference single and double excitation configuration interaction (MR-SDCI)+Davidson's correction (Q) calculations and size-consistent multireference coupled pair approximation (MRCPA) calculations. Calculations were performed under Cinfinityv symmetry using Slater-type basis functions. The electronic ground state was confirmed to be the 3Phi state. It was found that at least four reference configurations were needed to describe the ground 3Phi state correctly at the MR-SDCI+Q level, while the 5Phi state can be described well by one reference configuration, namely, the Hartree-Fock configuration. Larger dynamical electron correlation for the low-spin 3Phi state than that for the high-spin 5Phi state is discussed. Spectroscopic constants, i.e., equilibrium bond lengths (re), harmonic frequency (omegae), and excitation energy, obtained by the MR-SDCI+Q method showed good correspondence with experimental values. MRCPA calculations gave a slightly shorter value for re than experimental values, but improved omegae and the excitation energy bringing them very close to experimental values.     

Ab initio molecular orbital study of ground and low-lying electronic states of CoCN

The ground and low-lying excited states of CoCN have been studied by ab initio multireference single and double excitation configuration interaction (MR-SDCI) calculations with Davidson's correction Q and Cowan-Griffin's relativistic corrections. The electronic ground state of CoCN is (3)Phi(i) and the equilibrium geometry is linear with bond lengths of r(e)(Co-C)=1.8540 A and r(e)(C-N)=1.1677 A, substantially different from the experimentally derived values of r(0)(Co-C)=1.8827(7) A and r(0)(C-N)=1.1313(10) A. The first excited state is (3)Delta(i), separated from the ground state by 727 cm(-1). Larger dynamical electron correlation energy for the low-spin (3)Phi state than for the high-spin (5)Phi state makes the (3)Phi state to be the ground state, which is discussed in terms of the differences in natural orbitals. A new spin-orbit interaction scheme between the X (3)Phi(i) and 1 (3)Delta(i) states is proposed.     

Ground and lowest-lying electronic states of CoN. A multiconfigurational study

The lowest-lying X1Sigma+, a3Phi, b3II, c5Delta, A1Phi, and B1II electronic states of CoN have been investigated at the ab initio MRCI and MS-CASPT2 levels, with extended atomic basis sets and inclusion of scalar relativistic effects. Among the singlet states, the A1Phi and B1II states have been described for the first time. Potential energy curves, excitation energies, spectroscopic constants, and bonding character for all states are reported. Comparison with other early transition-metal nitrides (ScN, TiN, VN, and CrN), isoelectronic (NiC) and isovalent (RhN and IrN) species has been made, besides analyzing the B1II <=> X1+ electronic transition in terms of Franck-Condon factors, Einstein coefficients, and radiative lifetimes. At both levels of theory, the following energetic order has been obtained: X1Sigma+, a3Phi, b3II, c5Delta, A1Phi, and B1II, with good agreement with experimental results. In contrast, previous DFT and MRCI calculations predicted the ground state to be the 5Delta state.     

Low-lying electronic states of the Ti2 dimer: electronic absorption spectroscopy in rare gas matrices in concert with quantum chemical calculations

Absorption spectra were measured for Ti2 in Ne and Ar matrices. The spectra give evidence for several electronic transitions in the region between 4000 and 10 000 cm(-1) and provide important information about some excited electronic states of Ti2 in proximity to the ground state. The vibrational fine structure measured for these transitions allowed to calculate the force constants and the anharmonicity of the potential energy curves of the excited states, and to estimate changes in the internuclear Ti-Ti distances relative to the electronic ground state. The quantum chemical studies confirm the previously suggested (3)Delta(g) state as the ground state of Ti2. The equilibrium bond distance is calculated to be 195.4 pm. The calculated harmonic frequency of 432 cm(-1) is in good agreement with the experimental value of 407.0 cm(-1). With the aid of the calculations it was possible to assign the experimentally observed transitions in the region between 4000 and 10 000 cm(-1) to the 1 (3)Pi(u)<--(3)Delta(g), 1 (3)Phi(u)<--(3)Delta(g), 2 (3)Pi(u)<--(3)Delta(g), 2 (3)Phi(u)<--(3)Delta(g), and (3)Delta(u)<--(3)Delta(g) excitations (in the order of increasing energy). The calculated relative energies and harmonic frequencies are in pleasing agreement with the experimentally obtained values, with deviations of less than 5% and 2%, respectively. The bond distances estimated on the basis of the experimental spectra tally satisfactorily with the predictions of our calculations.     

