Polarization Propagator Approach Research Articles

Efficient and Parallel Implementation of Real and Complex Response Functions Employing the Second-Order Algebraic-Diagrammatic Construction Scheme for the Polarization Propagator.

We present the implementation of an efficient matrix-folded formalism for the evaluation of complex response functions and the calculation of transition properties at the level of the second-order algebraic-diagrammatic construction (ADC(2)) scheme. The underlying algorithms, in combination with the adopted hybrid MPI/OpenMP parallelization strategy, enabled calculations of the UV/vis spectra of a guanine oligomer series ranging up to 1032 contracted basis functions, thereby utilizing vast computational resources from up to 32,768 CPU cores. Further analysis of the convergence behavior of the involved iterative subspace algorithms revealed the superiority of a frequency-separated treatment of response equations even for a large spectral window, including 101 frequencies. We demonstrate the applicability to general quantum mechanical operators by the first reported electronic circular dichroism spectrum calculated with a complex polarization propagator approach at the ADC(2) level of theory.

Complex Linear Response Functions for a Multiconfigurational Self-Consistent Field Wave Function in a High Performance Computing Environment.

We present novel developments for the highly efficient evaluation of complex linear response functions of a multiconfigurational self-consistent field (MCSCF) wave function as implemented in MultiPsi. Specifically, expressions for the direct evaluation of linear response properties at given frequencies using the complex polarization propagator (CPP) approach have been implemented, within both the Tamm-Dancoff approximation (TDA) and the random phase approximation (RPA). Purely real algebra with symmetric and antisymmetric trial vectors in a shared subspace is used wherein the linear response equations are solved. Two bottlenecks of large scale MC-CPP calculations, namely, the memory footprint and computational time, are addressed. The former is addressed by limiting the size of the subspace of trial vectors by using singular value decomposition (SVD) on either orbital or CI subspaces. The latter is addressed using an efficient parallel implementation as well as the strategy of dynamically adding linear response equations at near-convergence to neighboring roots. Furthermore, a novel methodology for decomposing MC-CPP spectra in terms of intuitive orbital excitations in an approximate fashion is presented. The performance of the code is illustrated with several numerical examples, including the X-ray spectrum of a molecule with nearly one hundred atoms. Additionally, for X-ray spectroscopy, the effect of including or excluding the core orbital in the active space on small covalent metal complexes is discussed.

Characterization of tetrakis(thiadiazole)porphyrazine metal complexes by magnetic circular dichroism and magnetic circularly polarized luminescence.

The magnetic circular dichroism (MCD) spectra of metal complexes of tetrakis(thiadiazole)porphyrazines ([TTDPzM] with M = 2HI , ZnII , MgII (H2 O), and CdII ) have been recorded in dimethyl formamide solution. Together with the UV-Vis spectra, the MCD spectra provide useful information about the structure and electronic properties of the complexes. The experimental UV-Vis and MCD spectra compare pretty well with DFT calculations of two sorts, based either on the sum-over-states (SOS) approach or on the complex polarization propagator approach. They further corroborate the findings and interpretation of MCD spectra of porphyrazines based on the model of Michl for peripheral molecular orbitals. Magnetic circularly polarized luminescence (MCPL) spectra, quite uncommon in the literature, have been recorded for [TTDPzM] (M = 2HI , ZnII , MgII (H2 O)).

Relativistic and electron correlation effects on NMR J-coupling of Sn and Pb containing molecules

We studied the influence of relativistic and electron correlation effects on NMR J-couplings in the following set of heavy-atom containing molecules: \(XY_4\) and H\(_3XX\)H\(_3\) (X = Sn, Pb; Y = H, F, Cl, Br, I). We applied two formalisms, the relativistic polarization propagator approach at random phase level of approach (RelPPA-RPA) and density functional theory (DFT) with functionals as implemented in the DIRAC code. We have chosen four functionals that have different amount of HF exchange (PBE0, B3LYP, BLYP, BP86). For those molecular systems, results of calculations with BLYP functional have the best performance as compared with available experimental data. As was previously found for magnetic shieldings in other molecular systems we are able to show here that DFT functionals must be modified in order to obtain reliable results of NMR J-coupling within the relativistic regime. We can state that there is a non-linear dependence among both, electron correlation and relativistic effects that should be introduced in the functionals. The functionals implemented in the DIRAC code are standard nonrelativistic ones which were parameterized with data taken from light-atom containing molecules. This explains why they are not able to properly introduce relativistic effects on NMR parameters, like J-coupling constant. Lastly we show that in the analysis of J-couplings for the family of compounds mentioned above, one must consider the effects of a third heavy-atom that is close to the J-coupled atoms of the same molecule, specially for \(^n\)J(H–H). This kind of effect is similar to the newest and so called heavy-atom effect on vicinal heavy atoms, HAVHA, proposed for the NMR-shielding constant. Such effects are among the most important relativistic effects in the family of compounds studied in this work.

