Chemical accuracy in ab initio thermochemistry and spectroscopy: current strategies and future challenges

The current state of the art in wavefunction-based electronic structure methods is illustrated via discussions of the most important effects incorporated into a selection of high-accuracy methods chosen from the chemical literature. If one starts with a high-quality correlation treatment, such as provided by the CCSD(T) coupled cluster method, the leading effects include convergence of the results with respect to the 1-particle basis set, (outer)core/valence correlation, scalar relativistic effects and a number of smaller effects. For thermochemical properties such as the heat of formation, the zero-point vibrational energy also becomes important, introducing its own set of difficulties to the computational approach. Changes in the various components as the chemical systems incorporate heavier elements and as the size of the systems grows are also considered. Finally, challenges arising from the desire to extend existing methods to transition metal and heavier elements are considered.

[1]  J. L. Dunham The Wentzel-Brillouin-Kramers Method of Solving the Wave Equation , 1932 .

[2]  Marvin Douglas,et al.  Quantum electrodynamical corrections to the fine structure of helium , 1971 .

[3]  D. C. Griffin,et al.  Approximate relativistic corrections to atomic radial wave functions , 1976 .

[4]  G. A. Petersson,et al.  Complete basis set correlation energies. I. The asymptotic convergence of pair natural orbital expansions , 1981 .

[5]  Richard L. Martin,et al.  All-electron relativistic calculations on silver hydride. An investigation of the Cowan-Griffin operator in a molecular species , 1983 .

[6]  H. Schaefer,et al.  The diagonal correction to the Born–Oppenheimer approximation: Its effect on the singlet–triplet splitting of CH2 and other molecular effects , 1986 .

[7]  Hess,et al.  Relativistic electronic-structure calculations employing a two-component no-pair formalism with external-field projection operators. , 1986, Physical review. A, General physics.

[8]  Warren J. Hehre,et al.  AB INITIO Molecular Orbital Theory , 1986 .

[9]  H. Schaefer,et al.  Fluorine peroxide (FOOF): A continuing problem for normally reliable theoretical methods , 1987 .

[10]  G. A. Petersson,et al.  A complete basis set model chemistry. I. The total energies of closed‐shell atoms and hydrides of the first‐row elements , 1988 .

[11]  L. Curtiss,et al.  Gaussian‐1 theory: A general procedure for prediction of molecular energies , 1989 .

[12]  M. Head‐Gordon,et al.  A fifth-order perturbation comparison of electron correlation theories , 1989 .

[13]  T. H. Dunning Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[14]  Bernd A. Hess,et al.  Revision of the Douglas-Kroll transformation. , 1989, Physical review. A, General physics.

[15]  Krishnan Raghavachari,et al.  Gaussian‐1 theory of molecular energies for second‐row compounds , 1990 .

[16]  Krishnan Raghavachari,et al.  Gaussian-2 theory for molecular energies of first- and second-row compounds , 1991 .

[17]  G. A. Petersson,et al.  A complete basis set model chemistry. II. Open‐shell systems and the total energies of the first‐row atoms , 1991 .

[18]  G. A. Petersson,et al.  A complete basis set model chemistry. III. The complete basis set‐quadratic configuration interaction family of methods , 1991 .

[19]  David Feller,et al.  Application of systematic sequences of wave functions to the water dimer , 1992 .

[20]  T. Dunning,et al.  Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions , 1992 .

[21]  Krishnan Raghavachari,et al.  Gaussian-2 theory using reduced Moller--Plesset orders , 1993 .

[22]  Wesley D. Allen,et al.  The heat of formation of NCO , 1993 .

[23]  J. Laane,et al.  Structures and Conformations of Non-Rigid Molecules , 1993 .

[24]  Christopher S. Johnson,et al.  Characterization of the X̃ 1A’ state of isocyanic acid , 1993 .

[25]  Kirk A. Peterson,et al.  Benchmark calculations with correlated molecular wave functions. IV. The classical barrier height of the H+H2→H2+H reaction , 1994 .

[26]  John A. Montgomery,et al.  A complete basis set model chemistry. IV. An improved atomic pair natural orbital method , 1994 .

[27]  B. A. Hess,et al.  AB INITIO CALCULATION OF SPIN–ORBIT EFFECTS IN MOLECULES INCLUDING ELECTRON CORRELATION , 1995 .

[28]  D. Yarkony,et al.  Modern Electronic Structure Theory: Part I , 1995 .