A Fock space coupled cluster study on the electronic structure of the UO(2), UO(2) (+), U(4+), and U(5+) species

The ground and excited states of the UO(2) molecule have been studied using a Dirac-Coulomb intermediate Hamiltonian Fock-space coupled cluster approach (DC-IHFSCC). This method is unique in describing dynamic and nondynamic correlation energies at relatively low computational cost. Spin-orbit coupling effects have been fully included by utilizing the four-component Dirac-Coulomb Hamiltonian from the outset. Complementary calculations on the ionized systems UO(2) (+) and UO(2) (2+) as well as on the ions U(4+) and U(5+) were performed to assess the accuracy of this method. The latter calculations improve upon previously published theoretical work. Our calculations confirm the assignment of the ground state of the UO(2) molecule as a (3)Phi(2u) state that arises from the 5f(1)7s(1) configuration. The first state from the 5f(2) configuration is found above 10,000 cm(-1), whereas the first state from the 5f(1)6d(1) configuration is found at 5,047 cm(-1).     

Prediction of a Neutral Noble Gas Compound in the Triplet State

Discovery of the HArF molecule associated with H?Ar covalent bonding [Nature, 2000 , 406, 874–876] has revolutionized the field of noble gas chemistry. In general, this class of noble gas compound involving conventional chemical bonds exists as closed‐shell species in a singlet electronic state. For the first time, in a bid to predict neutral noble gas chemical compounds in their triplet electronic state, we have carried out a systematic investigation of xenon inserted FN and FP species by using quantum chemical calculations with density functional theory and various post‐Hartree–Fock‐based correlated methods, including the multireference configuration interaction technique. The FXeP and FXeN species are predicted to be stable by all the computational methods employed in the present work, such as density functional theory (DFT), second‐order Møller–Plesset perturbation theory (MP2), coupled‐cluster theory (CCSD(T)), and multireference configuration interaction (MRCI). For the purpose of comparison we have also included the Kr‐inserted compounds of FN and FP species. Geometrical parameters, dissociation energies, transition‐state barrier heights, atomic charge distributions, vibrational frequency data, and atoms‐in‐molecules properties clearly indicate that it is possible to experimentally realize the most stable state of FXeP and FXeN molecules, which is triplet in nature, through the matrix isolation technique under cryogenic conditions.     

Energy-consistent relativistic pseudopotentials for the 4d elements: atomic and molecular applications

Recently reported energy-consistent relativistic pseudopotentials have been used with series of matching correlation consistent basis sets in benchmark calculations of various atomic and molecular properties. The basis set convergence of the 4d metal electron affinities and 5s2-->5s0 excitation energies are reported at the CCSD(T) level of theory, and the effects of valence and 4s4p correlation are investigated. In addition the impact of correlating the low-lying 3d electrons was also studied in all-electron Douglas-Kroll-Hess (DKH) calculations, which also included the ionization potentials and 5s2-->5s1 excitation energies. For all four atomic properties, higher order coupled cluster calculations through CCSDTQ are reported. The final calculated values are generally all within 1 kcal/mol of experiment. A notable exception is the ionization potential of Tc, the currently accepted experimental value of which is suggested to be too high by about 3 kcal/mol. Molecular calculations are also reported for the low-lying electronic states of ZrO and RuF, as well as the ground electronic state of Pd2. The effects of spin-orbit coupling are investigated for these cases in pseudopotential calculations. Wherever possible, the pseudopotential results have been calibrated against DKH calculations with correlation consistent basis sets of triple-zeta quality. In all cases the calculated data for these species are in very good agreement with experiment. In particular, the correct electronic ground state for the RuF molecule (4Phi92) was obtained, which was made possible by utilizing systematic sequences of correlation consistent basis sets.     

