The Second-Order Polarization Propagator Approximation (SOPPA) method coupled to the polarizable continuum model

Abstract We present an implementation of the Polarizable Continuum Model (PCM) in combination with the Second-Order Polarization Propagator Approximation (SOPPA) electronic structure method. In analogy with the most common way of designing ground state calculations based on a Second-Order Moller–Plesset (MP2) wave function coupled to PCM, we introduce dynamical PCM solvent effects only in the Random Phase Approximation (RPA) part of the SOPPA response equations while the static solvent contribution is kept in both the RPA terms as well as in the higher order correlation matrix components of the SOPPA response equations. By dynamic terms, we refer to contributions that describe a change in environmental polarization which, in turn, reflects a change in the core molecular charge distribution upon an electronic excitation. This new combination of methods is termed PCM–SOPPA/RPA. We apply this newly defined method to the challenging cases of solvent effects on the lowest and intense electronic transitions in o -, m - and p -nitroaniline and o -, m - and p -nitrophenol and compare the performance of PCM–SOPPA/RPA with more conventional approaches. Compared to calculations based on time-dependent density functional theory employing a range-separated exchange–correlation functional, we find the PCM–SOPPA/RPA approach to be slightly superior with respect to systematicity. On the other hand, the absolute values of the predicted excitation energies are largely underestimated. This – however – is a well-know feature of the SOPPA model itself and is not connected to its combination with the PCM.

[1]  Martin J. Packer,et al.  A new implementation of the second‐order polarization propagator approximation (SOPPA): The excitation spectra of benzene and naphthalene , 1996 .

[2]  J. Olsen,et al.  Linear and nonlinear response functions for an exact state and for an MCSCF state , 1985 .

[3]  P. Åstrand,et al.  Ab Initio Calculation of the Electronic Spectrum of Azobenzene Dyes and Its Impact on the Design of Optical Data Storage Materials , 2000 .

[4]  Poul Jørgensen,et al.  Perturbative triple excitation corrections to coupled cluster singles and doubles excitation energies , 1996 .

[5]  Stephan P. A. Sauer,et al.  Molecular Electromagnetism: A Computational Chemistry Approach , 2011 .

[6]  S. Sauer,et al.  The magnetizability and g-factor surfaces of ammonia , 1991 .

[7]  Ove Christiansen,et al.  Atomic integral driven second order polarization propagator calculations of the excitation spectra of naphthalene and anthracene , 2000 .

[8]  S. Kirpekar,et al.  Erratum: “Nuclear spin–spin coupling in the acetylene isotopomers calculated from ab initio correlated surfaces for 1J(C, H), 1J(C, C), 2J(C, H), and 3J(H, H)” [J. Chem. Phys. 112, 3735 (2000)] , 2001 .

[9]  Ove Christiansen,et al.  A SECOND-ORDER DOUBLES CORRECTION TO EXCITATION ENERGIES IN THE RANDOM-PHASE APPROXIMATION , 1998 .

[10]  C. B. Nielsen,et al.  Response theory in the multipole reaction field model for equilibrium and nonequilibrium solvation: Exact theory and the second order polarization propagator approximation , 2003 .

[11]  M. Packer,et al.  Correlated dipole oscillator sum rules , 1994 .

[12]  Kurt V. Mikkelsen,et al.  Computational protocols for prediction of solute NMR relative chemical shifts. A case study of L‐tryptophan in aqueous solution , 2011, J. Comput. Chem..

[13]  K. Ruud,et al.  Multiconfigurational self-consistent field linear response for the polarizable continuum model: Theory and application to ground and excited-state polarizabilities of para-nitroaniline in solution , 2003 .

[14]  M. Levitt,et al.  Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. , 1976, Journal of molecular biology.

[15]  P. Sommer-Larsen,et al.  Five-membered rings as diazo components in optical data storage devices: an ab initio investigation of the lowest singlet excitation energies , 2000 .

[16]  Kurt V. Mikkelsen,et al.  On the importance of excited state dynamic response electron correlation in polarizable embedding methods , 2012, J. Comput. Chem..

[17]  V. McKoy.  The Equations of Motion Method: An Approach to the Dynamical Properties of Atoms and Molecules , 1980 .

[18]  J. Tomasi,et al.  Quantum mechanical continuum solvation models. , 2005, Chemical reviews.

[19]  Ove Christiansen,et al.  Response functions in the CC3 iterative triple excitation model , 1995 .

[20]  M. Milčić,et al.  Substituent and solvent effects on intramolecular charge transfer of 5-arylidene-2,4-thiazolidinediones. , 2012, Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy.

[21]  P. Åstrand,et al.  Ab initio calculations on 2-imidazolyl-2-thiazolyl azo compounds : an investigation of potential near-infrared absorbing structures , 2001 .