[29]  C. W. Bauschlicher,et al.  A modification of the Gaussian‐2 approach using density functional theory , 1995 .

[30]  Leo Radom,et al.  CALCULATION OF PROTON AFFINITIES USING THE G2(MP2,SVP) PROCEDURE , 1995 .

[31]  Thom H. Dunning,et al.  Gaussian basis sets for use in correlated molecular calculations. V. Core-valence basis sets for boron through neon , 1995 .

[32]  W. Kutzelnigg,et al.  Relativistic Hartree–Fock by means of stationary direct perturbation theory. I. General theory , 1995 .

[33]  John A. Montgomery,et al.  A complete basis set model chemistry. V. Extensions to six or more heavy atoms , 1996 .

[34]  Leo Radom,et al.  Gaussian‐2 (G2) theory: Reduced basis set requirements , 1996 .

[35]  David Feller The role of databases in support of computational chemistry calculations , 1996 .

[36]  Trygve Helgaker,et al.  Basis-set convergence of correlated calculations on water , 1997 .

[37]  W. Kutzelnigg The adiabatic approximation I. The physical background of the Born-Handy ansatz , 1997 .

[38]  Henry F. Schaefer,et al.  In pursuit of the ab initio limit for conformational energy prototypes , 1998 .

[39]  L. Curtiss,et al.  Gaussian-3 (G3) theory for molecules containing first and second-row atoms , 1998 .

[40]  C. Bauschlicher,et al.  The Heats of Formation of GaCl3 and its Fragments , 1998 .

[41]  Leo Radom,et al.  An assessment of theoretical procedures for the calculation of reliable free radical thermochemistry: A recommended new procedure , 1998 .

[42]  Russell M. Pitzer,et al.  Spin-Orbit Configuration Interaction Using the Graphical Unitary Group Approach and Relativistic Core Potential and Spin-Orbit Operators , 1999 .

[43]  Krishnan Raghavachari,et al.  Gaussian-3 theory using coupled cluster energies , 1999 .

[44]  Krishnan Raghavachari,et al.  Gaussian-3 theory using reduced Mo/ller-Plesset order , 1999 .

[45]  G. A. Petersson,et al.  A complete basis set model chemistry. VI. Use of density functional geometries and frequencies , 1999 .

[46]  C. Bauschlicher,et al.  Boron Heat of Formation Revisited: Relativistic Effects on the BF3 Atomization Energy , 1999 .

[47]  Jan M. L. Martin,et al.  TOWARDS STANDARD METHODS FOR BENCHMARK QUALITY AB INITIO THERMOCHEMISTRY :W1 AND W2 THEORY , 1999, physics/9904038.

[48]  Krishnan Raghavachari,et al.  GAUSSIAN-3 THEORY USING DENSITY FUNCTIONAL GEOMETRIES AND ZERO-POINT ENERGIES , 1999 .

[49]  Hans-Joachim Werner,et al.  Local perturbative triples correction (T) with linear cost scaling , 2000 .

[50]  L. Curtiss,et al.  Gaussian-3X (G3X) theory : use of improved geometries, zero-point energies, and Hartree-Fock basis sets. , 2001 .

[51]  L. Curtiss,et al.  Scalar relativistic effects on energies of molecules containing atoms from hydrogen through argon , 2001 .

[52]  C. Bauschlicher,et al.  Is the Lamb shift chemically significant , 2001 .

[53]  Robert J. Harrison,et al.  Parallel Douglas-Kroll Energy and Gradients in NWChem. Estimating Scalar Relativistic Effects Using Douglas-Kroll Contracted Basis Sets. , 2001 .

[54]  Kirk A. Peterson,et al.  Accurate correlation consistent basis sets for molecular core–valence correlation effects: The second row atoms Al–Ar, and the first row atoms B–Ne revisited , 2002 .

[55]  Branko Ruscic,et al.  On the Enthalpy of Formation of Hydroxyl Radical and Gas-Phase Bond Dissociation Energies of Water and Hydroxyl , 2002 .

[56]  W. A. Jong,et al.  Performance of coupled cluster theory in thermochemical calculations of small halogenated compounds , 2003 .

[57]  H. Stoll,et al.  Systematically convergent basis sets with relativistic pseudopotentials. II. Small-core pseudopotentials and correlation consistent basis sets for the post-d group 16–18 elements , 2003 .