A Polarization Propagator for Nonlinear X-ray Spectroscopies.

A complex polarization propagator approach has been developed to third order and implemented in density functional theory (DFT), allowing for the direct calculation of nonlinear molecular properties in the X-ray wavelength regime without explicitly addressing the excited-state manifold. We demonstrate the utility of this propagator method for the modeling of coherent near-edge X-ray two-photon absorption using, as an example, DFT as the underlying electronic structure model. Results are compared with the corresponding near-edge X-ray absorption fine structure spectra, illuminating the differences in the role of symmetry, localization, and correlation between the two spectroscopies. The ramifications of this new technique for nonlinear X-ray research are briefly discussed.

Surface-Enhanced Raman Scattering Due to Charge-Transfer Resonances: A Time-Dependent Density Functional Theory Study of Ag13-4-Mercaptopyridine

We have used time-dependent density functional theory in conjunction with the CAM-B3LYP functional and MWB28/aug-cc-pVDZ basis set to determine non-, near-, and on-resonance Raman spectra for a complex formed by 4-mercaptopyridine (4-Mpy) binding with a Ag13 cluster via the thiolate Ag–S bond. Geometry optimizations of the Ag13-4-Mpy complex showed an on-top structure directly bound to one Ag atom with the ring of the molecule almost flat with respect to two Ag atoms of the complex. The corresponding B3LYP/MWB28/aug-cc-pVDZ geometry is also an on-top structure directly bound to one Ag atom, but the molecule is directed away from the surface. The near-resonance Raman calculations were carried out in the infinite lifetime approximation, while the on-resonant Raman excitation profiles were calculated with the complex polarization propagator (CPP) approach, introducing a half width at half-maximum spectral broadening of 0.2 eV. Calculation of the UV–vis spectra of the isolated 4-Mpy and of the Ag13-4-Mpy comp...

4-Component relativistic calculations of L3 ionization and excitations for the isoelectronic species UO2(2+), OUN(+) and UN2.

We present a 4-component relativistic study of uranium 2p3/2 ionization and excitation in the isoelectronic series UO2(2+), OUN(+) and UN2. We calculate ionization energies by ΔSCF at the Hartree-Fock (HF) and Kohn-Sham (KS) level of theory. At the ΔHF level we observe a perfectly linear chemical shift of ionization energies with respect to uranium atomic charges obtained from projection analysis. We have also developed a non-canonical 2nd-order Møller-Plesset code for wave function based correlation studies. We observe the well-known failure of Koopmans' theorem for core ionization due to the dominance of orbital relaxation over electron correlation effects. More unexpectedly, we find that the correlation contribution has the same sign as the relaxation contribution and show that this is due to a strong coupling of relaxation and correlation. We simulate uranium L3 XANES spectra, dominated by 2p3/2 → U6d transitions, by restricted excitation window time-dependent density functional theory (REW-TDDFT) and the complex polarization propagator (CPP) approach and demonstrate that they give identical spectra when the same Lorentz broadening is chosen. We also simulate XANES spectra by the Hartree-Fock based static exchange (STEX) method and show how STEX excitation energies can be reproduced by time-dependent Hartree-Fock calculations within the Tamm-Dancoff approximation. We furthermore show that Koopmans' theorem provide a correct approximation of ionization energies in the linear response regime and use this observation to align REW-TDDFT and CPP spectra with STEX ones. We point out that the STEX method affords the most detailed assignment of spectra since it employs virtual orbitals optimized for the selected core ionization. The calculated XANES spectra reflect the loss of bound virtual orbitals as the molecular charge is reduced along the isoelectronic series.

On the truncation of the number of excited states in density functional theory sum-over-states calculations of indirect spin spin coupling constants.