Calculations of nuclear quadrupole coupling in noble gas-noble metal fluorides: interplay of relativistic and electron correlation effects

The nuclear quadrupole coupling constants (NQCCs) of noble gas and noble metal nuclei in the recently found noble gas-noble metal fluorides (NgMF, where Ng=Ar,Kr,Xe and M=Cu,Ag,Au) are obtained theoretically by high-level ab initio calculations, where both relativistic and electron correlation effects are included, and compared to experimental results. Fully relativistic four-component Dirac-Hartree-Fock (DHF) calculations are carried out at the basis set limit for electric field gradient that couples with the electric quadrupole moment of the nucleus, and uncorrelated relativistic effects are extracted by comparing DHF results to nonrelativistic (NR) HF calculations. Electron correlation effects are investigated both at fully relativistic second-order Moller-Plesset (DMP2) and at NR MP2 levels of theory, as well as at the NR coupled-cluster singles and doubles with perturbational triples [CCSD(T)] level. The validity of the approximation where relativistic effects, on the one hand, and nonrelativistically obtained correlation effects, on the other hand, are evaluated separately and assumed to be additive, is investigated by comparison with the DMP2 results. Inclusion of relativistic effects is shown to be necessary for obtaining the correct NQCC trends as the nucleus of interest and/or its neighbors become heavier. Electron correlation treatment is needed for approaching quantitative agreement with the experimental NQCCs. The assumption of additive electron correlation and relativistic effects, corresponding to the NR correlation treatment added on top of relativistic DHF data, gives qualitatively correct noble gas NQCCs. For noble metal NQCCs, correlation treatment at the relativistic level of theory is mandatory for reaching agreement with experimental results. Current work also confirms the experimental trends of NQCCs, which have been taken as an indication of nearly covalent interaction between noble gas and noble metal in the heaviest present systems, especially in XeAuF.     

The role of the beta-ionone ring in the photochemical reaction of rhodopsin

Time-dependent density functional theory (TDDFT) calculations on the photoabsorption process of the 11-cis retinal protonated Schiff base (PSB) chromophore show that the Franck-Condon relaxation of the first excited state of the chromophore involves a torsional twist motion of the beta-ionone ring relative to the conjugated retinyl chain. For the ground state, the beta-ionone ring and the retinyl chain of the free retinal PSB chromophore form a -40 degrees dihedral angle as compared to -94 degrees for the first excited state. The double bonds of the retinal are shorter for the fully optimized structure of the excited state than for the ground state suggesting a higher cis-trans isomerization barrier for the excited state than for the ground state. According to the present TDDFT calculations, the excitation of the retinal PSB chromophore does not primarily lead to a reaction along the cis-trans torsional coordinate at the C11-C12 bond. The activation of the isomerization center seems to occur at a later stage of the photo reaction. The results obtained at the TDDFT level are supported by second-order M?ller-Plesset (MP2) and approximate singles and doubles-coupled cluster (CC2) calculations on retinal chromophore models; the MP2 and CC2 calculations yield for them qualitatively the same ground state and excited-state structures as obtained in the density functional theory and TDDFT calculations.     

Homolytic vs heterolytic paths in the photochemistry of haloanilines

The photochemistry of 4-haloanilines and 4-halo-N,N-dimethylanilines has been studied in apolar, polar aprotic, and protic solvents. Photophysical and flash photolysis experiments show that the reaction proceeds in any case from the triplet state. It is rather unreactive in apolar media, the highest value being Phi = 0.05 for the iodoanilines in cyclohexane. Changing the solvent has little effect for iodoanilines and for the poorly reacting bromo analogue, while it leads to a variation of over 2 orders of magnitude in the quantum yield for the chloro and fluoro derivatives. The triplets have been characterized at the UB3LYP/6-31G(d) level of theory, evidencing a deformation and an elongation (except for C-F) of the C-X bond. Homolytic fragmentation is in every case endothermic, but calculations in acetonitrile solution show that heterolytic cleavage of C-Cl and C-Br is exothermic. Experimentally, the occurrence of heterolytic fragmentation has been monitored through selective trapping of the resulting phenyl cation by allyltrimethylsilane. Heterolytic dechlorination occurs efficiently in polar media (e.g., Phi = 0.77 in MeCN), while debromination remains ineffective due to the short lifetime of the triplet. Heterolytic defluorination is efficient only in protic solvents (Phi = 0.48 in MeOH), in accord with calculations showing that in the presence of an ancillary molecule of water fragmentation is exothermic due to the formation of the strong H-F bond. The energy profile for both homo- and heterolytic dissociation paths has been mapped along the reaction coordinates in the gas phase and in acetonitrile. The conditions determining the efficiency and mode of dehalogenation have been defined. This is significant for devising synthetic methods via photogenerated phenyl cations and for rationalizing the photodegradation of halogenated aromatic pollutants and the phototoxic effect of some fluorinated drugs.     

