skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: On the geometric dependence of the molecular dipole polarizability in water: A benchmark study of higher-order electron correlation, basis set incompleteness error, core electron effects, and zero-point vibrational contributions

Journal Article · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/1.5051458· OSTI ID:1543885

In this work, we investigate how geometric changes influence the static dipole polarizability ($$α$$) of a water molecule by explicitly computing the corresponding dipole polarizability surface (DPS) across 3125 total (1625 symmetry-unique) geometries using linear response coupled cluster theory including single, double, and triple excitations (LR-CCSDT) and the doubly augmented triple-$$ζ$$ basis set (d-aug-cc-pVTZ). Analytical formulae based on power series expansions of this $ab initio$ surface are generated using linear least-squares analysis and provide highly accurate estimates of this quantity as a function of molecular geometry (i.e., bond and angle variations) in a computationally tractable manner. An additional database, which consists of 25 representative molecular geometries and incorporates a more thorough treatment of both basis sets and core electron effects, is provided as a current benchmark for this quantity and the corresponding leading-order $$C_6$$ dispersion coefficient. This database has been utilized to assess the importance of these effects as well as the relative accuracy that can be obtained using several quantum chemical methods and a library of density functional approximations. In addition to high-level electron correlation methods (like CCSD) and our analytical least-squares formulae, we find that the SCAN0, PBE0, MN15, and B97-2 hybrid functionals yield the most accurate descriptions of the molecular polarizability tensor in H2O. Using first-order perturbation theory, we compute the zero-point vibrational correction to $$α$$ at the CCSDT/d-aug-cc-pVTZ level and find that this correction contributes approximately 3% to the isotropic ($$α$$iso) and nearly 50% to the anisotropic ($$α$$aniso) polarizability values. In doing so, we find that $$α$$iso = 9.8307 bohr3, which is in excellent agreement with the experimental value of 9.83 ± 0.02 bohr3 provided by Russell and Spackman. The DPS reported herein provides a benchmark-quality quantum mechanical estimate of this fundamental quantity of interest and should find extensive use in the development (and assessment) of next-generation force fields and machine-learning based approaches for modeling water in complex condensed-phase environments.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Univ. of California, Oakland, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1543885
Journal Information:
Journal of Chemical Physics, Vol. 149, Issue 20; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 9 works
Citation information provided by
Web of Science

References (152)

Time-dependent coupled-cluster calculations of polarizabilities and dispersion energy coefficients journal January 2007
The vibrational proton potential in bulk liquid water and ice journal April 2008
Predictions of the Properties of Water from First Principles journal March 2007
Complete basis set limit ofAb initio binding energies and geometrical parameters for various typical types of complexes journal January 2008
On equilibrium structures of the water molecule journal June 2005
On the representation of many-body interactions in water journal September 2015
Refractive Indices of Water Vapor and Carbon Dioxide at Low Pressure journal January 1949
Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis journal August 1980
A systematic and feasible method for computing nuclear contributions to electrical properties of polyatomic molecules journal August 1997
Polarisabilities and dispersion coefficients from the weighted exchange-hole model journal April 2013
High accuracy benchmark calculations on the benzene dimer potential energy surface journal October 2007
Cauchy moments and dispersion coefficients using coupled cluster linear response theory journal December 1997
Integral-direct coupled cluster calculations of frequency-dependent polarizabilities, transition probabilities and excited-state properties journal February 1998
Ab initio dynamic multipole polarizabilities and hyperpolarizabilities of H2O and the long-range interaction coefficients for its dimer journal January 1998
Ab Initio Water Pair Potential with Flexible Monomers journal March 2015
Hybrid exchange-correlation functional determined from thermochemical data and ab initio potentials journal November 2001
Vibrational effects on electric and magnetic susceptibilities: application to the properties of the water molecule journal January 2000
PNO-CI and PNO-CEPA studies of electron correlation effects: V. Static dipole polarizabilities of small molecules journal March 1976
Calculations of Molecular Properties in Hybrid Coupled-Cluster and Molecular Mechanics Approach journal June 2007
The H 2 O-H 2 O dispersion energy constant and the dispersion of the specific refractivity of dilute water vapour journal July 1975
Semilocal and hybrid meta-generalized gradient approximations based on the understanding of the kinetic-energy-density dependence journal January 2013
Dipole and quadrupole polarizabilities of the water molecule as a function of geometry: FULL PAPER journal June 2016