[58]  L. Radom,et al.  G3-RAD and G3X-RAD: Modified Gaussian-3 (G3) and Gaussian-3X (G3X) procedures for radical thermochemistry , 2003 .

[59]  P. Pyykkö,et al.  Search for effective local model potentials for simulation of quantum electrodynamic effects in relativistic calculations , 2003 .

[60]  B. Shepler,et al.  Mercury Monoxide: A Systematic Investigation of Its Ground Electronic State , 2003 .

[61]  J. Olsen,et al.  Coupled-cluster connected-quadruples corrections to atomization energies , 2003 .

[62]  K. Peterson Systematically convergent basis sets with relativistic pseudopotentials. I. Correlation consistent basis sets for the post-d group 13–15 elements , 2003 .

[63]  Mihaly Kallay,et al.  W3 theory: robust computational thermochemistry in the kJ/mol accuracy range. , 2003, Journal of Chemical Physics.

[64]  W. D. Allen,et al.  Toward subchemical accuracy in computational thermochemistry: focal point analysis of the heat of formation of NCO and [H,N,C,O] isomers. , 2004, The Journal of chemical physics.

[65]  G. Rauhut Efficient calculation of potential energy surfaces for the generation of vibrational wave functions. , 2004, The Journal of chemical physics.

[66]  Juana Vázquez,et al.  HEAT: High accuracy extrapolated ab initio thermochemistry. , 2004, The Journal of chemical physics.

[67]  Vincenzo Barone,et al.  Vibrational zero-point energies and thermodynamic functions beyond the harmonic approximation. , 2004, The Journal of chemical physics.

[68]  Vincenzo Barone,et al.  Anharmonic vibrational properties by a fully automated second-order perturbative approach. , 2005, The Journal of chemical physics.

[69]  Theresa L Windus,et al.  Thermodynamic properties of the C5, C6, and C8 n-alkanes from ab initio electronic structure theory. , 2005, The journal of physical chemistry. A.

[70]  Amir Karton,et al.  Comment on: “Estimating the Hartree–Fock limit from finite basis set calculations” [Jensen F (2005) Theor Chem Acc 113:267] , 2005, physics/0509216.

[71]  W. K. Cho,et al.  The spin−orbit energy estimated from two-component spin−orbit calculations as correction terms for the Gaussian-2 (G2) theory , 2005 .

[72]  Kirk A Peterson,et al.  Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc-Zn. , 2005, The Journal of chemical physics.

[73]  B. Shepler,et al.  Ab initio thermochemistry involving heavy atoms: an investigation of the reactions Hg + IX (X = I, Br, Cl, O). , 2005, The journal of physical chemistry. A.

[74]  D. Schwenke The extrapolation of one-electron basis sets in electronic structure calculations: how it should work and how it can be made to work. , 2005, The Journal of chemical physics.

[75]  K. Peterson,et al.  Multiple bonds to gold: a theoretical investigation of XAuC (X = F, Cl, Br, I) molecules , 2005 .

[76]  Cristina Puzzarini,et al.  Systematically convergent basis sets for transition metals. II. Pseudopotential-based correlation consistent basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements , 2005 .

[77]  T. Crawford,et al.  Sources of error in electronic structure calculations on small chemical systems. , 2006, The Journal of chemical physics.

[78]  Geoffrey P. F. Wood,et al.  A restricted-open-shell complete-basis-set model chemistry. , 2006, The Journal of chemical physics.

[79]  Nathan J DeYonker,et al.  The correlation-consistent composite approach: application to the G3/99 test set. , 2006, The Journal of chemical physics.

[80]  Juana Vázquez,et al.  High-accuracy extrapolated ab initio thermochemistry. II. Minor improvements to the protocol and a vital simplification. , 2006, The Journal of chemical physics.

[81]  Frederick R. Manby,et al.  R12 methods in explicitly correlated molecular electronic structure theory , 2006 .

[82]  Mihály Kállay,et al.  Analytic calculation of the diagonal Born-Oppenheimer correction within configuration-interaction and coupled-cluster theory. , 2006, The Journal of chemical physics.

[83]  J. Gauss,et al.  Rotational spectra of 1-chloro-2-fluoroethylene. II. Equilibrium structures of the cis and trans isomer. , 2006, The Journal of chemical physics.

[84]  B. Ruscic,et al.  W4 theory for computational thermochemistry: In pursuit of confident sub-kJ/mol predictions. , 2006, The Journal of chemical physics.