[22]  S. Kirpekar,et al.  Nuclear spin–spin coupling in the acetylene isotopomers calculated from ab initio correlated surfaces for 1J(C, H), 1J(C, C), 2J(C, H), and 3J(H, H) , 2000 .

[23]  V. Galasso.  Application of the equations-of-motion method to the calculation of the indirect nuclear spin-spin coupling tensors , 1985 .

[24]  David J Rowe,et al.  EQUATIONS-OF-MOTION METHOD AND THE EXTENDED SHELL MODEL. , 1968 .

[25]  J. Olsen,et al.  Quadratic response functions in a second-order polarization propagator framework. , 2005, The journal of physical chemistry. A.

[26]  Kurt V. Mikkelsen,et al.  Failures of TDDFT in describing the lowest intramolecular charge-transfer excitation in para-nitroaniline , 2013 .

[27]  Mark S. Gordon,et al.  Self‐consistent molecular orbital methods. XXIII. A polarization‐type basis set for second‐row elements , 1982 .

[28]  S. Sauer,et al.  Correlated polarization propagator calculations of static polarizabilities , 1994 .

[29]  J. Pople,et al.  Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules , 1972 .

[30]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[31]  Jacob Kongsted,et al.  Excited States in Solution through Polarizable Embedding , 2010 .

[32]  Jacob Kongsted,et al.  Molecular Properties through Polarizable Embedding , 2011 .

[33]  N. Handy,et al.  A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP) , 2004 .

[34]  K. Mikkelsen,et al.  A multipole second order Møller–Plesset solvent reaction field method , 2001 .

[35]  J. Kongsted,et al.  How to model solvent effects on molecular properties using quantum chemistry? Insights from polarizable discrete or continuum solvation models. , 2007, The journal of physical chemistry. A.

[36]  U. Singh,et al.  A combined ab initio quantum mechanical and molecular mechanical method for carrying out simulations on complex molecular systems: Applications to the CH3Cl + Cl− exchange reaction and gas phase protonation of polyethers , 1986 .

[37]  Chuan Yi Tang,et al.  A 2.|E|-Bit Distributed Algorithm for the Directed Euler Trail Problem , 1993, Inf. Process. Lett..

[38]  Jacob Kongsted,et al.  The polarizable embedding coupled cluster method. , 2011, Journal of Chemical Physics.

[39]  V. McKoy,et al.  HIGHER RANDOM-PHASE APPROXIMATION AS AN APPROXIMATION TO THE EQUATIONS OF MOTION. , 1970 .

[40]  E. Dalgaard.  Time‐dependent multiconfigurational Hartree–Fock theory , 1980 .

[41]  B. Mennucci,et al.  Linear response theory for the polarizable continuum model , 1999 .

[42]  Luca Frediani,et al.  The Dalton quantum chemistry program system , 2013, Wiley interdisciplinary reviews. Computational molecular science.

[43]  S. Sauer.  Second-order polarization propagator approximation with coupled-cluster singles and doubles amplitudes - SOPPA(CCSD): the polarizability and hyperpolarizability of , 1997 .

[44]  J. Kongsted,et al.  Benchmarking NMR indirect nuclear spin-spin coupling constants: SOPPA, SOPPA(CC2), and SOPPA(CCSD) versus CCSD. , 2010, The Journal of chemical physics.

[45]  P. Lazzeretti,et al.  Correlated and gauge invariant calculations of nuclear magnetic shielding constants using the continuous transformation of the origin of the current density approach , 2003 .

[46]  J. Tomasi,et al.  Time‐dependent variational principle for nonlinear Hamiltonians and its application to molecules in the liquid phase , 1996 .

[47]  Poul Jørgensen,et al.  The second-order approximate coupled cluster singles and doubles model CC2 , 1995 .

[48]  M. Karplus,et al.  A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations , 1990 .

[49]  Poul Jo,et al.  Transition moments and dynamic polarizabilities in a second order polarization propagator approach , 1980 .

[50]  A. D. McLACHLAN,et al.  Time-Dependent Hartree—Fock Theory for Molecules , 1964 .

[51]  D. Case,et al.  Generalized born models of macromolecular solvation effects. , 2000, Annual review of physical chemistry.

[52]  S. Rettrup,et al.  Benchmarking second order methods for the calculation of vertical electronic excitation energies: valence and Rydberg states in polycyclic aromatic hydrocarbons. , 2009, The journal of physical chemistry. A.

[53]  Jacopo Tomasi,et al.  A new integral equation formalism for the polarizable continuum model: Theoretical background and applications to isotropic and anisotropic dielectrics , 1997 .