On the Refraction and Dispersion of the Halogens, Halogen Acids, Ozone, Steam, Oxides of Nitrogen and Ammonia
  • Cuthbertson, C.; Cuthbertson, M.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 213, Issue 497-508 https://doi.org/10.1098/rsta.1914.0001
journal January 1914
Modelling Water: A Lifetime Enigma journal March 2015
Experimental static dipole–dipole polarizabilities of molecules journal December 2013
Systematic comparison of DFT and CCSD dipole moments, polarizabilities and hyperpolarizabilities journal August 2015
Advances in molecular quantum chemistry contained in the Q-Chem 4 program package journal September 2014
The calculation of frequency-dependent polarizabilities using current density functional theory journal October 1997
Calculation of frequency-dependent polarizabilities using general coupled-cluster models journal August 2006
Non-covalent interactions across organic and biological subsets of chemical space: Physics-based potentials parametrized from machine learning journal June 2018
On the connection between the supermolecular Møller-Plesset treatment of the interaction energy and the perturbation theory of intermolecular forces journal February 1988
Extrapolation of intermolecular interaction energies in weakly bound Van der Waals complexes journal August 2002
Dynamic polarizabilities of polyaromatic hydrocarbons using coupled-cluster linear response theory journal October 2007
Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties journal February 1994
MN15: A Kohn–Sham global-hybrid exchange–correlation density functional with broad accuracy for multi-reference and single-reference systems and noncovalent interactions journal January 2016
Theoretical study of molecular properties of low-lying electronic excited states of H 2 O and H 2 S journal October 2008
Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections journal January 2008
Frequency-dependent polarizabilities and first hyperpolarizabilities of CO and H2O from coupled cluster calculations journal May 1999
A finite field method for calculating molecular polarizability tensors for arbitrary multipole rank journal August 2011
Coupled-Cluster Based Linear Response Approach to Property Calculations: Dynamic Polarizability and Its Static Limit journal April 1995
On decomposition of second‐order Mo/ller–Plesset supermolecular interaction energy and basis set effects journal April 1990
Performance of W4 theory for spectroscopic constants and electrical properties of small molecules journal October 2010
Accurate prediction of static dipole polarizabilities with moderately sized basis sets journal November 1989
Automatic generation of force fields and property surfaces for use in variational vibrational calculations of anharmonic vibrational energies and zero-point vibrational averaged properties journal September 2006
Hydrogen-Bonding Polarizable Intermolecular Potential Model for Water journal November 2016
Computation of accurate electronic molecular polarizabilities journal October 1992
How well do static electronic dipole polarizabilities from gas-phase experiments compare with density functional and MP2 computations? journal October 2015
A Polarizable Water Model for Intramolecular and Intermolecular Vibrational Spectroscopies journal May 2011
Development of transferable interaction potentials for water. V. Extension of the flexible, polarizable, Thole-type model potential ( TTM3-F , v. 3.0) to describe the vibrational spectra of water clusters and liquid water journal February 2008
How accurate are static polarizability predictions from density functional theory? An assessment over 132 species at equilibrium geometry journal January 2018
A comparison of density-functional-theory and coupled-cluster frequency-dependent polarizabilities and hyperpolarizabilities journal January 2005
Improved density functional theory results for frequency‐dependent polarizabilities, by the use of an exchange‐correlation potential with correct asymptotic behavior journal August 1996
A precise solution of the rotation bending Schrödinger equation for a triatomic molecule with application to the water molecule journal January 1979
Finite field treatment of vibrational polarizabilities and hyperpolarizabilities: On the role of the Eckart conditions, their implementation, and their use in characterizing key vibrations journal July 1999
The influence of vibrations of polyatomic molecules on dipole moment and static dipole polarizability: theoretical study journal August 2017
Vibrational Contributions to Molecular Dipole Polarizabilities journal January 1982
Linear Response Properties of Liquid Water Calculated Using CC2 and CCSD within Different Molecular Mechanics Methods journal October 2004
Calculation, with the inclusion of vibrational corrections, of the dc-electric-field-induced second-harmonic-generation hyperpolarizability of methane journal November 1997
Mapping the genome of meta-generalized gradient approximation density functionals: The search for B97M-V journal February 2015
Electrical polarization in diatomic molecules journal March 1988
Accurate Description of Intermolecular Interactions Involving Ions Using Symmetry-Adapted Perturbation Theory journal May 2015
Intermolecular potential and second virial coefficient of the water-nitrogen complex journal March 2007
Vibrational averaging of electrical properties: Development of a routine theoretical method for polyatomic molecules journal April 1995