[85]  B. Shepler,et al.  On the spectroscopic and thermochemical properties of ClO, BrO, IO, and their anions. , 2006, The journal of physical chemistry. A.

[86]  Nathan J DeYonker,et al.  The correlation consistent composite approach (ccCA): an alternative to the Gaussian-n methods. , 2006, The Journal of chemical physics.

[87]  Mihály Kállay,et al.  Basis-set extrapolation techniques for the accurate calculation of molecular equilibrium geometries using coupled-cluster theory. , 2006, The Journal of chemical physics.

[88]  P. Taylor,et al.  Basis set convergence of post-CCSD contributions to molecular atomization energies. , 2007, The Journal of chemical physics.

[89]  J. Gauss,et al.  Basis set limit CCSD(T) harmonic vibrational frequencies. , 2007, The journal of physical chemistry. A.

[90]  Angela K. Wilson,et al.  Quantitative computational thermochemistry of transition metal species. , 2007, The journal of physical chemistry. A.

[91]  B. Ruscic,et al.  Benchmark atomization energy of ethane: Importance of accurate zero-point vibrational energies and diagonal Born–Oppenheimer corrections for a ‘simple’ organic molecule , 2007 .

[92]  L. Curtiss,et al.  Gaussian-4 theory using reduced order perturbation theory. , 2007, The Journal of chemical physics.

[93]  David Feller,et al.  Probing the limits of accuracy in electronic structure calculations: is theory capable of results uniformly better than "chemical accuracy"? , 2007, The Journal of chemical physics.

[94]  L. Curtiss,et al.  Gaussian-4 theory. , 2007, The Journal of chemical physics.

[95]  H. Hsin,et al.  Vibrational spectroscopy of 1,1-difluorocyclopropane-d0, -d2, and -d4: the equilibrium structure of difluorocyclopropane. , 2007, The journal of physical chemistry. A.

[96]  J. Gauss,et al.  Perturbative treatment of scalar-relativistic effects in coupled-cluster calculations of equilibrium geometries and harmonic vibrational frequencies using analytic second-derivative techniques. , 2007, The Journal of chemical physics.

[97]  Michael Dolg,et al.  Energy-consistent relativistic pseudopotentials and correlation consistent basis sets for the 4d elements Y-Pd. , 2007, The Journal of chemical physics.

[98]  Hans-Joachim Werner,et al.  Systematically convergent basis sets for explicitly correlated wavefunctions: the atoms H, He, B-Ne, and Al-Ar. , 2008, The Journal of chemical physics.

[99]  Hans-Joachim Werner,et al.  Explicitly correlated RMP2 for high-spin open-shell reference states. , 2008, The Journal of chemical physics.

[100]  N. Craig,et al.  Ab initio structures for 90 degrees -twisted s-trans-1,3-butadiene and cyclooctatetraene: the naked sp2-sp2 bond. , 2008, The journal of physical chemistry. A.

[101]  V. Barone,et al.  Assessment of a computational strategy approaching spectroscopic accuracy for structure, magnetic properties and vibrational frequencies of organic free radicals: the F(2)CN and F(2)BO case. , 2008, Physical chemistry chemical physics : PCCP.

[102]  Branko Ruscic,et al.  High-accuracy extrapolated ab initio thermochemistry. III. Additional improvements and overview. , 2008, The Journal of chemical physics.

[103]  J. Gauss,et al.  The accuracy of rotational constants predicted by high-level quantum-chemical calculations. I. molecules containing first-row atoms. , 2008, The Journal of chemical physics.

[104]  David Feller,et al.  A survey of factors contributing to accurate theoretical predictions of atomization energies and molecular structures. , 2008, The Journal of chemical physics.

[105]  G. A. Petersson,et al.  The CCSD(T) complete basis set limit for Ne revisited. , 2008, The Journal of chemical physics.

[106]  C. Puzzarini Extrapolation to the complete basis set limit of structural parameters: comparison of different approaches. , 2009, The journal of physical chemistry. A.

[107]  N. Craig,et al.  High level ab initio energies and structures for the rotamers of 1,3-butadiene. , 2009, The journal of physical chemistry. A.

[108]  Michael Dolg,et al.  Energy-consistent pseudopotentials and correlation consistent basis sets for the 5d elements Hf-Pt. , 2009, The Journal of chemical physics.