It is investigated, whether the number of excited (pseudo)states can be truncated in the sum-over-states expression for indirect spin-spin coupling constants (SSCCs), which is used in the Contributions from Localized Orbitals within the Polarization Propagator Approach and Inner Projections of the Polarization Propagator (IPPP-CLOPPA) approach to analyzing SSCCs in terms of localized orbitals. As a test set we have studied the nine simple compounds, CH4, NH3, H2O, SiH4, PH3, SH2, C2H2, C2H4, and C2H6. The excited (pseudo)states were obtained from time-dependent density functional theory (TD-DFT) calculations with the B3LYP exchange-correlation functional and the specialized core-property basis set, aug-cc-pVTZ-J. We investigated both how the calculated coupling constants depend on the number of (pseudo)states included in the summation and whether the summation can be truncated in a systematic way at a smaller number of states and extrapolated to the total number of (pseudo)states for the given one-electron basis set. We find that this is possible and that for some of the couplings it is sufficient to include only about 30% of the excited (pseudo)states.

Excited electronic states of thiophene: high resolution photoabsorption Fourier transform spectroscopy and ab initio calculations.

The recently introduced synchrotron radiation-based Fourier transform spectroscopy has been employed to study the excited electronic states of thiophene. A highly resolved photoabsorption spectrum has been measured between ∼5 and 12.5 eV, providing a wealth of new data. High-level ab initio computations have been performed using the second-order algebraic-diagrammatic construction (ADC(2)) polarization propagator approach, and the equation-of-motion coupled-cluster (EOM-CC) method at the CCSD and CC3 levels, to guide the assignment of the spectrum. The adiabatic energy corrections have been evaluated, thereby extending the theoretical study beyond the vertical excitation picture and leading to a significantly improved understanding of the spectrum. The low-lying π→π* and π→σ* transitions result in prominent broad absorption bands. Two strong Rydberg series converging onto the X(~)(2)A2 state limit have been assigned to the 1a2→npb1(1)B2 and the 1a2→nda2(1)A1 transitions. A second, and much weaker, d-type series has been assigned to the 1a2→ndb1(1)B2 transitions. Excitation into some of the Rydberg states belonging to the two strong series gives rise to vibrational structure, most of which has been interpreted in terms of excitations of the totally symmetric ν4 and ν8 modes. One Rydberg series, assigned to the 3b1→nsa1(1)B1 transitions, has been identified converging onto the Ã(2)B1 state limit, and at higher energies Rydberg states converging onto the B(~)(2)A1 state limit could be identified. The present spectra reveal highly irregular vibrational structure in certain low energy absorption bands, and thus provide a new source of information for the rapidly developing studies of excited state non-adiabatic dynamics and photochemistry.

On the interplay between chirality and exciton coupling: a DFT calculation of the circular dichroism in π-stacked ethylene.

The chirality of stacked weakly interacting π-systems was interpreted in terms of Frenkel exciton states and the formation of excitonic circular dichroism (CD) bands was monitored for ethylene stacks of varying sizes. Convergence of CD bands with respect to the system size was observed for stacks involving around 10 molecules. By means of rotation around the C-C double bond in ethylene, chirality was induced in the monomeric system and which was shown to dominate the spectral responses, even for polymer aggregates. In helical assemblies of chiral entities, there will always be a mix of excitonic and monomeric contributions to the CD signal and it is demonstrated that the complex polarization propagator approach in combination with Density Functional Theory is a suitable method to address this situation.

Efficient Calculations of Molecular Linear Response Properties for Spectral Regions.

Molecular spectra can be determined from molecular response functions, by solving the so-called damped response equations using the complex polarization propagator approach. The overall structure of response equations is identical for variational wave functions such as the Hartree-Fock, multiconfiguration self-consistent field, and Kohn-Sham density functional theory, and the key program module is the linear response equation solver. We present an implementation of the solver using the algorithm with symmetrized vectors, optimized for addressing spectral regions of a width of some 5-10 eV and a resolution below 0.1 eV. The work is illustrated by the consideration of UV-vis as well as near carbon K -edge absorption spectra of the C60 fullerene. We demonstrate that it is possible to converge tightly response equations for hundreds of optical frequencies in resonance regions of the spectrum at a cost not much exceeding the solution of a single response equation in the nonresonant region. Our work is implemented in the molecular orbital based module of the Dalton program and serves as a documentation of the code distributed in the Dalton2013 release version.