Bonding of multiple noble-gas atoms to CUO in solid neon: CUO(Ng)n (Ng=Ar, Kr, Xe; n=1, 2, 3, 4) complexes and the singlet-triplet crossover point

Laser-ablated U atoms co-deposited with CO in excess neon produce the novel CUO molecule, which forms distinct Ng complexes (Ng=Ar, Kr, Xe) with the heavier noble gases. The CUO(Ng) complexes are identified through CO isotopic and Ng reagent substitution and comparison to results of DFT frequency calculations. The U[bond]C and U[bond]O stretching frequencies of CUO(Ng) complexes are slightly red-shifted from neon matrix (1)Sigma(+) CUO values, which indicates a (1)A' ground state for the CUO(Ng) complexes. The CUO(Ng)(2) complexes in excess neon are likewise singlet molecules. However, the CUO(Ng)(3) and CUO(Ng)(4) complexes exhibit very different stretching frequencies and isotopic behaviors that are similar to those of CUO(Ar)(n) in a pure argon matrix, which has a (3)A" ground state based on DFT vibrational frequency calculations. This work suggests a coordination sphere model in which CUO in solid neon is initially solvated by four or more Ne atoms. Up to four heavier Ng atoms successively displace the Ne atoms leading ultimately to CUO(Ng)(4) complexes. The major changes in the CUO stretching frequencies from CUO(Ng)(2) to CUO(Ng)(3) provides evidence for the crossover from a singlet ground state to a triplet ground state.     

Substituent effects on the energetics and aromaticity of aminomethylbenzoic acids

The standard (p0 = 0.1 MPa) molar enthalpies of combustion of six aminomethylbenzoic acids were measured at T = 298.15 K by static bomb calorimetry. With these values, the standard molar enthalpies of formation in the crystalline state were obtained. Combining these results with the standard molar enthalpies of sublimation, the standard molar enthalpies of formation in the gaseous phase were derived. For the 10 possible isomers, the obtained experimental results were compared to and correlated with the relative stability obtained by ab initio calculations at the B3LYP/6-311++G(d,p) level of theory. Seeking a better understanding of the aromatic behavior and energetics of aminomethylbenzoic acids in the gas phase, calculations of NICS values, HOMA indices, and dihedral angles between the aromatic carbon and the amino group, Phi(Ar-NHH), were also performed computationally. The significant differences observed in the energetics, as well as in the NICS values, HOMA indices, and Phi(Ar-NHH) dihedral angles for these 10 isomers suggest a strong dependency on the identity and relative position of the three substituents on the benzene ring. This study points out a marked tendency for a decrease of the ring aromaticity, accompanied by an increase in the respective system stability, as the conjugation between the substituents becomes more extensive.     

Noble gas-actinide complexes of the CUO molecule with multiple Ar,Kr, and Xe atoms in noble-gas matrices

Laser-ablated U atoms react with CO in excess argon to produce CUO, which is trapped in a triplet state in solid argon at 7 K, based on agreement between observed and relativistic density functional theory (DFT) calculated isotopic frequencies ((12)C(16)O, (13)C(16)O, (12)C(18)O). This observation contrasts a recent neon matrix investigation, which trapped CUO in a linear singlet state calculated to be about 1 kcal/mol lower in energy. Experiments with krypton and xenon give results analogous to those with argon. Similar work with dilute Kr and Xe in argon finds small frequency shifts in new four-band progressions for CUO in the same triplet states trapped in solid argon and provides evidence for four distinct CUO(Ar)(4-n)(Ng)(n) (Ng = Kr, Xe, n = 1, 2, 3, 4) complexes for each Ng. DFT calculations show that successively higher Ng complexes are responsible for the observed frequency progressions. This work provides the first evidence for noble gas-actinide complexes, and the first example of neutral complexes with four noble gas atoms bonded to one metal center.     