[109]  Guntram Rauhut,et al.  Accurate calculation of vibrational frequencies using explicitly correlated coupled-cluster theory. , 2009, The Journal of chemical physics.

[110]  Michael J Frisch,et al.  Unrestricted Coupled Cluster and Brueckner Doubles Variations of W1 Theory. , 2009, Journal of chemical theory and computation.

[111]  Hans-Joachim Werner,et al.  Extrapolating MP2 and CCSD explicitly correlated correlation energies to the complete basis set limit with first and second row correlation consistent basis sets. , 2009, The Journal of chemical physics.

[112]  Hans-Joachim Werner,et al.  Simplified CCSD(T)-F12 methods: theory and benchmarks. , 2009, The Journal of chemical physics.

[113]  Angela K. Wilson,et al.  Computation of potential energy surfaces with the multireference correlation consistent composite approach. , 2009, The Journal of chemical physics.

[114]  Brian P. Prascher,et al.  The resolution of the identity approximation applied to the correlation consistent composite approach. , 2009, The Journal of chemical physics.

[115]  Angela K. Wilson,et al.  Structures and thermochemistry of the alkali metal monoxide anions, monoxide radicals, and hydroxides. , 2009, The journal of physical chemistry. A.

[116]  H. Stoll,et al.  Energy-consistent pseudopotentials for the 5d elements--benchmark calculations for oxides, nitrides, and Pt(2). , 2009, Journal of Physical Chemistry A.

[117]  Nathan J. DeYonker,et al.  Accurate thermochemistry for transition metal complexes from first-principles calculations. , 2009, The Journal of chemical physics.

[118]  David A Dixon,et al.  Accurate thermochemistry for transition metal oxide clusters. , 2009, The journal of physical chemistry. A.

[119]  Thomas R. Cundari,et al.  Towards the intrinsic error of the correlation consistent Composite Approach (ccCA) , 2009 .

[120]  Hans-Joachim Werner,et al.  Benchmark Studies for Explicitly Correlated Perturbation- and Coupled Cluster Theories. javascript:filterformular(´3´) , 2010 .

[121]  Kirk A Peterson,et al.  Molecular core-valence correlation effects involving the post-d elements Ga-Rn: benchmarks and new pseudopotential-based correlation consistent basis sets. , 2010, The Journal of chemical physics.

[122]  David Feller,et al.  Calibration study of the CCSD(T)-F12a/b methods for C2 and small hydrocarbons. , 2010, The Journal of chemical physics.

[123]  Jan M. L. Martin,et al.  Performance of W4 theory for spectroscopic constants and electrical properties of small molecules. , 2010, The Journal of chemical physics.

[124]  J Grant Hill,et al.  Correlation consistent basis sets for molecular core-valence effects with explicitly correlated wave functions: the atoms B-Ne and Al-Ar. , 2010, The Journal of chemical physics.

[125]  David A Dixon,et al.  Third row transition metal hexafluorides, extraordinary oxidizers, and Lewis acids: electron affinities, fluoride affinities, and heats of formation of WF6, ReF6, OsF6, IrF6, PtF6, and AuF6. , 2010, Inorganic chemistry.

[126]  D. Dixon,et al.  Refined theoretical estimates of the atomization energies and molecular structures of selected small oxygen fluorides. , 2010, Journal of Physical Chemistry A.

[127]  D. Dixon,et al.  Ab initio coupled cluster determination of the heats of formation of C2H2F2, C2F2, and C2F4. , 2011, The journal of physical chemistry. A.

[128]  P. Schwerdtfeger,et al.  Accurate potential energy curves for the group 12 dimers Zn2, Cd2, and Hg2 , 2011 .

[129]  David Feller,et al.  On the effectiveness of CCSD(T) complete basis set extrapolations for atomization energies. , 2011, The Journal of chemical physics.

[130]  D. C. Mckean,et al.  Ab initio coupled cluster determination of the equilibrium structures of cis- and trans-1,2-difluoroethylene and 1,1-difluoroethylene. , 2011, The journal of physical chemistry. A.

[131]  W. Jiang,et al.  Multireference composite approaches for the accurate study of ground and excited electronic states: C2, N2, and O2. , 2011, The Journal of chemical physics.

[132]  J. S. Francisco,et al.  Ab initio spectroscopic characterization of the HNNO and ONHN radicals. , 2011, The Journal of chemical physics.