Full four‐component relativistic calculations of the one‐bond 77Se–13C spin‐spin coupling constants in the series of selenium heterocycles and their parent open‐chain selenides

Four-component relativistic calculations of (77)Se-(13)C spin-spin coupling constants have been performed in the series of selenium heterocycles and their parent open-chain selenides. It has been found that relativistic effects play an essential role in the selenium-carbon coupling mechanism and could result in a contribution of as much as 15-25% of the total values of the one-bond selenium-carbon spin-spin coupling constants. In the overall contribution of the relativistic effects to the total values of (1)J(Se,C), the scalar relativistic corrections (negative in sign) by far dominate over the spin-orbit ones (positive in sign), the latter being of less than 5%, as compared to the former (ca 20%). A combination of nonrelativistic second-order polarization propagator approach (CC2) with the four-component relativistic density functional theory scheme is recommended as a versatile tool for the calculation of (1)J(Se,C). Solvent effects in the values of (1)J(Se,C) calculated within the polarizable continuum model for the solvents with different dielectric constants (ε 2.2-78.4) are next to negligible decreasing negative (1)J(Se,C) in absolute value by only about 1 Hz. The use of the locally dense basis set approach applied herewith for the calculation of (77)Se-(13)C spin-spin coupling constants is fully justified resulting in a dramatic decrease in computational cost with only 0.1-0.2-Hz loss of accuracy.

One‐bond 29Si‐1H spin‐spin coupling constants in the series of halosilanes: benchmark SOPPA and DFT calculations, relativistic effects, and vibrational corrections

A number of most representative second order polarization propagator approach (SOPPA) based wavefunction methods, SOPPA, SOPPA(CC2) and SOPPA(CCSD), and density functional theory (DFT) based methods, B3LYP, PBE0, KT2, and KT3, have been benchmarked in the calculation of the one-bond (29)Si-(1)H spin-spin coupling constants in the series of halosilanes SiH(n)X(4-n) (X = F, Cl, Br, I), both at the non-relativistic and full four-parameter Dirac's relativistic levels taking into account vibrational corrections. At the non-relativistic level, the wavefunction methods showed much better results as compared with those of DFT. At the DFT level, out of four tested functionals, the Perdew, Burke, and Ernzerhof's PBE0 showed best performance. Taking into account, relativistic effects and vibrational corrections noticeably improves wavefunction methods results, but generally worsens DFT results.

CLOPPA Analysis of the Molecular Polarizability and the Energy of Strong Intramolecular Hydrogen Bonds: Resonance Assisted?

The contributions from localized orbitals within the polarization propagator approach (CLOPPA) method is applied to investigate the influence of the π system on the polarizability of the intramolecular hydrogen bond of malonaldehyde, in order to address if this linear response property provides evidence for the existence of the resonance assisted HB (RAHB) mechanism. On the same grounds, this influence on the energy of the hydrogen bond and the potential energy curve of the proton are also evaluated. Results obtained seem to confirm that the π system delocalizes on the hydrogen bond region, and this effect of delocalization is partially responsible for the unusual strength of this intramolecular hydrogen bond.

Open‐chain unsaturated selanyl sulfides: stereochemical structure and stereochemical behavior of their 77Se–1H spin–spin coupling constants

Stereochemical structure of nine Z-2-(vinylsulfanyl)ethenylselanyl organyl sulfides has been investigated by means of experimental measurements and second-order polarization propagator approach calculations of their (1)H-(1)H, (13)C-(1)H, and (77)Se-(1)H spin-spin coupling constants together with a theoretical conformational analysis performed at the MP2/6-311G** level. All nine compounds were shown to adopt the preferable skewed s-cis conformation of their terminal vinylsulfanyl group, whereas the favorable rotational conformations with respect to the internal rotations around the C-S and C-Se bonds of the internal ethenyl group are both skewed s-trans. Stereochemical trends of (77)Se-(1)H spin-spin coupling constants originating in the geometry of their coupling pathways and the selenium lone pair effect were rationalized in terms of the natural J-coupling analysis within the framework of the natural bond orbital approach.

Structural trends of 29Si–1H spin–spin coupling constants across double bond

The calculations of geminal and vicinal (29)Si-(1)H spin-spin coupling constants across double bond in 15 alkenylmethylsilanes and alkenylchlorosilanes were carried out at the second-order polarization propagator approach level in a good agreement with experiment. Two structural trends, namely, (i) the geometry of the coupling pathway and (ii) the effect of the electrowithdrawing substituent, have been interpreted in terms of the natural J-coupling analysis within the framework of the natural bond orbital approach. Thus, the marked difference between cisoidal and transoidal (29)Si-(1)H spin-spin coupling constants across double bond was accounted for the delocalization contributions including bonding and antibonding Si-C and C-H orbitals, whereas the chlorine effect was explained in terms of the steric contributions including bonding Si-Cl orbitals.