Effects of localized triplet exciton on reactivity of photoinduced omega-bond dissociation in naphthyl phenyl ketones having pi,pi* lowest triplet (T1) states studied by laser flash photolysis

Photochemical properties of photoinduced omega-bond dissociation in naphthyl phenyl ketones having a phenylthiyl moiety as a leaving group, p-(alpha-naphthoyl)benzyl phenyl sulfide (NBPS) and 4-benzoyl-1-naphthylmethyl phenyl sulfide (BNMPS), in solution were investigated by laser flash photolysis techniques. Both ketones were shown to undergo photoinduced omega-bond cleavage of the C-S bond to release the phenyl thiyl radical (PTR) at room temperature. Irrespective of excitation wavelengths of NBPS, a quantum yield (Phi(rad)) of the PTR formation was obtained to be 0.1, whereas that for BNMPS was found to depend on the excitation wavelength, i.e., absorption bands from the ground state (S0) to the excited singlet states, S3, S2, and S1 of BNMPS; Phi(rad)(S3) = 0.77 and Phi(rad)(S2) = Phi(rad)(S1) = 1.0. By using triplet sensitization of p-phenylbenzophenone (PBP), efficiencies (alpha(rad)) of the radical formation in the lowest triplet state (T1(pi,pi*)) of NBPS and BNMPS were determined to be 0 and 1.0, respectively. The agreement between Phi(rad)(S1) and alpha(rad) values for BNMPS indicates that the C-S bond dissociation occurs in the T1 state via the S1 state via a fast intersystem crossing from the S1 to the T1 state. The wavelength dependence of the radical yields upon direct excitation of BNMPS was interpreted in terms of the C-S bond cleavage in the S3 state competing with internal conversion from the S3 to the S2 state. The smaller value of Phi(rad)(S3) than those of Phi(rad)(S1) and Phi(rad)(S2) was proposed to originate from the geminate recombination of singlet radical pairs produced by the bond dissociation via the S3 state. Photoinduced omega-cleavage of NBPS was concluded to take place only in the S1(n,pi*) state. Difference in reactivity of omega-cleavage between the triplet states of NBPS and BNMPS was interpreted in terms of localized triplet exciton in the naphthoyl moieties.     

The electronic spectrum of the UO2 molecule

The electronic spectrum of the UO(2) molecule has been determined using multiconfigurational wave functions together with the inclusion spin-orbit coupling. The molecule has been found to have a (5fphi)(7s), (3)Phi(2u), ground state. The lowest state of gerade symmetry,( 3)H(4g), corresponding to the electronic configuration (5f)(2) was found 3330 cm(-1) above the ground state. The computed energy levels and oscillator strengths were used for the assignment of the experimental spectrum in the energy range 17,000-19,000 and 27,000-32,000 cm(-1).     

On the noble-gas-induced intersystem crossing for the CUO molecule: experimental and theoretical investigations of CUO(Ng)n (Ng = Ar, Kr, Xe; n = 1, 2, 3, 4) complexes in solid neon

Uranium atoms excited by laser ablation react with CO in excess neon to produce the novel CUO molecule, which forms distinct Ng complexes (Ng = Ar, Kr, Xe) when the heavier noble gases are added. The CUO(Ng) complexes are identified through CO isotopic and Ng substitution on the neon matrix infrared spectra and by comparison to DFT frequency calculations. The U-C and U-O stretching frequencies of CUO(Ng) complexes are slightly red-shifted from frequencies for the (1)Sigma(+) CUO ground state, which identifies singlet ground state CUO(Ng) complexes. In solid neon the CUO molecule is also a complex CUO(Ne)(n), and the CUO(Ne)(n-1)(Ng) complexes are likewise specified. The next singlet CUO(Ne)(x)(Ng)(2) complexes in excess neon follow in like manner. However, the higher CUO(Ne)(x)(Ng)(n) complex (n = 3, 4) stretching modes approach pure argon matrix CUO(Ar)(n) values and isotopic behavior, which are characterized as triplet ground state complexes by DFT frequency calculations. This work suggests that the singlet-triplet crossing occurs with 3 Ar, 3 Kr, or 4 Xe and a balance of Ne atoms coordinated to CUO in the neon matrix host.     