Semilocal density functional obeying a strongly tightened bound for exchange journal January 2015
Polarizable molecules in the vibrational spectroscopy of water journal August 2005
Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields journal November 1994
Hyperpolarizability of H2O revisited: accurate estimate of the basis set limit and the size of electron correlation effects journal June 1998
Development of a “First-Principles” Water Potential with Flexible Monomers. III. Liquid Phase Properties journal July 2014
Time-dependent density functional theory scheme for efficient calculations of dynamic (hyper)polarizabilities journal May 2007
Strongly Constrained and Appropriately Normed Semilocal Density Functional journal July 2015
Improving the Accuracy of Hybrid Meta-GGA Density Functionals by Range Separation journal October 2011
Accurate and Efficient Quantum Chemistry Calculations for Noncovalent Interactions in Many-Body Systems: The XSAPT Family of Methods journal December 2014
Correlated van der Waals coefficients for dimers consisting of He, Ne, H 2 , and N 2 journal May 1988
Density-Functional-Based Determination of Vibrational Polarizabilities in Molecules within the Double-Harmonic Approximation:  Derivation and Application journal May 2005
Many‐body perturbation theory of frequency‐dependent polarizabilities and van der Waals coefficients: Application to H 2 O–H 2 O and Ar–NH 3 journal October 1992
Frequency‐dependent polarizabilities and first hyperpolarizabilities of H 2 O journal May 1993
Dispersion-corrected Mo̸ller–Plesset second-order perturbation theory journal January 2009
Nonlocal van der Waals density functional: The simpler the better journal December 2010
Stereoelectronic, Vibrational, and Environmental Contributions to Polarizabilities of Large Molecular Systems: A Feasible Anharmonic Protocol journal May 2014
Determination of higher electric polarizability tensors from unrelaxed coupled cluster density matrix calculations of electric multipole moments journal February 1994
Basis set convergence of the coupled-cluster correction, δMP2CCSD(T): Best practices for benchmarking non-covalent interactions and the attendant revision of the S22, NBC10, HBC6, and HSG databases journal November 2011
Padé Approximants for Two‐ and Three‐Body Dipole Dispersion Interactions journal July 1970
Geometry-dependent distributed polarizability models for the water molecule journal January 2016
Polarizability and volume journal March 1993
mBEEF: An accurate semi-local Bayesian error estimation density functional journal April 2014
Development of a “First Principles” Water Potential with Flexible Monomers: Dimer Potential Energy Surface, VRT Spectrum, and Second Virial Coefficient journal November 2013
Variational calculation of vibrational linear and nonlinear optical properties journal May 2005
Dispersion energy constants C 6 (A, B), dipole oscillator strength sums and refractivities for Li, N, O, H 2 , N 2 , O 2 , NH 3 , H 2 O, NO and N 2 O journal April 1977
The multipole polarizabilities and hyperpolarizabilities of the water molecule in liquid state: an ab initio study journal July 2001
Density-functional exchange-energy approximation with correct asymptotic behavior journal September 1988
The Dalton quantum chemistry program system: The Dalton program
  • Aidas, Kestutis; Angeli, Celestino; Bak, Keld L.
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 4, Issue 3 https://doi.org/10.1002/wcms.1172
journal September 2013
Time-independent coupled cluster theory of the polarization propagator. Implementation and application of the singles and doubles model to dynamic polarizabilities and van der Waals constants† journal July 2006
Polarizabilities of CO, N2, HF, Ne, BH, and CH+ from ab initio calculations: Systematic studies of electron correlation, basis set errors, and vibrational contributions journal September 1998
Recent Advances in Wave Function-Based Methods of Molecular-Property Calculations journal December 2011
Why Is MP2-Water “Cooler” and “Denser” than DFT-Water? journal February 2016
XCC2—a new coupled cluster model for the second-order polarization propagator journal January 2010
Static polarizabilities at large internuclear separations for homonuclear diatomic ions journal October 1979
Molecular vibrational and rotational motion in static and dynamic electric fields journal April 1990
The Refraction and Dispersion of Air for the Visible Spectrum journal February 1939
Development of a “First Principles” Water Potential with Flexible Monomers. II: Trimer Potential Energy Surface, Third Virial Coefficient, and Small Clusters journal March 2014
SCAN-based hybrid and double-hybrid density functionals from models without fitted parameters journal January 2016
NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations journal September 2010
Vibration-rotation effects on properties of symmetric tops and linear molecules journal June 1981
Analytical TDHF second derivatives of dynamic electronic polarizability with respect to nuclear coordinates. Application to the dynamic ZPVA correction journal January 2001
Density‐functional thermochemistry. III. The role of exact exchange journal April 1993
Understanding the many-body expansion for large systems. II. Accuracy considerations journal April 2016
An efficient approach for calculating vibrational wave functions and zero-point vibrational corrections to molecular properties of polyatomic molecules journal February 2000