Atomic C 6 dispersion coefficients: a four-component relativistic Kohn–Sham study

We present C 6 homo- and heteroatomic dispersion coefficients for all closed-shell atoms of the periodic table based on dipole–dipole polarizabilities at imaginary frequencies calculated using our recent extension of the complex polarization propagator approach to the four-component relativistic Kohn–Sham approach. Lack of proper reference data bars definite conclusions as to which density functional shows the overall best performance, and we therefore call for state-of-the-art wave function-based correlated calculations of dispersion coefficients. Scalar relativistic effects are significant already for elements as light as zinc, whereas spin–orbit effects must be taken into account only for very heavy elements.

Algebraic-diagrammatic construction polarization propagator approach to indirect nuclear spin–spin coupling constants

A new polarization propagator approach to indirect nuclear spin-spin coupling constantans is formulated within the framework of the algebraic-diagrammatic construction (ADC) approximation and implemented at the level of the strict second-order approximation scheme, ADC(2). The ADC approach possesses transparent computational procedure operating with Hermitian matrix quantities defined with respect to physical excitations. It is size-consistent and easily extendable to higher orders via the hierarchy of available ADC approximation schemes. The ADC(2) method is tested in the first applications to HF, N(2), CO, H(2)O, HCN, NH(3), CH(4), C(2)H(2), PH(3), SiH(4), CH(3)F, and C(2)H(4). The calculated indirect nuclear spin-spin coupling constants are in good agreement with the experimental data and results of the second-order polarization propagator approximation method. The computational effort of the ADC(2) scheme scales as n(5) with respect to the number of molecular orbitals n, which makes this method promising for applications to larger molecules.

Resonance assignments of diastereotopic CH2 protons in the anomeric side chain of selenoglycosides by means of 2J(Se,H) spin‐spin coupling constants

Unambiguous resonance assignments of diastereotopic CH(2) protons in the anomeric side chain of nine alkyl- and aralkylselenoglycosides have been carried out on the basis of experimental CPMG-HSQMBC measurements and theoretical second order polarization propagator approach (SOPPA) calculations of geminal (77) Se-(1) H spin-spin coupling constants involving diastereotopic pro-R and pro-S protons. Theoretical conformational analyses have been performed at the MP2/6-311G** level. The conformational space of each of the selenoglycosides under study could be adequately described as a mixture of six interconverting conformers with the molar fractions depending on the nature of the side chain substituent at the selenium atom. The good agreement observed between measured and the weighted conformational averaged values of the calculated coupling constants provides a basis for reliable diastereotopic assignments in this type of carbohydrate structures.

The analysis of NMR J-couplings of saturated and unsaturated compounds by the localized second order polarization propagator approach method

Calculations of NMR J-coupling with polarization propagators are not invariant under unitary transformations at second order level of approach, second order polarization propagator approach (SOPPA). They are only invariant at first order or random phase level of approach (RPA). We performed "localized" SOPPA (Loc-SOPPA), calculations of J-couplings applying two different schemes for the localization of molecular orbitals(LMO): Foster-Boys and Pipek-Mezey. We show here that results of such Loc-SOPPA calculations are different though not much: they are less than 6% different in the worst case. Therefore it is possible to apply them with confidence in the analysis of the transmission of different coupling mechanisms within the molecule. We are able now to get reliable information on what LMOs are the most important (and so which are not important) for a given J-coupling in a molecule. This information can then be used for selecting which are the paths that should be described with the highest possible accuracy for that J-coupling calculation. A few unsaturated compounds are analyzed: ethene, trans-difluoroethene or DiF-ethene, and imine. It is shown that different lone pairs (of p(z) or p(x/y) type) are responsible for the vicinal F-F J-coupling in DiF-ethene; and also the fact that the main LP contributor is not the same for the fermi contact and the spin-dipolar mechanisms. We also studied phosphorous containing compounds such as phosphine and cis-propylene phosphine. In both cases the analysis of the main LMO contributing to one-bond P-H coupling and through-space P-C coupling were performed. The above mentioned unsaturated molecular systems have quasiinstability problems that arise at RPA level of approach. We show here that they are mostly originated in the antibonding π∗ LMO, corresponding to the C=C or C=N double bonds. We performed the analysis of the origin of quasiinstabilities for the SD mechanism. The contribution of each kind of excitation terms to SOPPA calculations were considered, meaning the main contributions by single and double excitations. It is shown that one can get more than 97% of the total electron correlation contribution when including terms that mainly contain single excitations (though double-excitation matrix elements should still be calculated).