Theoretical study of the external heavy atom effect on phosphorescence of free-base porphin molecule

The radiative lifetime of phosphorescence of free-base porphin (H2P) molecule and its complexes with noble-gas atoms are calculated by time-dependent density functions theory (TD DFT) with quadratic response functions for account of spin-orbit coupling and electric dipole activity. The complexes with Ne, Ar, Kr, and Xe are used to simulate the external heavy atom (EHA) effect on phosphorescence of the H2P molecule in the corresponding noble gas matrices. The B3LYP functional and small basis set (3-21G) are used throughout the study and comparison of all complexes but other basis sets are also utilized to support the chosen approach. A slow radiative rate constant of free-base porphin phosphorescence (about 10(-3) s(-1)) is obtained with all basis sets being in the order of magnitude agreement with experimental estimations. A strong enhancement of the H2P phosphorescence rate (by 360 times) is calculated for Xe complex; while for Ne, Ar, and Kr complexes, the enhancement is equal to 1.1, 1.3, and 10.3 times, respectively. In these complexes, the noble gas atom is disposed at 3.6 A above the center of the porphin ring. In spite of shortcomings of the chosen simple model, the TD DFT calculations explain the most important features of the EHA effect on phosphorescence of free-base porphin. Calculations of the hyperfine coupling tensors for all magnetic nuclei in the lowest triplet state of H2P molecule and its complexes with noble-gas atoms indicate an appreciable penetration of the spin density to the EHA region. This can be connected with the enhancement of spin-orbit coupling in the H2P molecule.     

Potential energy surfaces and dynamics of Ni2+ ion aqueous solution: molecular dynamics simulation of the electronic absorption spectrum

We develop a model effective Hamiltonian for describing the electronic structures of first-row transition metals in aqueous solutions using a quasidegenerate perturbation theory. All the states consisting of 3d(n) electronic configurations are determined by diagonalizing a small effective Hamiltonian matrix, where various intermolecular interaction terms such as the electrostatic, polarization, exchange, charge transfer, and three-body interactions are effectively incorporated. This model Hamiltonian is applied to constructing the ground and triplet excited states potential energy functions of Ni(2+) in aqueous solution, based on the ab initio multiconfiguration quasidegenerate perturbation theory calculations. We perform molecular dynamics simulation calculations for the ground state of Ni(2+) aqueous solution to calculate the electronic absorption spectral shape as well as the ground state properties. Agreement between the simulation and experimental spectra is satisfactory, indicating that the present model can well describe the Ni(2+) excited state potential surfaces in aqueous solution.     

Analytic energy gradients in combined second order Møller-Plesset perturbation theory and conductorlike polarizable continuum model calculation

The analytic energy gradients in combined second order M?ller-Plesset perturbation theory and conductorlike polarizable continuum model calculations are derived and implemented for spin-restricted closed shell (RMP2), Z-averaged spin-restricted open shell (ZAPT2), and spin-unrestricted open shell (UMP2) cases. Using these methods, the geometries of the S(0) ground state and the T(1) state of three nucleobase pairs (guanine-cytosine, adenine-thymine, and adenine-uracil) in the gas phase and aqueous solution phase are optimized. It is found that in both the gas phase and the aqueous solution phase the hydrogen bonds in the T(1) state pairs are weakened by ~1 kcal/mol as compared to those in the S(0) state pairs.     

Identification of the matrix shift: a fingerprint for neutral neon complex?

Ar-NiCO and Ne-NiCO have been predicted as novel neutral noble gas charge-transfer complexes, with binding energies of 7.70 and 2.16 kcal/mol, respectively, by the highly correlated coupled-cluster singles and doubles including a perturbational estimate of triple excitations calculations. The calculated shifts in the Ni-C-O bending frequency are 48 and 36 cm(-1) for Ar-NiCO and Ne-NiCO, while the corresponding experimental matrix shifts are 46 and 36 cm(-1), respectively. The anharmonicity effects for these frequencies are verified to be very small. The interaction between a noble gas atom and NiCO is discussed through natural population analyses and the electron density difference map. We further examined the noble gas matrix effects on the geometrical structure and vibrational frequencies of NiCO by performing density functional theory calculations for the Ng31-NiCO (Ng = Ar, Ne, He) system. The present results will inspire the further experimental investigation on the complexes of noble gas and transition metal compounds generated in the matrix isolation experiments.