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University of Helsinki Faculty of Science

Molecular spectroscopy and theoretical chemistry


Contact Information

Laboratory of Physical Chemistry
Department of Chemistry
A.I. Virtasen aukio 1
(P.O. BOX 55)
FI-00014 University of Helsinki

Group leader
Prof. Lauri Halonen, D.Sc. CV
Phone: +358(0)2941 50280
email: lauri.halonen


Computational atmospheric chemistry and theoretical spectroscopy

Fig. 1. Vibrational energy level structure of sulfuric acid.

The high-level computational investigation of spectroscopic properties of atmospherically important molecules and complexes has a long standing tradition in our laboratory. Water clusters and complexes play a key role in atmospheric processes such as cloud formation, the greenhouse effect and acid rain catalysis, and therefore our studies have focused on complexes such as (H2O)2, H2O x NH3 [1], H2O x H2SO4 and (H2O)3. By limiting ourselves to small complex sizes, we have been able to make use of highly accurate quantum chemical methods to obtain highly accurate results.

Even in small water complexes such as (H2O)2, an accurate theoretical treatment of vibrational motions is an active challenge. To overcome this challenge, our main interests have been the efficient choice of the coordinate system, the formation of the kinetic energy operator, and the interactions between large and small amplitude vibrations. In connection with our theoretical work, we have developed and employed various approximate approaches such as variational calculations with suitable basis sets, perturbation theory, and adiabatic approximations. As a result of these efforts, we are typically able to calculate energies from fundamentals up to high overtones. Most recently, we have applied these theoretical and numerical approaches to explain the effect of large-amplitude motions on the vibrational transition frequency redshift in hydrogen bonded complexes [2] and energy level calculations of sulfuric acid [3] and sulfuric acid monohydrate [4].

Fig. 2. Potential energy surface of sulfuric acid monohydrate showing several conformer structures.

In many of our studies we have made use of a branch of mathematics called geometric algebra, in which the set of real numbers is extended by endowing it with the geometric concept of direction resulting in new objects such as surfaces with an orientation. While geometric algebra has seen use in some areas of physics, its applications to chemical problems remain scarce. However, we have found that geometric algebra provides an ideal tool for the description of the physical reality behind many of the problems we have faced and its application has yielded some fruitful and very original results. For example, we have shown that the previous formulation of molecular vibrations has been incomplete and have devised a both simpler and faster way to algebraically form vibrational and rovibrational quantum mechanical Hamiltonian operators. We have also been able to produce the first practical method to form volume elements of integration, and to form molecular Hamiltonians in non-orthogonal molecule-fixed axis systems. Finally, we have developed original mathematical tools needed to formulate geometry in a coordinate-independent manner, which we have then applied, for example, to solve the problem of Eckart frame vibration-rotation Hamiltonians [5, 6].

[1] E. Sälli, T. Salmi, and L. Halonen, Computational high-frequency overtone spectra of the water-ammonia complex, J. Phys. Chem. A 115, 11594-11605 (2011).
[2] K. Mackeprang, H. G. Kjaergaard, T. Salmi, V. Hänninen, and L. Halonen, The effect of large amplitude motions on the transition frequency redshift in hydrogen bonded complexes: A physical picture, J. Chem. Phys., 140, 184309 (2014).
[3] L. Partanen, J. Pesonen, E. Sjöholm, and L. Halonen, A rotamer energy level study of sulfuric acid, J. Chem. Phys., 139, 144311 (2013).
[4] L. Partanen, V. Hänninen, and L. Halonen, Ab initio structural and vibrational investigation of sulfuric acid monohydrate, J. Phys. Chem. A 116, 2867-2879 (2012).
[5] J. Pesonen, Eckart frame vibration-rotation Hamiltonians: Contravariant metric tensor, J. Chem. Phys., 140, 074101 (2014).
[6] J. Pesonen, Constrained molecular vibration-rotation Hamiltonians: Contravariant metric tensor, J. Chem. Phys., 139, 144310 (2013).