High-Accuracy ab Initio Rotation-Vibration Transitions for Water journal January 2003
ωB97X-V: A 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy journal January 2014
Geometry-dependent atomic multipole models for the water molecule journal October 2017
The Influence of Retardation on the London-van der Waals Forces journal February 1948
Gaussian basis sets for use in correlated molecular calculations. V. Core‐valence basis sets for boron through neon journal September 1995
Calculation of frequency-dependent polarizabilities and hyperpolarizabilities by the second-order Møller-Plesset perturbation theory journal March 1996
Ab initio potential and dipole moment surfaces for water. II. Local-monomer calculations of the infrared spectra of water clusters journal April 2011
The Flexible, Polarizable, Thole-Type Interaction Potential for Water (TTM2-F) Revisited journal March 2006
The second-order approximate coupled cluster singles and doubles model CC2 journal September 1995
Numerical Study on the Partitioning of the Molecular Polarizability into Fluctuating Charge and Induced Atomic Dipole Contributions journal May 2015
Improving virtual Kohn–Sham orbitals and eigenvalues: Application to excitation energies and static polarizabilities journal December 1998
Anharmonic force constant calculations journal December 1972
Toward reliable density functional methods without adjustable parameters: The PBE0 model journal April 1999
ω B97M-V: A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation journal June 2016
Vibrational effects on properties of spherical tops journal April 1984
Molecular hyperpolarizabilities journal February 1993
Static polarizabilities for excited states within the spin-conserving and spin-flipping equation-of-motion coupled-cluster singles and doubles formalism: Theory, implementation, and benchmarks journal November 2016
Computing vibrational spectra from ab initio molecular dynamics journal January 2013
An Assessment of Theoretical Methods for Nonbonded Interactions: Comparison to Complete Basis Set Limit Coupled-Cluster Potential Energy Curves for the Benzene Dimer, the Methane Dimer, Benzene−Methane, and Benzene−H 2 S journal September 2009
Polarizable interaction potential for water from coupled cluster calculations. I. Analysis of dimer potential energy surface journal March 2008
Many-body calculations of molecular electric polarizabilities in asymptotically complete basis sets journal October 2011
Development of transferable interaction models for water. IV. A flexible, all-atom polarizable potential (TTM2-F) based on geometry dependent charges derived from an ab initio monomer dipole moment surface journal January 2002
The origin of deficiency of the supermolecule second-order Møller-Plesset approach for evaluating interaction energies journal October 2007
Coupled-cluster dynamic polarizabilities including triple excitations journal June 2008
The Theory of Intermolecular Forces book January 2013
A comparative analysis of two methods for the calculation of electric‐field‐induced perturbations to molecular vibration journal September 1993
Accurate dipole polarizabilities for water clusters n=2–12 at the coupled-cluster level of theory and benchmarking of various density functionals journal December 2009
Ab initio dipole polarizability surfaces of water molecule: Static and dynamic at 514.5nm journal April 2005
The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental data journal March 1997
Molecular electric properties: an assessment of recently developed functionals journal January 1999
Electrostatic calculation of linear and non-linear optical properties of ice Ih, II, IX and VIII journal January 2001
A standard grid for density functional calculations journal July 1993
Correlated, Static and Dynamic Polarizabilities of Small Molecules. Comparison of Four “Black Box” Methods journal July 1998
Density functional calculations of molecular polarizabilities and hyperpolarizabilities journal November 1998
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density journal January 1988
Flexible, ab initio potential, and dipole moment surfaces for water. I. Tests and applications for clusters up to the 22-mer journal March 2011
A finite field method for calculating molecular polarizability tensors for arbitrary multipole rank text January 2011
Predictions of the Properties of Water from First Principles. journal May 2007
Analytical TDHF second derivatives of dynamic electronic polarizability with respect to nuclear coordinates. Application to the dynamic ZPVA correction journal October 2002
Symmetry-Adapted Machine Learning for Tensorial Properties of Atomistic Systems. text January 2018
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density text January 1988
Nonlocal van der Waals density functional: The simpler the better text January 2010
Semilocal and Hybrid Meta-Generalized Gradient Approximations Based on the Understanding of the Kinetic-Energy-Density Dependence text January 2013
Strongly Constrained and Appropriately Normed Semilocal Density Functional preprint January 2015
SCAN-based hybrid and double-hybrid density functionals from models without fitted parameters text January 2015

Cited By (2)

Quantum mechanical static dipole polarizabilities in the QM7b and AlphaML showcase databases journal August 2019
Accurate molecular polarizabilities with coupled cluster theory and machine learning journal February 2019